Three-dimensional (3D) self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing

Abstract

The present invention relates to the technical field of structural engineering, and relates to a three-dimensional (3D) self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing. The method comprises the following steps: recognizing a printing curved surface of a given structure, integrated optimization of a structure, and 3D printing integrated manufacturing. The beneficial effects of the present invention are: an optimization structure and corresponding printing surfaces thereof are obtained by taking an optimization result of a traditional layout and an optimization result of a geometric optimization as initial values, and the printing surfaces of the optimization structure are obtained by means of a local printing direction optimization problem; moreover, overhang components are reduced or eliminated by means of an integrated optimization method for adjusting the structure and the printing surfaces at the same time, and a semi-integrated iteration method is provided so as to improve the mass of an initial solution of an integrated optimization problem, so that the overhang characteristics in the structure are reduced, thereby realizing the multi-axis 3D printing optimization design of the 3D self-supporting truss.

Description

Optimal design and manufacturing method of three-dimensional self-supporting trusses based on multi-axis 3D printing

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on September 18, 2023, with application number 202311199312.5 and invention name “Optimization design and manufacturing method of three-dimensional self-supporting truss based on multi-axis 3D printing”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present invention belongs to the field of structural engineering technology, and in particular relates to an optimization design and manufacturing method for a three-dimensional self-supporting truss based on multi-axis 3D printing. Multi-axis refers to a 3D printing with a total number of rotation axes greater than three, including the rotation axis of the print head and the rotation axis of the base. Background Art

[0003] In recent years, 3D printing technology has been widely adopted in numerous industries, including mechanical engineering, aerospace, and biomedicine. However, traditional 3D printing utilizes a three-axis configuration, requiring the addition of support structures during the manufacturing process. This leads to material waste and difficulty in removing these supports. In metal 3D printing, removing these supports can even damage the finished component.

[0004] Compared to traditional manufacturing processes, 3D printing technology has advantages such as high efficiency and high precision, and is more suitable for the processing and manufacturing of complex structures. However, 3D printing still needs to meet corresponding manufacturing constraints to ensure the success of the printing process. Among various manufacturing constraints, the draping effect caused by gravity is one of the main manufacturing constraints of 3D printing. When the angle between the structure boundary and the horizontal plane is less than a critical value, gravity will cause the material to collapse during the deposition process, thereby affecting the printing quality of the structure and even causing printing failure. This manufacturing constraint greatly limits the ability of 3D printing to manufacture components with complex geometries.

[0005] To overcome the overhang effect, a commonly used method is to add support structures to the overhanging parts, but this method will introduce additional material consumption and is difficult to remove later for some materials. Another method is to introduce angle constraints from the perspective of structural design to optimize the design in order to obtain the optimal structural form that can be self-supporting at a specific angle. However, this method currently focuses on 3-axis 3D printing. Although self-supporting structures can be obtained, it may lead to material waste and reduced structural performance in some cases.

[0006] Compared to three-axis methods, multi-axis 3D printing achieves more degrees of freedom by introducing a rotatable print platform, allowing the printing direction to change dynamically during the printing process. The corresponding slice layers are no longer restricted to a flat surface, achieving greater manufacturing flexibility, thereby helping to alleviate or even resolve support issues caused by overhang effects. As a promising manufacturing method, support-free process path planning for multi-axis 3D printing technology is a hot research topic in this field.

[0007] A new approach to combining structural optimization with multi-axis 3D printing is to first decompose the design domain into multiple partitions and then use optimization methods to determine the local printing direction for each partition. However, this method is primarily applicable to two-dimensional truss structures and encounters numerical difficulties when solving three-dimensional truss problems. Therefore, it is necessary to develop an optimized design and manufacturing method for three-dimensional self-supporting trusses based on multi-axis 3D printing.

[0008] Summary of the Invention

[0009] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing.

[0010] This method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing includes the following steps:

[0011] S1. Identify the printing surface of a given structure: After inputting the truss design parameters, the 3D design domain is segmented and the local printing direction is expressed. Then, a printing surface continuity constraint is established to limit the projection rotation angle of adjacent partitions. The 3D printing surface is optimized to obtain the optimized printing path.

[0012] S2. Integrated optimized structure: Based on the optimization problem in step S1, the constraints of minimizing overhang violations and preventing component nodes and partitions from shrinking to infinitesimal sizes are introduced. The semi-integrated optimization of the structure printing path is iterated until the initial solution is determined and fully self-supporting is achieved.

[0013] S3, 3D printing integrated manufacturing: 3D modeling is performed on the optimization result obtained in step S2, and support-free printing manufacturing is performed after solid model slicing and printing path generation.

[0014] In an exemplary embodiment, in step S1: the expression for 3D printing surface optimization is

[0015] Where, β μ,v,w γ μ,v,w are the projections of the overhang angles of each component on the xoz and yoz planes respectively; φ x,μ,v,w φ y,μ,v,ware the projections of the local printing directions of each partition on the xoz and yoz planes respectively; θ x,μ,v,w ,θ y，μ，v，w are the projections of the orientation angles of each component on the xoz and yoz planes, φ max is the maximum overhang angle set; e is a 0-1 mapping matrix used to link node coordinates to their partitions; μ, v, w are the indices of the partitions, n μ 、n v and n w are the number of rows, columns and depth of the partition respectively; φ t,max is the maximum printing rotation angle; φ x,t 、φ y,t are the projection rotation angles of the local printing direction of each partition on the xoz and yoz planes respectively; is the projection relative parameter; V μ,v,w is the volume of each partition; Respectively indicate that the rows, columns, and depth of the partition are within the boundary of the design domain in that direction;

[0016] Formula (1a) is the optimization objective, Formulas (1b) to (1c) are the overhang constraints after projection, Formulas (1d) to (1e) are the printing surface continuity constraints, and Formulas (1f) to (1g) are the projection rotation angle constraints of adjacent partitions.

[0017] In an exemplary embodiment, in step S1, when partitioning the 3D design domain and expressing the local printing direction, the local printing direction and component direction of each partition are first projected onto the xoz and yoz planes, and then the overhang constraint on each surface is considered according to a two-dimensional method; where the printing surface is perpendicular to the local printing direction, the overhang constraint expression after projection is

[0018] β=|φ x e-θ x -φ max e|+|φ x e-θ x +φ max e| (2a)

[0019] γ=|φ y e-θ y -φ max e|+|φ y e-θ y +φ max e| (2b)

[0020] Where β and γ are the projections of the overhang angles of each component on the xoz and yoz planes, respectively; φ x 、φ y are the projections of the local printing directions of each partition on the xoz and yoz planes respectively; θx ,θ y are the projections of the orientation angles of each component on the xoz and yoz planes respectively.

[0021] In an exemplary embodiment, in step S1, the specific method of establishing the print surface continuity constraint is that adjacent local print surfaces share a common projection line on the middle plane, and the corresponding print surface continuity constraint expression is:

[0022] In an exemplary embodiment, in step S1: to avoid collision between the printing nozzle and the printed structure, the constraint expression for limiting the projection rotation angle of adjacent partitions is:

[0023] φ x,t ≤φ t,max e (4a)

[0024] φ y,t ≤φ t,max e (4b)

[0025] Where, φ x,t 、φ y，t The expression is

[0026] In an exemplary embodiment, in step S2: the calculation of the structural overhang violation value is introduced into the objective function of the integrated optimization problem to achieve the goal of minimizing the structural overhang violation characteristics, and the expression is:

[0027] Where p is the penalty factor for the overhang constraint violation; η μ,v,w is the projection relative parameter; a=a1,a2,…,a m ] T is the cross-sectional area of ​​the component unit; m is the number of components; q=[q1,q2,…,q m ] T is the internal force of the component unit, which is defined as positive for tension and negative for compression; l=[l1,l2,…,l m ] T is the length of each component unit; B is the equilibrium matrix including the component direction; f α is the node load vector; α is the load case number; σ - , σ + They are the ultimate compressive and tensile strengths of the material respectively; are the boundary coordinates of the relevant cube partition in the x, y and z directions respectively; w x,min 、w y,min and w z,min is the lower limit of the length of the cube partition in the x, y and z directions;

[0028] Formula (6a) is the optimization objective. Formulas (6b), (6c), and (6o) are the constraints of structural internal and external force balance, material strength limit, and area not less than zero, respectively. Formulas (6d) to (6e) and (6g) to (6h) are defined in the same way as in step S1. Formulas (6i) to (6k) are constraints that prevent the partition from shrinking to infinitesimal size. Formulas (6l) to (6n) are constraints on the coordinates of the component nodes.

[0029] In an exemplary embodiment, in step S2, the method of constraining the component nodes is to restrict each component to move within its initially assigned partition, specifically constraining the component node coordinates

[0030] In an exemplary embodiment, in step S2: the partition boundary is used as an additional variable, and the partitions arranged in the same row and column share the same boundary position variable, and constraints are set to prevent the partition from shrinking to an infinitely small size.

[0031] In an exemplary embodiment, in step S2: Equation (6a) is a nonlinear non-convex problem, and the initial solution of the problem is determined by an iterative semi-integrated method, which starts from the obtained printing surface; when the printing surface is known, the projected overhang angle violation values ​​β and γ of the base structure and the component to be added are calculated; for components spanning multiple partitions, the overhang angle violation value is selected as the maximum value calculated in each partition; then the layout optimization problem is re-solved, and the components in the base structure and potential components that violate the overhang constraint are penalized; the expression of the semi-integrated optimization model is

[0032] Where p0 is the penalty factor for overhang angle violation.

[0033] The beneficial effects of the present invention are:

[0034] 1) The present invention provides a method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing. Printing and manufacturing constraints are considered during each optimization process to optimize the generation of a self-supporting truss. No additional supports are required during the printing process, saving material costs and printing time, and achieving a support-free, one-piece 3D truss design.

[0035] 2) The three-dimensional self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing provided by the present invention uses the optimization results of traditional layout and geometric optimization as initial values ​​to obtain the optimized structure and its corresponding printing surface and obtains the printing surface of the optimized structure through local printing direction optimization problem. The overhanging components are reduced or eliminated by an integrated optimization method that simultaneously adjusts the structure and the printing surface, and an iterative semi-integrated method is proposed to improve the quality of the initial solution of the integrated optimization problem, thereby reducing the overhanging features in the structure and realizing the multi-axis 3D printing optimization design of the three-dimensional self-supporting truss.

[0036] 3) The optimized design and manufacturing method of a three-dimensional self-supporting truss based on multi-axis 3D printing provided by the present invention dynamically adjusts the printing direction during the printing process to avoid the overhang effect of the structure during the printing process, thereby realizing the optimal configuration printing of complex self-supporting structures at any inclination angle, which is conducive to designing a more efficient and ideal truss structure than traditional methods, achieving higher material utilization and higher manufacturing flexibility.

[0037] Figures in the specification

[0038] FIG1 is a specific flow chart of the method for optimizing the design and manufacturing of a three-dimensional self-supporting truss structure based on multi-axis 3D printing according to the present invention;

[0039] Figure 2 is a schematic diagram of 3D design domain partitioning;

[0040] FIG3 is a schematic diagram of a projection of a local printing direction;

[0041] FIG4 is a schematic diagram showing the effect of print surface continuity constraints on the print surface;

[0042] FIG5 is a schematic diagram of a projection rotation angle;

[0043] Figure 6 is a schematic diagram showing the effect of the partition boundary position variables on the optimization process in the same layer;

[0044] FIG7 is a schematic diagram of a rotating cantilever beam calculation example;

[0045] FIG8 is a schematic diagram of a rotating cantilever beam calculation example when the penalty factor p0 is 5.0;

[0046] Figure 9 is a schematic diagram of a cantilever beam calculation example;

[0047] Figure 10 is a schematic diagram of a double-force truss calculation example;

[0048] FIG11 is a schematic diagram of the optimized structure with different horizontal partition sizes. DETAILED DESCRIPTION

[0049] The present invention will be further described below with reference to the following examples. The following examples are provided only to facilitate understanding of the present invention. It should be noted that, without departing from the principles of the present invention, it is possible for a person skilled in the art to make various modifications to the present invention, and such improvements and modifications fall within the scope of the claims of the present invention.

[0050] Example 1

[0051] As an embodiment, this method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing solves 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, thereby achieving the multi-axis 3D printing integrated design and manufacturing of the optimal configuration of a three-dimensional self-supporting truss. The method includes the following steps:

[0052] This three-dimensional self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing aims to reduce the structural performance loss caused by overhang constraints by considering multi-axis rotation; first, a nominal solution is solved from traditional layout optimization; since overhang constraints are not considered in this step, the nominal solution is only a strict lower limit of the overhang constraint problem; using the optimization results of traditional layout and geometric optimization as initial values, the optimized structure and its corresponding printing surface are obtained, and through the local printing direction optimization problem, the printing surface of the optimized structure is obtained. The overhang components are reduced or eliminated by an integrated optimization method that simultaneously adjusts the structure and the printing surface, and an iterative semi-integrated method is proposed to improve the quality of the initial solution of the integrated optimization problem, thereby reducing the overhang features in the structure, and realizing the multi-axis 3D printing optimization design and manufacturing of three-dimensional self-supporting trusses.

[0053] Specifically, it includes three processes: identifying the printing surface of a given structure, optimizing the structure in one piece, and 3D printing integrated manufacturing; as shown in Figure 1.

[0054] S1. Identify the printing surface of a given structure. The process of identifying the printing surface of a given structure includes 3D design domain segmentation, 3D local printing direction representation, establishing printing surface continuity constraints, limiting the projection rotation angles of adjacent partitions to prevent collisions, and 3D printing surface optimization. A new optimization method is used to identify the printing surface of a given structure to maximize the structure's printable ratio (i.e., the structure's non-overhang volume / total volume). Since the structure remains unchanged in this step, it cannot be guaranteed that the structure can be fully printed. When the printable ratio falls below a set threshold, the second step is performed.

[0055] Step S1 is specifically as follows:

[0056] S11. 3D design domain segmentation. Specifically, similar to the 2D method, the design domain in the 3D problem is first segmented into several 3D partitions by cutting planes, as shown in Figure 2.

[0057] S12, 3D local printing direction representation.

[0058] Specifically, in a two-dimensional problem, the overhang angle of a component can be expressed as the angle between the printing direction and the component direction. In a three-dimensional problem, the local printing direction and component direction of each partition are simplified and projected onto two mutually perpendicular planes, xoz and yoz. Subsequently, the overhang constraints on each surface are considered according to the two-dimensional method. These constraints are numerically conservative. The printing surface is a plane perpendicular to the local printing direction. The relationship between the printing surface and the printing direction is shown in Figure 3. The overhang constraint expression after projection is shown in Equation (2).

[0059] β=|φx e -θ x -φ max e|+|φ x e-θ x +φ max e| (2a)

[0060] γ=|φ y e-θ y -φ max e|+|φ y e-θ y +φ max e| (2b)

[0061] Where β and γ are the projections of the overhang angles of each component on the xoz and yoz planes, respectively; φ x 、φ y are the projections of the local printing directions of each partition on the xoz and yoz planes respectively; θ x ,θ y are the projections of the orientation angles of each component on the xoz and yoz planes respectively; φ max is the maximum overhang angle that is set.

[0062] Furthermore, although the constraint condition (2) may lead to the optimization result being numerically conservative, this is because when the intersection angles of the projection component direction and the local printing direction on the xoz and yoz planes are equal to φ max When the angle between the original component direction and the local printing direction is greater than φ max Nevertheless, these two constraints are convex, which can greatly reduce the numerical differences.

[0063] S13. Establish printing surface continuity constraints.

[0064] Specifically, unlike two-dimensional problems, in three-dimensional problems, adjacent local printed surfaces need to share a common projection line on the midplane to ensure the continuity of the entire printed surface, as shown in Figure 4. Part (a) of Figure 4 shows the impact on the printed surface when the printed surface continuity constraint is violated, and part (b) of Figure 4 shows the impact on the printed surface when the printed surface continuity constraint is satisfied. Therefore, it is necessary to establish a printed surface continuity constraint, and the constraint expression is shown in Equation (3).

[0065] Where, φ x，μ，v，w ,φ y，μ，v，w is the projection of the local printing direction of each partition on the xoz and yoz planes, μ, v and w are the indexes of the partitions respectively, n μ 、n e and n w are the number of rows, columns and depth of the partition, respectively, φ x,i,j,k is the i-th row (i=1,2,...,μ,...,n μ ), the jth column (j=1,2,...,v,...,n v ), the kth depth (k=1,2,...,w,...,n w )’s local printing direction on the xoz plane; y,i,j,k is the i-th row (i=1,2,...,μ,...,n μ ), the jth column (j=1,2,...,v,...,n v ), the kth depth (k=1,2,...,w,...,n w )'s local printing direction on the yoz plane.

[0066] S14. Limit the projection rotation angles of adjacent partitions to prevent collision.

[0067] Specifically, a surface with a large rotation angle may cause a collision between the printing nozzle and the printed structure. Constraints are used to limit the projected rotation angles of adjacent partitions, as shown in FIG5 . The constraint expression is shown in Equation (4).

[0068] φ x,t ≤φ t，max e (4a)

[0069] φ y，t ≤φ t，max e (4b)

[0070] S15. 3D printing surface optimization. Introducing the above constraints, the expression of the 3D printing surface optimization problem is shown in formula (1).

[0071] Where, β μ，v，w , γ μ，v，w are the projections of the overhang angles of each component on the xoz and yoz planes; φ x，μ，v，w ,φ y，μ，v，w are the projections of the local printing directions of each partition on the xoz and yoz planes respectively; θ x，μ，v，w ,θ y，μ，v，w are the projections of the orientation angles of each component on the xoz and yoz planes; φ t,max is the maximum print rotation angle.

[0072] φ y,t With φ x,t The expression is similar to .

[0073] By using the projected printing direction in each partition, the optimization problem becomes a linear programming problem, which can also be effectively solved using the interior point solver and ensure that the optimization result is the global optimal.

[0074] S2. Integrated optimization structure. Take the result obtained in step S1 as the starting point; although the process of identifying the printing surface of a given structure can obtain the globally optimal printing direction identification result, since the optimized structure is predetermined, the identified printing surface may not guarantee that the structure is completely printable; to solve this problem, it is necessary to adjust the structure and the printing surface at the same time through integrated optimization structure to reduce or eliminate overhanging components; since the structural morphology change has additional design freedom, the printability ratio and structural performance can be further improved. The integrated optimization structure process includes optimizing the structure to minimize overhang violation features, constraining component nodes, setting constraints to prevent partitions from shrinking to infinitesimal sizes, and iterating semi-integrated methods to determine the initial solution to the nonlinear non-convex problem; this step is based on the problem of geometric optimization, and simultaneously modifies the structure and the printing surface.

[0075] Step S2 specifically includes:

[0076] S21. The optimized structure has the least overhang violation features.

[0077] Specifically, the structural overhang violation value calculated based on Equations (1b) to (1c) is introduced into the objective function of the integrated optimization problem to achieve the goal of minimizing the overhang violation features of the optimized structure. The overhang violation features are penalized by the parameter p and added to the structural volume, as shown in Equation (6a).

[0078] S22, constrained component node.

[0079] Specifically, since the overhang violation value of each component is calculated based on its originally assigned partition, it is necessary to restrict each component to move within its originally assigned partition, which is achieved by constraining the component node coordinates, as shown in Equation (7).

[0080] Where, are the bounding coordinates of the relevant cube partition in the x, y, and z directions, respectively.

[0081] S23. Set constraints to prevent the partition from shrinking to an infinite size.

[0082] Since step S22 significantly restricts the movement of structural nodes, the visible partition boundary serves as an additional variable, which adds additional design freedom to the integrated optimization problem. During the optimization process, unfilled partitions will result in the inability to completely cover the design domain of the layer when planning the printing path, as shown in part (a) of Figure 6. Part (a) of Figure 6 shows the influence of the partition boundary position variables in the same layer on the optimization process when the independent variables are used. Therefore, partitions arranged in the same row and column share the same boundary position variables, as shown in part (b) of Figure 6. Part (b) of Figure 6 shows the influence of the partition boundary position variables in the same layer on the optimization process when the same row and column share the partition position vector. In order to prevent the partition from shrinking to infinitesimal, the constraint condition formula (8) is used for restriction.

[0083] Furthermore, by combining the above constraints and problem solutions, the expression of the integrated optimization model is shown in Equation (6).

[0084] Where p is the penalty factor for overhang constraint violation; e is a 0-1 mapping matrix that links node coordinates to their partitions; are the boundary coordinates of the relevant cube partition in the x, y and z directions respectively; w x,min 、w y,min and w z,min is the lower limit of the length of the cube partition in the x, y and z directions; is the i-th row (i=1,2,...,μ-1,μ,...,n μ ), the jth column (j=1,2,...,v-1,v,...,n v ), the kth depth (k=1,2,...,w-1,w,...,n w )'s boundary coordinates in the x-direction of the cube partition; is the i-th row (i=1,2,...,μ-1,μ,...,n μ ), the jth column (j=1,2,...,v-1,v,...,nv ), the kth depth (k=1,2,...,w-1,w,...,n w )'s boundary coordinates in the y direction of the cube partition; is the i-th row (i=1,2,...,μ-1,μ,...,n μ ), the jth column (j=1,2,...,v-1,v,...,n v ), the kth depth (k=1,2,...,w-1,w,...,n w )'s boundary coordinates in the z-direction of the cube partition.

[0085] S24. Iterative semi-integrated method to determine the initial solution of nonlinear nonconvex problems.

[0086] Since this problem is a nonlinear and non-convex problem, the initial value has a significant impact on the quality of the final optimization result. This application proposes an iterative semi-integrated method to determine the initial solution of the problem, thereby reducing the overhang features in the structure. The method starts from the obtained printed surface. When the printed surface is known, the projected overhang angle violation values ​​β and γ of the base structure and the component to be added can be calculated by formula (2). For components spanning multiple partitions, the overhang angle violation value is selected as the maximum value calculated in each partition. Then the layout optimization problem is re-solved, and the components in the base structure and potential components that violate the overhang constraint are penalized. The expression of the semi-integrated optimization model is shown in formula (9).

[0087] Where p0 is the penalty factor for the overhang angle violation value;

[0088] The semi-integrated optimization model can obtain a structure with fewer overhanging features, and a further optimized printing surface can be obtained by optimizing the printing path; the iterative process will continue until the maximum number of iterations is reached; in this method, the maximum number of iterations can generally be set to 5 times; semi-integrated optimization is a linear problem and can be solved using an interior point solver, and the computational efficiency can be further improved by adding components; although the iterative process can overcome the overhang effect in some cases, since the node and partition boundary positions in this method are immutable, its design freedom is not as good as that of integrated optimization; therefore, the optimization results of the improved semi-integrated optimization method can be used as the initial solution for integrated optimization to further improve structural efficiency and reduce overhanging components.

[0089] S3. The 3D printing integrated manufacturing includes 3D modeling of optimization results, solid model slicing and printing path generation, and support-free printing manufacturing.

[0090] The three-dimensional self-supporting truss optimization design method based on multi-axis 3D printing provided in this embodiment can be applied to an application environment including a terminal, a network, and a server. The terminal communicates with the server via a network. A data storage system can store data that the server needs to process. The data storage system can be set up separately, integrated on the server, or placed on a cloud or other server. The terminal can send truss design parameters to the server. After the server receives the truss design parameters, the server can perform steps S1 and S2 for the truss design parameters. S1: After receiving the truss design parameters, the 3D design domain is segmented and the local printing direction is represented. Then, a printing surface continuity constraint is established to limit the projection rotation angle of adjacent partitions, and the 3D printing surface is optimized to obtain an optimized printing path. S2: Based on the optimization problem in step S1, the constraints of minimizing the overhang violation features of the optimized structure and constraining the component nodes and partitions to not shrink to infinitesimal sizes are introduced. The semi-integrated optimization of the structure printing path is iterated until an initial solution is determined and fully self-supporting is achieved. The server can feedback the optimization results obtained in step S2 to the terminal. In addition, in some embodiments, the three-dimensional self-supporting truss optimization design method based on multi-axis 3D printing can also be implemented independently by a server or a terminal. For example, the terminal can directly process the truss design parameters, or the server can obtain the truss design parameters from a data storage system and process the truss design parameters.

[0091] The terminal can also have built-in 3D modeling software and 3D printing slicing software. In step S3, in order to save support materials, reduce printing costs and improve manufacturing efficiency, for the application scenario of unsupported 3D printing manufacturing of 3D truss structures in the fields of mechanical construction, aerospace and biomedicine, after obtaining the optimization results of step S2 and feeding them back to the terminal, the structure and path information are extracted on the terminal, including node coordinates, component connections, cross-sectional dimensions, path parameters, etc.; after component assembly and node generation processing are performed in the 3D modeling software of the terminal, a 3D solid model is established; the 3D solid model is imported into the 3D printing slicing software of the terminal, and the solid model is sliced ​​and the printing path is generated according to the path parameters; the printing path is imported into the multi-axis 3D printer, and the multi-axis rotation is controlled to perform unsupported printing manufacturing of the 3D truss. Thus, unsupported 3D printing manufacturing of the 3D truss structure is achieved through the terminal and the multi-axis 3D printer.

[0092] Among them, 3D modeling software includes Rhino, SolidWorks, etc.; 3D printing slicing software includes Cura, Matlab, etc.; multi-axis 3D printers are composed of robotic arms, positioners, etc., and the total number of rotation axes is greater than 3 axes, including the rotation axis of the print head and the rotation axis of the base.

[0093] Terminals include, but are not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices include smart speakers, smart TVs, smart air conditioners, and smart car devices. Portable wearable devices include smart watches, smart bracelets, and head-mounted devices. Servers can be implemented as standalone servers or server clusters consisting of multiple servers, or even cloud servers.

[0094] Example 2

[0095] As another embodiment, this embodiment 2 uses the three-dimensional self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing proposed in embodiment 1 to optimize the design and manufacture of a three-dimensional self-supporting truss based on multi-axis 3D printing for a rotating cantilever beam example.

[0096] Part (a) of Figure 7 shows the design domain and boundary conditions of the example. In order to analyze the influence of the penalty factor p0 on the optimized structure, the design problem shown in part (a) of Figure 7 is optimized and tested with different p0 values ​​ranging from 0.01 to 100; the maximum overhang angle is set to 50°, and the vertical partition size S is set to 100. z is 2.0, the horizontal partition size is S x and S y are all 1.0, and the design domain segmentation is shown in part (b) of Figure 7 .

[0097] The nominal optimal solution obtained using the traditional layout optimization method is shown in Figure 7(c), and the nominal optimal solution is used to evaluate the volume increase caused by considering the overhang constraint. The dark components in Figure 7(c) indicate that the overhang angle of the corresponding components is less than 50°.

[0098] Part (e) of Figure 7 shows the optimization results obtained using the method in step S1. It is the optimized structure when the penalty factor p0 is between 1.0 and 7.0. The dark color indicates the components that cannot be printed. Part (e1) of Figure 7 shows that when p0 = 0.01, the volume increases by 10.75%, and the total violation degree η total >0.1 optimization results; Part (e2) of Figure 7 shows p0=0.10, the volume increases by 11.52%, and the total violation η total>0.1; Part (e3) of Figure 7 shows the optimization result of p0=1.00, with a volume increase of 6.64%; Part (e4) of Figure 7 shows the optimization result of p0=3.00, with a volume increase of 9.04%; Part (e5) of Figure 7 shows the optimization result of p0=5.00, with a volume increase of 8.35%; Part (e6) of Figure 7 shows the optimization result of p0=7.00, with a volume increase of 12.39%; Part (e7) of Figure 7 shows the optimization result of p0=10.00, with a volume increase of 20.12%; Part (e8) of Figure 7 shows the optimization result of p0=100.00, with a volume increase of 54.60%. The results show that when the p0 value is set to 0.01 and 0.1, the optimized structure contains unprintable components; conversely, when p0 is set to 10 or greater, the volume of the structure increases significantly; for this embodiment, a penalty factor in the range of 1.0-7.0 can produce acceptable results; a penalty factor that is too small may not adequately penalize components that violate the overhang constraint, resulting in the structure being unable to be printed; a penalty factor that is too large will lead to a significant increase in material usage, similar to the hard constraint method.

[0099] Furthermore, to demonstrate the impact of the semi-integrated optimization method, the optimized structure obtained without semi-integrated optimization, shown in Figure 7(d), is selected for comparison. Its volume increases by 20.20% compared to Figure 7(c). In Figure 7(e), the volume increases for structures with penalty factors p0 between 1.0 and 7.0 range from 6.64% to 20.12%, which is much smaller than the volume increase in Figure 7(d). This effectively demonstrates that the semi-integrated optimization method can effectively control the increase in structure volume.

[0100] During the optimization process, curved printing surfaces were generated for all the structures in Figure 7; part (a) of Figure 8 shows the printing surface of each layer of the structure, which corresponds to the printing surface of the structure when p0=5.0, and the structure is layered and sliced ​​according to the printing surface of each layer to obtain the printing path. The local slice printing path of the second layer is shown in part (b) of Figure 8.

[0101] It should be noted that the parts in this embodiment that are the same or similar to those in the first embodiment can be referenced to each other and will not be described in detail in this application.

[0102] Example 3

[0103] As another embodiment, this third embodiment also uses the three-dimensional self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing proposed in the first embodiment to perform optimization design and manufacturing of a self-supporting truss structure for a cantilever beam example.

[0104] The design domain and boundary conditions of the cantilever beam are shown in Figure 9(a). In this example, the penalty factor p0 is set to 4.0, Sx Set to 2.0, S y 、S z Set to 1.0, and the maximum overhang angles are set to 45°, 50°, 55°, and 60° respectively.

[0105] The nominal optimization results of the traditional layout and geometric optimization are shown in part (b) of Figure 9 , where the dark components indicate that the overhang angle of the corresponding components is less than 45°.

[0106] When the maximum overhang angle is set to 60°, the optimization results obtained by the three-axis optimization method are shown in part (c) of Figure 9. Part (c) of Figure 9 shows the optimized structure using the three-axis plane printing scheme and setting the maximum overhang angle to 60°. Compared with the nominal optimization result, its volume increases by 117.19%; after considering the overhang constraint, the optimized structures using the curved surface printing scheme and setting the maximum overhang angles to 60°, 55°, 50°, and 45° are shown in parts (d), (e), (f), and (g) of Figure 9, respectively. The optimized structures obtained are all three-dimensional truss self-supporting structures. Compared with the nominal optimization structure, the corresponding volumes increase by 1.85%, 2.97%, 3.24%, and 3.98%, respectively.

[0107] It can be seen that as the maximum overhang angle decreases, the volume of the structure increases, and the components in the structure tend to be more vertical. Since the higher flexibility brought by multi-axis rotation is taken into account, the volume increase caused by the overhang effect is alleviated. The volume increase of the structure in parts (d) to (g) of Figure 9 is less than 4%, and a self-supporting optimized structure can be obtained without excessively increasing the volume of the body structure.

[0108] It should be noted that the parts in this embodiment that are the same or similar to those in the first embodiment can be referenced to each other and will not be described in detail in this application.

[0109] Example 4

[0110] As another embodiment, this fourth embodiment also uses the three-dimensional self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing proposed in the first embodiment to perform self-supporting truss structure optimization design and manufacturing on a double-force truss example.

[0111] The design domain and boundary conditions for this double-force truss example are shown in Figure 10(a). For comparison, Figure 10(b) shows the optimization results for the nominally optimized structure without considering the overhang constraint. In this example, the maximum overhang angle is set to 45°.

[0112] The examples are divided into two groups. In the first group, the partition level size S x 、S y Fixed to 1.0, while using curved printing scheme and partition vertical size Sz When the values ​​are set to 1.0, 2.0, 3.0, and 4.0, respectively, the corresponding optimized structures are shown in part (c), part (d), part (e), and part (f) of Figure 10, respectively. Compared with the nominal optimized structure, the corresponding volumes increase by 5.10%, 1.11%, 0.35%, and 1.13%, respectively.

[0113] The results showed that S z When the value is 3.0, the volume of the optimized structure increases the least, by only 0.35%, and the structure is the simplest. In comparison, part (g) of Figure 10 shows the optimized structure using the horizontal printing scheme. Compared with the nominal optimized structure, the structure volume increases by 12.43%. In the integrated optimization step, because the structural nodes are restricted by their corresponding partitions, too many partitions will limit the design freedom of the integrated optimization, resulting in high structural complexity and relatively large volume, as shown in part (c) of Figure 10.

[0114] In the second group, the vertical size of the partition S z Fixed to 1.0, while the double-force truss case uses the surface printing scheme and the partition horizontal size S x 、S y When the values ​​are set to 0.5, 1.0, 2.0, and 4.0, the corresponding optimized structures are shown in Figures 11(a), 11(b), 11(c), and 11(d), respectively. Compared to the nominal optimized structure, the corresponding volume increases by 0.91%, 0.82%, 0.61%, and 1.21%, respectively. The results show that larger horizontal partition sizes increase the complexity of the structure; however, changes in the horizontal partition size have little effect on the structure's volume.

[0115] It should be noted that the parts in this embodiment that are the same or similar to those in the first embodiment can be referenced to each other and will not be described in detail in this application.

[0116] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

Claims

1. A three-dimensional self-supporting truss optimization design and manufacturing method based on multi-axis 3D printing, characterized in that: The following steps are involved: S1. Identify the printing surface of a given structure: After inputting the truss design parameters, perform 3D design domain segmentation and indicate the local printing direction, then establish printing surface continuity constraints, limit the projection rotation angle of adjacent partitions, and perform 3D printing surface optimization to obtain the optimized printing path; S2, integrated optimized structure: Based on the optimization problem in step S1, the constraint conditions of minimizing the overhang violation characteristics of the optimized structure and constraining the component nodes and partitions not to be reduced to infinitesimal are introduced, and the semi-integrated optimization iteration of the structure printing path is performed until the initial solution is determined and fully self-supporting is achieved; S3, 3D printing integrated manufacturing: 3D modeling is performed on the optimization result obtained in step S2, and support-free printing is performed after solid model slicing and printing path generation.

2. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 1, characterized in that: In step S1: the expression for 3D printing surface optimization is In the formula, β μ，v，w , γ μ，v，w are the projections of the overhang angles of each component on the xoz and yoz planes; φ x,μ,v,w ,φ y,μ,v,w are the projections of the local printing directions of each partition on the xoz and yoz planes; θ x，μ，v，w ,θ y，μ，v，w are the projections of the orientation angles of each component on the xoz and yoz planes, respectively, max is the maximum overhang angle set; e is a 0-1 mapping matrix used to link node coordinates to their partitions; μ, v, w are the indices of the partitions, n μ 、n v and n w are the number of rows, columns and depth of the partition respectively; φ t,max is the maximum printing rotation angle; φ x,t ,φ y,t They are the local printing directions of each partition. Projection rotation angle on the xoz, yoz plane; is the projection relative parameter; V μ,v,w is the volume of each partition; Respectively indicate that the row, column and depth of the partition are within the boundary of the design domain in that direction; Formula (1a) is the optimization objective, formulas (1b) to (1c) are the overhang constraints after projection, formulas (1d) to (1e) are the printing surface continuity constraints, and formulas (1f) to (1g) are the adjacent partition projection rotation angle constraints.

3. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 2, characterized in that: In step S1: when dividing the 3D design domain and expressing the local printing direction, the local printing direction and component direction of each partition are first projected onto the xoz and yoz planes, and then the overhang constraint on each surface is considered according to the two-dimensional method; the printing surface is perpendicular to the local printing direction, and the overhang constraint expression after projection is β=|φ x e-θ x -φ max e|+|φ x e-θ x +φ max e| (2a) γ=|φ y e-θ y -φ max e|+|φ y e-θ y +φ max e| (2b) Where β and γ are the projections of the overhang angles of each component on the xoz and yoz planes respectively; φ x ,φ y are the projections of the local printing directions of each partition on the xoz and yoz planes respectively; θ x ,θ y are the projections of the direction angles of each component on the xoz and yoz planes respectively.

4. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 2, characterized in that: In step S1: the specific method of establishing the print surface continuity constraint is that adjacent local print surfaces share a common projection line on the middle plane, and the corresponding print surface continuity constraint expression is:

5. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 2, characterized in that: In step S1: the constraint expression for limiting the projection rotation angle of adjacent partitions is φ x，t ≤φ t，max e (4a) φ y，t ≤φ t，max e (4b) In the formula, φ x，t ,φ y,t The expression is 6. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 2, characterized in that: In step S2: the calculation of the structural overhang violation value is introduced into the objective function of the integrated optimization problem to achieve the goal of minimizing the overhang violation characteristics of the optimized structure. The expression is: Where p is the penalty factor for the overhang constraint violation value; η μ,v,w is the projection relative parameter; a=[a1,a2,…,a m ] T is the cross-sectional area of ​​the component unit; m is the number of components; q=[q1,q2,…,q m ] T is the internal force of the component unit, which is defined as positive for tension and negative for compression; l = [l1, l2, …, l m ] T is the length of each component unit; B is the equilibrium matrix including the component direction; f α is the node load vector; α is the load condition number; σ - , σ + They are the ultimate compressive and tensile strengths of the material respectively; are the boundary coordinates of the relevant cube partition in the x, y and z directions respectively; w x,min 、w y,min and w z,min is the lower limit of the length of the cube partition in the x, y and z directions; Formula (6a) is the optimization objective, Formula (6b), (6c), and (6o) are respectively the constraints of structural internal and external force balance, material strength limit, and area not less than zero, Formula (6d) to (6e), Formula (6g) to (6h) are defined as in step S1, Formula (6i) to (6k) are constraints to prevent the partition from shrinking to infinitesimal, and Formula (6l) to (6n) are constraints on the coordinates of the component nodes.

7. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 6, characterized in that: In step S2: the method of constraining the component nodes is to restrict each component to move within its initially assigned partition, specifically constraining the component node coordinates 8. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 7, characterized in that: In step S2: the partition boundaries are taken as additional variables, and the partitions in the same row and column arrangement share the same boundary position variables, and constraints are set to prevent the partitions from shrinking to an infinite size.

9. The method for optimizing the design and manufacturing of a three-dimensional self-supporting truss based on multi-axis 3D printing according to claim 6, characterized in that: In step S2: Formula (6a) is a nonlinear non-convex problem. The initial solution of the problem is determined by an iterative semi-integrated method. The method starts from the obtained printing surface. When the printing surface is known, the projected overhang angle violation values ​​β and γ of the base structure and the component to be added are calculated. For components spanning multiple partitions, the overhang angle violation value is the maximum value calculated in each partition. Then the layout optimization problem is re-solved, and the components that violate the overhang constraint in the base structure and potential components are penalized. The expression of the semi-integrated optimization model is: Where p0 is the penalty factor for the overhang angle violation value.

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