Equally-spaced continuous fiber printing path planning method based on streamline theory and Euler path

Abstract

The invention discloses an equal-interval continuous fiber printing path planning method based on a streamline theory and an Euler path, and relates to the technical field of continuous fiber reinforced composite 3D printing. Comprising the following steps: solving a material unit density and a fiber angle under a finite element unit grid based on a maximum stiffness topological optimization mathematical model to obtain a macroscopic topological structure and local fiber orientation; and performing streamline processing based on local fiber orientation, and integrating discretized grid units to obtain a short streamline fiber path. Carrying out integration according to a short streamline to generate an equidistant discrete fiber distribution diagram; enabling the aggregated fiber distribution to be equivalent to a non-Euler diagram, and carrying out the path processing, so as to modify the nodes and edges which do not meet the Euler path conditions in the original diagram, and obtaining an Euler diagram which meets the Euler path conditions; and performing continuous Euler path solving on the Euler diagram to generate continuous Euler paths at equal intervals. The printing structure performance and the forming manufacturing efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of 3D printing of continuous fiber reinforced composites, and particularly to an equidistant continuous fiber printing path planning method based on streamline theory and Euler path. Background Art

[0002] Due to its excellent properties, continuous fiber reinforced composites have a wide range of application scenarios in various fields. The popularization of 3D printing technology has provided convenience for the application of continuous fiber reinforced composites, greatly accelerating the speed of their design and manufacturing. In the 3D printing of continuous fiber reinforced composites, the planning of the printing path determines the laying position of continuous fibers, directly determining the performance of the printed structure. The continuous fiber path planning method has been increasingly emphasized. However, there are many interruptions and intersections in the existing printing paths of continuous fiber reinforced composites, and the generated fiber spacing is uneven. The printing idle travel caused by fiber path interruption not only increases the printing time, but also the frequent fiber interruption and uneven fiber distribution will also affect the performance of the printed structure.

[0003] For the 3D printing of continuous fiber reinforced composites, path planning design is the technical key to realizing the process from design to manufacturing. At present, the 3D printing process technology for continuous fiber reinforced composites is not yet perfect. Through the existing literature and patents, the currently available public information on continuous fiber printing path planning includes: a 3D printing path planning method for continuous fiber composites without breakpoints in the whole domain based on the distribution of connection points of component structure features (application publication number: CN114013043A); a 3D printing path planning method for continuous fiber reinforced composites (application publication number: CN110001067A); a 3D printing path planning method for continuous fiber reinforcement considering strength (application publication number: CN112776343A); a continuous fiber path planning method based on topology optimization and Euler diagram (application publication number: CN118153373A).

[0004] Patent CN114013043A is based on the discrete structural features. By offsetting the contour line and adopting the strategy of cross-bridge connection of adjacent paths within the layer, a 3D printing path without breakpoints within the layer is obtained, forming an isocontour line with the path as the structural outer contour. However, it does not consider the combination relationship between the force distribution of the structure and the continuous fiber orientation. The formed design scheme does not fully exert the mechanical properties of continuous fibers, reducing the material utilization efficiency. Patent CN110001067A uses finite element simulation technology to simulate and analyze the stress distribution of components under load. According to the stress distribution direction of the components, the additive manufacturing printing path of continuous fiber reinforced composites is planned. However, the formed printing path is locally continuous but still requires multiple cuts, greatly reducing the forming rate and printing performance of continuous fibers. Patent CN112776343A obtains the single-layer stress vector diagram according to the printing layer height and mechanical simulation model of the part to be printed; according to the single-layer printing contour information and the single-layer stress vector diagram, a single-layer printing path is obtained, and the path still needs to be cut multiple times, reducing the forming rate and printing performance. Patent CN112776343A is based on the optimized discrete fiber distribution, clusters the units to obtain the connected partition structural features, and equivalent each partition structural feature to an undirected Euler graph for path solving to obtain the continuous fiber reinforced composite printing path. However, the formed path has the problem of uneven path spacing, and the mechanical properties of the structure are uneven. The uneven fiber density and resin filling increase the difficulty of printing and manufacturing.

[0005] Therefore, it is an urgent problem for those skilled in the art to propose an equidistant continuous fiber printing path planning method based on streamline theory and Euler path. Summary of the Invention

[0006] In view of this, the present invention provides an equidistant continuous fiber printing path planning method based on streamline theory and Euler path. Based on topological optimization design, the topological structure and fiber orientation are determined. While considering the anisotropic mechanical properties of continuous fibers, an equidistant and uninterrupted continuous fiber printing path is formed, improving the printing structure performance and forming manufacturing efficiency.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] An equidistant continuous fiber printing path planning method based on streamline theory and Euler path, comprising the following steps:

[0009] S1. Based on the three-dimensional model of the part to be printed, the three-dimensional model is divided to obtain a finite element unit mesh;

[0010] S2. Using the maximum stiffness topological optimization model, solve the element density and fiber angle under the finite element unit mesh obtained in S1 to obtain the optimized three-dimensional model geometric structure and unit fiber angle;

[0011] S3. Based on the optimized three-dimensional model geometric structure and unit fiber angles obtained in S2, regard the fiber angle distribution as a vector field, fit and draw short streamlines, and integrate the short streamlines to obtain an equidistant non-Eulerian graph;

[0012] S4. Use the equidistant non-Eulerian graph obtained in S3 to perform path processing on the original non-Eulerian graph to modify the nodes and edges in the original non-Eulerian graph that do not meet the Euler path conditions, and obtain an Eulerian graph that meets the Euler path conditions;

[0013] S5. Use the Eulerian graph that meets the Euler path conditions obtained in S4 to solve the continuous path to obtain the continuous fiber path planning result.

[0014] For the above method, optionally, the maximum stiffness topology optimization model in S2 is as follows:

[0015] find: ρ = {ρ1, ρ2, ρ3, …, ρ n} T

[0016] θ = {θ1, θ2, θ3, …, θ n} T

[0017]

[0018] In the formula, c is the optimization goal of minimizing the compliance of the structure, ρ is the set of structural element densities, θ represents the set of fiber angles in each discrete element in the structure, K is the overall stiffness matrix of the structure, U is the overall displacement matrix of the structure, F is the global force vector, ρ e is the density of element e, θ e is the angle of element e, E e is the interpolated elastic modulus, k e is the element stiffness matrix, u e is the element displacement matrix, V is the volume of the structural material, V0 is the volume of the material in the design domain, and f is the optimization constraint condition, that is, the volume fraction.

[0019] For the above method, optionally, during the solution of the element density and fiber angles under the finite element cell mesh in S2, the fiber sensitivity is filtered to obtain the filtered sensitivity, and the specific content is as follows:

[0020]

[0021] In the formula, H ei is the weight factor, γ is a small positive number, and its value is equal to 10 -3 , N eis a set of elements that satisfy the following condition: the center-to-center distance between element i and element e is less than the filtering radius r min .

[0022] For the above method, optionally, the specific content of S3 is as follows:

[0023] S301. Based on topological optimization, the optimized result of the unit angle is the fiber angle set θ, which is regarded as a vector field

[0024] S302. Extract the position information (x, y) and direction information (u, v) of each vector in the vector field;

[0025] S303. Based on the structure unit density set ρ obtained by topological optimization, extract the unit coordinates (x’, y’) with a density of 0 in the unit grid;

[0026] S304. Consider the vector field as a flow field vector field, solve the streamline differential equation using the Runge-Kutta method, and ignore the vectors at the positions of (x’, y’), and obtain a fitted short streamline diagram;

[0027] S305. Integrate the fitted short streamline diagram, perform connection processing from the outside of the structure to the inside, connect the short points of each streamline to the nearest streamline, and form a closed path.

[0028] For the above method, optionally, the specific content of S4 is as follows:

[0029] S401. Based on the closed path obtained in S3, regard it as a graph G(V, E), where V are the various nodes in the graph and E are the various undirected edges in the graph;

[0030] S402. First, traverse all the nodes in the graph G(V, E) and determine whether the number of odd-degree nodes is less than or equal to 2;

[0031] S403. If so, jump to S412; otherwise, sequentially search for odd-degree nodes, starting from the odd-degree node v1, and find the nearest odd-degree node v2;

[0032] S404. Determine whether there is any other edge e crossed at the shortest distance between the two nodes v1 and v2. If so, jump to S409; otherwise, enter S405;

[0033] S405. Extend outward from two nodes on the adjacent path to obtain two new points, and the distance between the new and old points is determined by the path spacing;

[0034] S406. Connect the new points with a smooth curve parallel to the adjacent path;

[0035] S407. Remove the lines that extend through in S404 to obtain the modified graph;

[0036] S408. Judge the condition for the existence of an Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to S402; otherwise, jump to S412;

[0037] S409. Connect these two nodes and generate new nodes when passing through the existing path;

[0038] S410. The degrees of both the new node and the previous node become 4. Split each of these nodes into two nodes with a degree of 2, and the newly generated path nodes satisfy the Euler path condition;

[0039] S411. Judge the condition for the existence of an Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to S402; otherwise, jump to S412;

[0040] S412. For the modified path graph G’(V,E), the number of odd-degree nodes is less than or equal to 2, satisfying the Euler path condition.

[0041] For the above method, optionally, the specific content of S5 is as follows:

[0042] Determine the starting node and the ending node in the Euler graph, and use the odd-degree nodes as the starting node and the ending node;

[0043] Calculate the graph G’(V,E) through the Fluery algorithm, and the algorithm obtains the node connection order that satisfies the completely continuous path according to the given starting node;

[0044] Integrate the obtained node connection order and the coordinate parameters of each node and edge in the Euler graph to obtain the complete path.

[0045] As can be seen from the above technical solutions, compared with the prior art, the present invention provides an equidistant continuous fiber printing path planning method based on streamline theory and Euler path, having the following beneficial effects:

[0046] 1. Through the continuous fiber reinforced composite material topology optimization method, obtain the optimized geometric structure and discrete fiber orientation. Regard the optimization result as a vector field for streamline fitting processing as the basis for subsequent path planning, fully considering and utilizing the material performance, and providing a reasonable design basis for subsequent continuous path design;

[0047] 2. By considering the non-Eulerian graph processing method of the number of odd-degree nodes, connecting adjacent odd-degree nodes, and simultaneously correcting the involved edges, the transformation from a non-Eulerian graph to an Eulerian graph is achieved. Based on the obtained Eulerian graph, an uninterrupted continuous fiber printing path is formed, and the printing path has a uniform path spacing, improving the printing structure performance and the forming manufacturing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0049] Figure 1 It is a flowchart of a method for planning an equidistant continuous fiber printing path based on streamline theory and Euler path disclosed by the present invention;

[0050] Figure 2 It is a geometric structure and unit fiber orientation diagram after topological optimization disclosed in the embodiments of the present invention;

[0051] Figure 3 It is a fitting short streamline result diagram disclosed in the embodiments of the present invention;

[0052] Figure 4 It is a non-Eulerian graph with equal path spacing obtained by integrating short streamlines disclosed in the embodiments of the present invention;

[0053] Figure 5 It is a flowchart of a correction method for obtaining an Eulerian graph satisfying the Euler path condition from a non-Eulerian graph disclosed in the embodiments of the present invention;

[0054] Figure 6 It is an example of a method for correcting adjacent odd-degree nodes disclosed in the embodiments of the present invention;

[0055] Figure 7 It is an example of a method for correcting cross-edge odd-degree nodes disclosed in the embodiments of the present invention;

[0056] Figure 8 It is a schematic diagram of the result of path planning disclosed in the embodiments of the present invention;

[0057] Figure 9 It is a schematic diagram of a 3D printed component disclosed in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0059] In the present application, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or sequence between these entities or operations. The term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0060] The present invention provides an equidistant continuous fiber printing path planning method based on streamline theory and Euler path. Based on topology optimization, the geometric structure and local fiber orientation of the design are determined. The short streamline distribution is obtained by solving through the flow field theory. After integrating the short streamlines, a non-Euler graph is obtained. Then, path processing is performed on the non-Euler graph to modify the nodes and edges in the original graph that do not meet the Euler path conditions, resulting in an Euler graph that meets the Euler path conditions to generate an equidistant continuous Euler path. The obtained continuous path not only meets the optimized fiber orientation, but also has no cut-off points and has a uniform path spacing in the path, improving the structural performance and printing efficiency. The specific technical solutions are as follows:

[0061] See Figure 1 As shown, the present invention discloses an equidistant continuous fiber printing path planning method based on streamline theory and Euler path, including the following steps:

[0062] S1. Based on the three-dimensional model of the part to be printed, the three-dimensional model is divided to obtain a finite element unit mesh;

[0063] S2. Using the maximum stiffness topology optimization model, the element density and fiber angle in the finite element unit mesh obtained in S1 are solved to obtain the optimized three-dimensional model geometric structure and unit fiber angle;

[0064] S3. Based on the optimized three-dimensional model geometric structure and unit fiber angle obtained in S2, the fiber angle distribution is regarded as a vector field, and uniform short streamlines are fitted and drawn. The short streamlines are integrated to obtain an equidistant non-Euler graph;

[0065] S4. Use the equidistant non-Eulerian graph obtained in S3 to process the paths of the original non-Eulerian graph, so as to modify the nodes and edges in the original non-Eulerian graph that do not meet the Euler path conditions, and obtain an Eulerian graph that meets the Euler path conditions;

[0066] S5. Use the Eulerian graph that meets the Euler path conditions obtained in S4 to solve the continuous path and obtain the continuous fiber path planning result.

[0067] Further, the maximum stiffness topology optimization model in S2 is as follows:

[0068] find: ρ = {ρ1, ρ2, ρ3, …, ρ n} T

[0069] θ = {θ1, θ2, θ3, …, θ n} T

[0070]

[0071] In the formula, c is the optimization objective to minimize the compliance of the structure, ρ is the set of structural element densities, θ represents the set of fiber angles in each discrete element in the structure, K is the overall stiffness matrix of the structure, U is the overall displacement matrix of the structure, F is the global force vector, ρ e is the density of element e, θ e is the angle of element e, F e is the interpolated elastic modulus, k e is the element stiffness matrix, u e is the element displacement matrix, V is the volume of the structural material, V0 is the volume of the material in the design domain, and f is the optimization constraint condition, that is, the volume fraction.

[0072] Further, during the solution of the element density and fiber angle under the finite element cell mesh in S2, the fiber sensitivity is filtered to obtain the filtered sensitivity, and the specific content is as follows:

[0073]

[0074] In the formula, H ei is the weight factor, γ is a small positive number, and its value is equal to 10 -3 , N e is the set of elements that meet the following conditions: the distance from the center of element i to the center of element e is less than the filtering radius r min .

[0075] Further, the specific content of S3 is as follows:

[0076] S301. The optimized result of the unit angle obtained by topology optimization is the fiber angle set θ, which is regarded as a vector field.

[0077] S302. Extract the position information (x, y) and direction information (u, v) of each vector in the vector field.

[0078] S303. Based on the structural unit density set ρ obtained by topology optimization, extract the cell coordinates (x’, y’) with a density of 0 in the cell grid.

[0079] S304. Regard the vector field as a flow field vector field, solve the streamline differential equation by the Runge - Kutta method, and ignore the vectors at the positions with coordinates (x’, y’), to obtain a fitted short streamline diagram.

[0080] S305. Integrate the fitted short streamline diagram, perform connection processing from the outside to the inside of the structure, so that the short points of each streamline are connected to the nearest streamline to form a closed path.

[0081] Further, the specific content of S4 is as follows:

[0082] S401. Based on the closed path obtained in S3, regard it as a graph G(V, E), where V are the various nodes in the graph and E are the various undirected edges in the graph.

[0083] S402. First, traverse all the nodes in the graph G(V, E) and judge whether the number of odd - degree nodes is less than or equal to 2.

[0084] S403. If so, jump to S412; otherwise, search for odd - degree nodes in turn. Starting from the odd - degree node v1, find the nearest odd - degree node v2.

[0085] S404. Judge whether there is any other edge e crossed at the shortest distance between the two nodes v1 and v2. If so, jump to S409; otherwise, enter S405.

[0086] S405. Extend outward from the two nodes on the adjacent path to obtain two new points, and the distance between the new and old points is determined by the path spacing.

[0087] S406. Connect the new points with a smooth curve parallel to the adjacent path.

[0088] S407. Remove the lines passed through during the extension in S404 to obtain a modified graph.

[0089] S408. Judge the condition for the existence of an Euler path, whether the number of odd - degree nodes is less than or equal to 2. If not, return to S402; otherwise, jump to S412.

[0090] S409. Connect these two nodes and generate new nodes when passing through the existing path;

[0091] S410. The degrees of both the new node and the previous node become 4. Split each of these nodes into two nodes with degree 2. The newly generated path nodes satisfy the Euler path condition;

[0092] S411. Judge the condition for the existence of the Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to S402. Otherwise, jump to S412;

[0093] S412. In the modified path graph G’(V,E), the number of odd-degree nodes is less than or equal to 2, satisfying the Euler path condition.

[0094] Furthermore, the specific content of S5 is:

[0095] Determine the starting node and the ending node in the Euler graph, and preferentially use the odd-degree nodes as the starting node and the ending node;

[0096] Calculate the graph G’(V,E) through the Fluery algorithm. The algorithm obtains the node connection order that satisfies the completely continuous path according to the given starting node;

[0097] Integrate the obtained node connection order and the coordinate parameters of each node and edge in the Euler graph to obtain the complete path.

[0098] Embodiment 1

[0099] To solve the problems in the traditional existing path planning methods, such as not considering the anisotropic mechanical properties of the reinforcing fiber phase, having many path cutting breakpoints, and uneven fiber path spacing, this embodiment discloses an equal-spacing continuous fiber printing path planning method based on streamline theory and Euler path. Here, continuous fibers generally refer to all manufacturable continuous materials, including carbon fiber, glass fiber, basalt fiber, etc. This method determines the topological structure and fiber orientation based on topological optimization design, integrates the discrete fiber orientations through streamline theory and integrates them to obtain a non-Euler graph with equal path spacing, and integrates the nodes and edges in the non-Euler graph that do not satisfy the Euler condition to obtain an Euler graph that satisfies the continuous path condition, and finally obtains a continuous printing path. The inventive method can form a continuous fiber printing path with uninterrupted and equal fiber path spacing while considering the anisotropic mechanical properties of continuous fibers, improving the printing structure performance and the forming manufacturing efficiency.

[0100] In this embodiment, an equal-spacing continuous fiber printing path planning method based on streamline theory and Euler path specifically includes the following steps 1 to 4.

[0101] Step 1: Optimize the geometric topology configuration and the unit fiber orientation of the MBB beam structure based on the maximum stiffness topology optimization model to obtain the macroscopic topological structure and the local fiber orientation.

[0102] In this embodiment, solving the maximum stiffness problem is equivalent to solving the minimum compliance of the structure. The topology optimization mathematical model is as follows:

[0103] find: ρ = {ρ1, ρ2, ρ3, …, ρ n} T

[0104] θ = {θ1, θ2, θ3, …, θ n} T

[0105]

[0106] In the above optimization model, the optimization objective is to minimize the compliance c of the structure, that is, to maximize the stiffness of the structure. The optimization variables include two. One is ρ representing the set of structural element densities, and the other is θ representing the set of fiber angles in each discrete element of the structure. K is the overall stiffness matrix of the structure, U is the overall displacement matrix of the structure, and F is the global force vector. ρ e is the density of element e, and θ e is the angle of element e. p is the penalty factor, which is used to reduce the elements with intermediate densities (gray elements) and ensure that the values tend to 0 or 1. Generally, p = 3. k e and u e are the element stiffness matrix and the element displacement matrix respectively. V and V0 are the structural material volume and the design domain material volume respectively. f is the optimization constraint condition, that is, the volume fraction. Based on the maximum stiffness topology optimization mathematical model, given the external force load F and setting the allowable volume ratio f of the structure, the material density ρ and the fiber angle θ under the finite element cell grid can be solved. The calculation results are as Figure 2 shown, which are the macroscopic topological structure and the local fiber orientation.

[0107] In the maximum stiffness topology optimization mathematical model of this embodiment, compared with other anisotropic composite material topology optimization models, the fiber angle sensitivity filtering is introduced in the sensitivity calculation. Using the filtered fiber angle sensitivity during the calculation can ensure the continuity of adjacent fiber angles, reduce the fiber fluctuations of adjacent elements, and is more conducive to the subsequent continuous fiber path planning. Filter the fiber sensitivity The filtering method is as follows:

[0108]

[0109] In the formula, is the filtered sensitivity, and N eis a set of elements that satisfy the following condition: for element i and element e, the center-to-center distance is less than the filtering radius r min ; H ei is the weight factor, γ is a small positive number, and its value is equal to 10 -3 , with the aim of avoiding division by zero.

[0110] In step 2, the specific content of fitting uniform short streamlines and integrating them to obtain a non-Eulerian graph with equal spacing is as follows:

[0111] Step 201: Based on topological optimization, the optimized result of the unit angle is θ of the fiber angle set, which is regarded as a vector field

[0112] Step 202: Extract the position information (x, y) and direction information (u, v) of each vector in the vector field;

[0113] Step 203: Based on the structural unit density set ρ obtained from topological optimization, extract the unit coordinates (x’, y’) with a density of 0 in the unit grid;

[0114] Step 204: Regard the vector field as the flow field vector field. In this embodiment, the second-order Runge-Kutta method is used to solve the streamline differential equation, and the vector at the position of (x’, y’) is ignored, resulting in a fitted short streamline diagram, as Figure 3 shown;

[0115] Step 205: Integrate the fitted short streamline diagram, connect and organize it from the outside to the inside of the structure, ensuring that the short points of each streamline are connected to the nearest streamline to form a closed path. Since a symmetric model is used in the optimization, there is actually a corresponding connection path at the symmetry axis, and the node degree is considered to be 2. In the complete model, the path is already closed, so the nodes on the symmetry axis are considered to be closed paths and are not processed. As Figure 4 shown.

[0116] Step 3: Process the non-Eulerian graph for the paths, handle the nodes and edges that do not meet the Euler path conditions in the graph, and obtain an Eulerian graph that meets the Euler path conditions.

[0117] In this embodiment, the process of handling the nodes and edges in the non-Eulerian graph is based on the Euler path criterion, that is, the number of nodes with an odd degree in the connected graph is less than or equal to two. Since a symmetric model is used in the optimization, there is actually a corresponding connection path at the symmetry axis, and the node degree is considered to be 2. Therefore, in the subsequent process, the path is symmetrically processed along the symmetry axis before proceeding with the subsequent process. The process is as Figure 5 shown, and the specific process is as follows:

[0118] Step 301: Based on the closed path obtained in Step 2, it can be regarded as a graph G(V, E), where V are the various nodes in the graph and E are the various undirected edges in the graph;

[0119] Step 302: First, traverse all the nodes in the graph and determine whether the number of odd-degree nodes is less than or equal to 2;

[0120] Step 303: If so, jump to Step 312; otherwise, sequentially search for odd-degree nodes. Starting from the odd-degree node v1, find the odd-degree node v2 closest to it;

[0121] Step 304: Determine whether there is another edge e crossed at the shortest distance between the two nodes v1 and v2. If so, jump to Step 309; otherwise, continue;

[0122] Step 305: Extend outward from the two nodes on the adjacent path to obtain two new points, and the distance between the new and old points is determined by the path spacing;

[0123] Step 306: Connect the extended new points with a smooth curve parallel to the adjacent path;

[0124] Step 307: Remove the line passed through during the extension in Step 304 to obtain the modified graph, as Figure 6 shown;

[0125] Step 308: Determine the condition for the existence of an Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to Step 302; otherwise, jump to Step 312;

[0126] Step 309: Connect these two nodes and generate new nodes when passing through the existing path;

[0127] Step 310: The degrees of both the new node and the previous node become 4. Split each of these nodes into two nodes with a degree of 2. The newly generated path nodes satisfy the Euler path condition, as Figure 7 shown;

[0128] Step 311: Determine the condition for the existence of an Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to Step 302; otherwise, jump to Step 312;

[0129] Step 312: For the modified path graph G’(V, E), the number of odd-degree nodes is less than or equal to 2, satisfying the Euler path condition, and end.

[0130] Step 4: Based on the obtained Euler graph that satisfies the Euler path, solve the continuous path to obtain the continuous fiber path planning result.

[0131] Determine the starting node and ending node in the Eulerian graph, and preferably use the nodes with odd degrees as the starting node and ending node;

[0132] Calculate the modified path graph G’(V,E) through the Fluery algorithm. The algorithm obtains the node connection order that satisfies the completely continuous path according to the given starting node. Since a symmetric model is adopted, after restoring its symmetry to the complete model, there are independent completely continuous paths in the path. Connect each independent path simply through two short parallel lines to obtain a complete continuous path, as Figure 8 shown;

[0133] Integrate the obtained node connection order and the coordinate parameters of each node and edge in the Eulerian graph to obtain a complete path. Importing into CAD can obtain a complete continuous fiber printing path. After generating a DXF file and importing it into the 3D printing path code conversion software, a G-code file for the actual printing device can be generated. After setting the printing process parameters, the printing of the example structure can be completed through the printing device, as Figure 9 shown.

[0134] In summary, the equal-spacing continuous fiber printing path planning method based on the streamline theory and Euler path in this embodiment can complete the integrated forming scheme from structural design to printing manufacturing. While considering the anisotropic mechanical properties of continuous fibers, it forms an uninterrupted and equal-path-spacing continuous fiber printing path, improving the printing structure performance and forming manufacturing efficiency.

[0135] It should be noted that in the preferred solution, the topology optimization solution in this embodiment can be replaced by various methods, such as the density method (SIMP), the orthogonal unit density (SOMP), the level set method (level-set), etc., as long as the optimization result includes the macroscopic topological structure and the local fiber orientation of the unit.

[0136] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for planning an equidistant continuous fiber printing path based on streamline theory and Euler path, characterized in that, It includes the following steps: S1. Based on the 3D model of the part to be printed, divide the 3D model to obtain a finite element cell mesh; S2. Use the maximum stiffness topology optimization model to solve the element density and fiber angle under the finite element cell mesh obtained in S1, and obtain the optimized 3D model geometric structure and element fiber angle; S3. Based on the optimized 3D model geometric structure and element fiber angle obtained in S2, regard the fiber angle distribution as a vector field, fit and draw short streamlines, and integrate the short streamlines to obtain an equidistant non-Eulerian graph; S4. Use the equidistant non-Eulerian graph obtained in S3 to process the path of the original non-Eulerian graph, modify the nodes and edges in the original non-Eulerian graph that do not meet the Euler path conditions, and obtain an Eulerian graph that meets the Euler path conditions; S5. Use the Eulerian graph that meets the Euler path conditions obtained in S4 to solve the continuous path and obtain the continuous fiber path planning result.

2. A method for equidistant continuous fiber printing path planning based on streamline theory and Euler path according to claim 1, characterized in that The maximum stiffness topology optimization model in S2 is as follows: find: ρ = {ρ1, ρ2, ρ3, …, ρ n} T θ = {θ1, θ2, θ3, …, θ n} T Wherein, c is the optimization objective to minimize the compliance of the structure, ρ is the set of structural element densities, θ represents the set of fiber angles in each discrete element of the structure, K is the overall stiffness matrix of the structure, U is the overall displacement matrix of the structure, F is the global force vector, ρ e is the density of element e, and θ e is the angle of element e, E e is the interpolated elastic modulus, k e is the element stiffness matrix, u e is the element displacement matrix, V is the volume of the structural material, V0 is the volume of the material in the design domain, and f is the optimization constraint condition, i.e., the volume fraction.

3. A method for equidistant continuous fiber printing path planning based on streamline theory and Euler path according to claim 2, characterized in that During the solution of the element density and fiber angle under the finite element cell mesh in S2, the fiber sensitivity is filtered to obtain the filtered sensitivity, and the specific content is as follows: where H ei is a weight factor, γ is a small positive number whose value is equal to 10 -3 , N e is the set of elements satisfying the following condition: the center-to-center distance of element i from element e is less than the filtering radius r min .

4. A method for equidistant continuous fiber printing path planning based on streamline theory and Euler path according to claim 3, characterized in that The specific content of S3 is: S301. The optimized result of the unit angle obtained by topology optimization is the fiber angle set θ, which is regarded as a vector field S302. Extract the position information (x, y) and direction information (u, v) of each vector in the vector field ; S303. Based on the set of structural element densities ρ obtained by topology optimization, extract the element coordinates (x’, y’) with a density of 0 in the element mesh; S304. Treat the vector field as a flow field vector field, solve the streamline differential equation using the Runge-Kutta method, ignore the vector at the position of (x’, y’), and obtain the fitted short streamline diagram; S305. Integrate the fitted short streamline diagram, and perform connection processing from the outside of the structure to the inside, so that the short points of each streamline are connected to the nearest streamline to form a closed path.

5. A method for equidistant continuous fiber printing path planning based on streamline theory and Euler path according to claim 4, characterized in that The specific content of S4 is: S401. Based on the closed path obtained in S3, regard it as a graph G(V, E), where V are the various nodes in the graph and E are the various undirected edges in the graph; S402. First, traverse all the nodes in the graph G(V, E) and judge whether the number of odd-degree nodes is less than or equal to 2; S403. If so, jump to S412; otherwise, search for odd-degree nodes in turn, start from the odd-degree node v1, and find the nearest odd-degree node v2; S404. Judge whether there is other edge e crossed at the nearest distance between the two nodes v1 and v2. If so, jump to S409; otherwise, enter S405; S405. Extend outward from the two nodes on the adjacent path to obtain two new points, and the distance between the new and old points is determined by the path spacing; S406. Connect the new points with a smooth curve parallel to the adjacent path; S407. Remove the line passed by the extension in S404 to obtain the modified graph; S408. Judge the condition for the existence of the Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to S402; otherwise, jump to S412; S409. Connect these two nodes and generate new nodes when passing through the existing path; S410. The degrees of both the new node and the previous node become 4. Split each of these nodes into two nodes with degree 2. The newly generated path nodes satisfy the Euler path condition; S411. Determine the condition for the existence of the Euler path, whether the number of odd-degree nodes is less than or equal to 2. If not, return to S402. Otherwise, jump to S412; S412. In the modified path graph G’(V,E), the number of odd-degree nodes is less than or equal to 2, satisfying the Euler path condition.

6. A method for equal-spacing continuous fiber printing path planning based on streamline theory and Euler path according to claim 5, characterized in that The specific content of S5 is: Determine the starting node and the ending node in the Euler graph, and use the odd-degree nodes as the starting node and the ending node; Calculate the graph G’(V,E) through the Fluery algorithm. The algorithm obtains the node connection order that satisfies the completely continuous path according to the given starting node; Integrate the obtained node connection order and the coordinate parameters of each node and edge in the Euler graph to obtain a complete path.

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