An efficient design system for three-periodic minimal surface structures for multiple application scenarios

Abstract

The invention discloses an efficient design system for three-periodic minimal surface structures for multiple application scenarios, comprising two filling modules, namely a direct filling module based on a signed distance field and a conformal filling module based on isoparametric unit method mapping; the direct filling module based on the signed distance field is used for the creation of a discretized grid / target model distance field, the creation of a three-periodic minimal surface distance field and Boolean operations on the distance field; the conformal filling module based on isoparametric unit method mapping is used for the creation of a hexahedral grid of a target model, the creation of basic cells of a three-periodic minimal surface and isoparametric unit method mapping; the design requirements are determined according to different application scenarios, and a direct filling module or a conformal filling module suitable for the task is selected; the invention is guided by application scenarios and can realize the efficient construction of various simple or complex TPMS customized models, and is suitable for various fields such as advanced heat exchangers, energy storage or conversion devices, biological implants, aerospace, sound absorption and energy absorption.

Description

Technical Field

[0001] The present invention relates to the field of three-dimensional implicit modeling and industrial design and manufacturing technology, and in particular to an efficient design system for three-periodic minimal surface structures for multiple application scenarios. Background Art

[0002] With the deepening of economic globalization and awareness of energy conservation and emission reduction, green and low-carbon development has become a common consensus among countries around the world. Under the guidance of the "dual carbon" goal, the coordinated development of digitalization, intelligence and greening of the manufacturing industry has become an important guide for building a manufacturing power. The rapid development of additive manufacturing technology in recent years has injected new vitality into the deepening reform of the manufacturing industry. Additive manufacturing technology has subverted the design concept and production mode of traditional manufacturing, especially in personalized and lightweight design and manufacturing. Additive manufacturing significantly reduces product weight and required materials, reduces production costs, and also reduces carbon dioxide emissions. Among them, porous structures play a pivotal role in personalization and lightweight. Compared with traditional porous structures (random foam structures, truss structures, and thin-walled structures, etc.), triply periodic minimal surfaces (TPMS) are self-supporting surface structures with the characteristics of zero average curvature, which can avoid stress concentration caused by morphological mutations and are also conducive to additive manufacturing. The surface structure is accurately expressed by mathematical formulas, and can customize geometric features such as personalized porosity, pore size, and topological morphology. At the same time, the structure also has excellent mechanical properties, permeability and flow disturbance capabilities, and therefore has attracted much attention.

[0003] Common methods for constructing customized models with TPMS structures as filling cores include the following: First, first, generate a TPMS structure array within the maximum filling domain of the target model. Then, import the generated TPMS structure array into the CAD software in STL format. Next, convert the target model into a triangular facet through the CAD software. Finally, perform geometric Boolean operations on the TPMS structure array and the target model, such as the one-piece liquid-cooled chip radiator and manufacturing method filled with three-periodic minimal surfaces disclosed in patent CN114256179A; second, reconstruct the signed distance field of the target model, and then calculate the signed distance field of the TPMS structure within the maximum filling domain. Finally, perform distance field Boolean operations on the target model and the TPMS structure, such as a high-efficiency heat exchanger flow channel design method and system based on implicit fields disclosed in patent CN116933527A); third, perform hexahedral meshing on the target model. Then construct a TPMS basic cell with a regular shape in the natural coordinate system. Finally, the basic cell is mapped to each hexahedral unit through the shape function isoparametric unit method, such as a conformal design method and system for an aircraft engine fuel oil heat exchanger disclosed in patent CN116933529A. However, these methods all have their own limitations. In the first method, the Boolean operation occurs after the triangular facets (solid file) have been generated. Due to the large number of triangular facets in the TPMS structure array, the geometric Boolean operation (processing the relationship between points, lines and faces) not only runs slowly, but even errors occur. The number of discrete grid points (sampling points) in the second method has a great influence on the accuracy of the customized model. The fewer sampling points, the faster the model generation speed, but this is at the expense of model quality. On the contrary, the higher the accuracy of the model, the greater the processing time; in addition, the "complex" TPMS structure implemented by the existing public scheme refers to a hybrid TPMS or multi-scale TPMS generated in a specific direction or in a regular filling domain. These schemes cannot implement personalized filling in the specified filling domain of the target model. The third method is not suitable for extremely complex target models (hexahedral meshing is difficult), and only TPMS structures that conform to three-axis symmetry can be used to build customized models.

[0004] In addition, most of the existing public patents focus on innovations in three aspects: new topological structures, new filling methods, and applications based on TPMS structures. There is still a lack of a user-friendly, highly integrated, versatile, and efficient design system for three-periodic minimal surface structures that is oriented to a wide range of scenarios, which brings great inconvenience to researchers or engineers in conducting scientific research and engineering applications of TPMS structures. Therefore, it is urgent to explore a more versatile and efficient design system for three-periodic minimal surface structures that is oriented to a wider range of application scenarios. Summary of the invention

[0005] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to provide an efficient design system for three-periodic minimal surface structures for multiple application scenarios, including two core filling modules: a direct filling module based on signed distance field and a conformal filling module based on isoparametric element method mapping. It is application scenario-oriented and can realize the efficient construction of various simple or complex TPMS customized models. It is not only suitable for the design of new heat exchangers, but also can be used in biomedicine, structural lightweight, optical acoustics and other fields, providing comprehensive and convenient solutions for researchers and engineers.

[0006] In order to achieve the above object, the technical solution of the present invention is:

[0007] An efficient design system for three-periodic minimal surface structures for multiple application scenarios, including two filling modules, a direct filling module based on signed distance field and a conformal filling module based on isoparametric element method mapping;

[0008] The direct filling module based on the signed distance field is used for the creation of discretized grid / target model distance field, the creation of three-periodic minimal surface distance field and distance field Boolean operation;

[0009] The conformal filling module based on isoparametric element method mapping is used for the creation of hexahedral meshing of the target model, the creation of basic cells of three-periodic minimal surfaces and isoparametric element method mapping;

[0010] Determine the design requirements according to different application scenarios, and select the direct filling module based on the signed distance field or the conformal filling module based on the isoparametric element method mapping that is suitable for the task.

[0011] The function operation of the direct filling module based on the signed distance field includes the following steps:

[0012] S1a, import the triangle face file of the target model, extract the vertex coordinate matrix [x, y, z] of all triangle faces, and create a bounding box based on the coordinate information to completely cover the target model. The internal space of the bounding box is the maximum filling domain. The maximum filling domain of the bounding box is evenly discretized, and the truncation distance is introduced to quickly calculate the discrete grid points. The signed distance field φ to the target model GEO ;

[0013] S2a, select the design module, cell type and geometric parameters according to the design requirements, and construct the implicit equation φ of the TPMS structure in the maximum filling domain TPMS ;

[0014] S3a, perform distance field Boolean operations on the TPMS structure and target model, and then obtain a TPMS customized model φ that meets the design requirements OBJ,Then, the marching cubes algorithm is used to generate a one-sided file of the customized model.

[0015] In step S1a, the cutoff distance is introduced to quickly calculate the signed distance field φ from the discrete grid point to the target model. GEO The specific method is:

[0016] (1) Uniformly discretize the maximum filling domain to obtain the coordinates of three-dimensional discrete grid points Calculate the number and distance d of the discrete grid point closest to each vertex of the triangle face, including the maximum distance d max ; and extract the content The coordinates of the adjacent discrete grid points That is, the discretized grid points in a small range near the target model, the cutoff distance therefore, It is further subdivided into the internal point coordinates of the target model Coordinates of external points of the target model and the coordinates of the adjacent discrete grid points Right now

[0017] (2) Initialize the signed distance field from X to the target model Will Initially set to be greater than the maximum distance d max For any value of Signed distance field to target model and will Update to the corresponding coordinates get

[0018] (3) Setting temporary variables Obviously, Then will Convert to logical matrix therefore, and Also equal to 0; calling the infill function will Set to 1, so the coordinates of the remaining logical 0 are

[0019] (4) Set to -d max , the signed distance field φ of the target model can be reconstructed quickly and efficiently GEO .

[0020] In step S2a, a design module is selected according to the design requirements, and the design modules include simple filling, complex filling and radial filling;

[0021] The simple filling refers to a filling method in which the cell type and geometric parameters of the TPMS remain unchanged within the maximum filling domain. Taking the Schware-P surface as an example, it is described by the following formula:

[0022]

[0023]

[0024] Where l represents the basic cell length, which is a constant in simple filling; x, y, and z are the coordinate component values ​​of discrete grid points; C1 and C2 are used to control the wall thickness, porosity, and topological structure of the TPMS structure, which are constant in simple filling; Sheet and Sketchetal refer to sheet-like and skeleton-like TPMS structures, respectively.

[0025] The complex filling refers to a filling method that performs personalized design within a specified sub-filling domain of the target model, can fill TPMS structures of any type and geometric parameters, and realizes smooth connection of adjacent sub-filling structures. The specific steps are as follows:

[0026] Step (1), importing the target model into CAD software, and cutting and dividing the target model into blocks according to the filling requirements, thereby obtaining a series of sub-models, the internal space of these sub-models is the sub-filling domain, converting these sub-models into triangular facets, and adjusting the facet quality to avoid excessive aspect ratio, and then exporting all sub-models and their original models in STL format;

[0027] Step (2), import the STL files of the target model and the sub-model into Matlab in order of volume size from small to large, and store them in the form of cell arrays; create a bounding box to completely cover the target model, and the internal space of the bounding box is the maximum filling domain;

[0028] Step (3), the internal point coordinates of the sub-model The set relationship between them determines the geometric relationship between the sub-models, thereby determining the point set of each sub-filling domain

[0029] Step (4), through all the points in the sub-filling domain The TPMS structures that meet the design requirements are allocated to the sub-filling domains. To ensure a smooth transition between adjacent sub-filling structures and keep the overall operation simple, weighting coefficients are introduced to define the complex filling core φ TPMS , described by the formula as follows:

[0030]

[0031]

[0032] In the formula, is the signed distance field of the TPMS structure of the ith sub-filling domain; yes Variables for customizing the wall thickness, porosity, and topology of TPMS structures; is the weight coefficient of the ith sub-filling structure, defined by the radial basis function:

[0033]

[0034] In the formula, γ i is the transition gradient coefficient, which is used to adjust the smoothness between adjacent sub-filling structures; refers to the coordinates of the jth point in the ith sub-filling domain; m refers to the number of discrete grid points in the ith sub-filling domain.

[0035] The radial filling refers to a circular TPMS structure distributed along the radial gradient. The concept of coordinate transformation is used to transform the regular TPMS structure in the Cartesian coordinate system into a radial structure in the polar coordinate system. The specific steps are as follows:

[0036] (1) Determine the inner and outer diameters, filling height, rotation axis, rotation angle, and circumferential arrangement number of radial filling according to design requirements; then construct a suitable three-periodic minimal surface structure in the corresponding rectangular filling domain before transformation;

[0037] (2) Extract the vertex coordinates [x, y, z] and connection order of the triangular facets of the regular TPMS structure, and transform the vertex coordinates into real polar coordinates to obtain the radially transformed three-periodic minimal surface structure. Take the rotation around the z-axis as an example:

[0038]

[0039] In the formula, l represents the basic cell length; m is the circumferential arrangement number, that is, the number of basic cells of the three-periodic minimal surface in the circumferential direction;

[0040] (3) A customized model based on radial filling technology can be constructed by performing Boolean operations on the radially transformed annular TPMS structure and the target geometry.

[0041] The cell types in step S2a include common TPMS such as Gyroid surface, Diamond surface, I-WP surface, Schware-P surface, etc., and implicit surfaces can also be customized; the controllable geometric parameters include cell size and C value.

[0042] In step S3a, distance field Boolean operation is performed on the TPMS and the target model, and the calculation formula is:

[0043]

[0044] The specific functional operation of the conformal filling module based on isoparametric element method mapping includes the following steps:

[0045] S1b, cutting the target model into sub-models of multiple shapes, performing hexahedral meshing on the sub-models after the block processing, and then extracting the mesh unit and node information;

[0046] S2b, select the cell type and geometric parameters according to the design requirements, construct the basic cell of TPMS in the unit cube, and extract the vertices and connection list of the triangular faces constituting the cell;

[0047] S3b, using shape function isoparametric transformation to map the regular cell into each hexahedral unit; finally, performing Boolean operations on the mapped conformal core and the target model, a customized model based on conformal filling technology can be obtained.

[0048] The specific method of dividing the target model into hexahedral grids in step S1b is:

[0049] (1) Determine whether the geometric features of the target model are relatively simple. If the conditions are met, proceed to the subsequent steps; otherwise, the target model needs to be cut into several sub-models with simpler shapes through CAD software, and then the subsequent meshing process is performed;

[0050] (2) Import all sub-models into the meshing tool; select the appropriate mesh size according to the design requirements, which determines the size of the cells involved in the filling; then perform hexahedral meshing and export the mesh in inp format. If the target model consists of a series of sub-models, the mesh on the interface of the sub-models must remain continuous;

[0051] (3) Import the inp file into Matlab and read the hexahedral unit and node information.

[0052] In step S3b, shape function isoparametric transformation is used to map the regular cell to each hexahedral unit, and the specific method is as follows:

[0053] (1) According to the design requirements, create the basic cell of TPMS in the unit cube, construct it using the marching cube algorithm, and extract the vertices and connection list of the triangular face of the cell;

[0054] (2) The shape function is used to transform the regular-shaped cell in the natural coordinate system into the irregular-shaped cell in the Cartesian coordinate system. The shape function equation is as follows:

[0055]

[0056]

[0057] Where (x, y, z) is the coordinate point inside the hexahedral unit in the Cartesian coordinate system, that is, the Cartesian coordinates of the vertices of each triangular face of the cell after the isoparametric transformation; (x i ,y i ,z i ) are the coordinate values ​​of the eight vertices of the hexahedral unit in the Cartesian coordinate system; N i is the node shape function; is the coordinate point inside the regular cube unit in the natural coordinate system, that is, the natural coordinate of the vertex of each triangular face of the cell before the isoparametric transformation; are the coordinate points of the eight vertices of the regular cube unit in the natural coordinate system;

[0058] (3) The mapped complex core is imported into CAD software, and Boolean operations are performed on the target model. Then, geometric repair is performed on the model that has completed the Boolean operation, thereby realizing a customized model based on conformal filling technology.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1. The design system proposed in the present invention is application scenario-oriented and includes two core filling modules: a direct filling module based on signed distance field and a conformal filling module based on isoparametric element method mapping. It can construct a customized TPMS model with regular or irregular shapes that meets various design requirements.

[0061] 2. Introducing the cutoff distance in the process of reconstructing the signed distance field of the target model can significantly improve the reconstruction speed of the distance field, making it possible to build a more complex customized TPMS model.

[0062] 3. The introduction of the concepts of set-geometry relationship and radial basis function enables personalized design within the specified sub-filling domain of the target model, filling TPMS of any type and geometric parameters, and smoothly connecting adjacent sub-filling structures.

[0063] In summary, the present invention provides an efficient design system for TPMS structures that integrates the technical advantages of direct filling and conformal filling. It has strong versatility and a wide range of scenarios, and can provide comprehensive and convenient solutions for researchers and engineers; it can efficiently and conveniently build various simple or complex TPMS customized models. Combining the advantages of direct filling technology based on signed distance fields with conformal filling technology based on isoparametric element method mapping, a multifunctional, integrated design is achieved, providing researchers and engineers with a comprehensive, efficient and convenient solution. The present invention is also applicable to a variety of application scenarios, including but not limited to: compact heat exchangers based on TPMS structures, phase change energy storage systems using TPMS thermal conductive skeletons, solar thermal utilization and heat conversion devices based on TPMS structures, new catalyst or adsorbent carriers, artificial bones that conform to actual bone density distribution, lightweight load-bearing components in aerospace, and sound-absorbing and energy-absorbing sandwich panels based on TPMS structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a flow chart of an efficient design system for three-periodic minimal surface structures for multiple application scenarios of the present invention.

[0065] Figure 2 A schematic diagram of a femoral head model and a sub-filling area provided in the first embodiment of the present invention. Figure 2 (a) is the femoral head model. Figure 2 (b) is a schematic diagram of the sub-filling domain. Sub-filling domains ① and ③ are filled with Sheet-Gyroid structures with a cell size of 5 mm and a C value of 0.3; sub-filling domain ② is filled with Sheet-Diamond structures with a cell size of 5 mm and a C value of 0.3; sub-filling domain ④ is set as a solid domain.

[0066] Figure 3 A schematic diagram of introducing the truncation distance to quickly calculate the signed distance field from discrete grid points to the target model. Figure 3 (a) is the signed distance field from the adjacent discrete grid point to the femoral head model; Figure 3 (b) is the logic matrix after subtracting 100 and transforming; Figure 3 (c) is the logic matrix after filling the internal "holes"; Figure 3 (d) in the figure sets the signed distance value of the external point division to 100.

[0067] Figure 4 The invention is to quickly determine the discrete grid points in the sub-filling domain through the set-geometry relationship Schematic diagram of .

[0068] Figure 5The cross-sectional structure diagram of the customized femoral head model based on the TPMS structure realized by utilizing the complex filling function in the direct filling module proposed in the present invention, unless otherwise specified, it will be referred to as: customized femoral head model hereinafter.

[0069] Figure 6 This is a connecting rod model of a vehicle engine provided in the second embodiment of the present invention.

[0070] Figure 7 is a schematic diagram of the shape function transformation process. Figure 7 (a) is the regular Sheet-Schware-P structure in the natural coordinate system; Figure 7 (b) The Sheet-Schware-P structure after shape function transformation.

[0071] Figure 8 The customized connecting rod model based on TPMS conformal filling realized by the conformal filling module proposed by the present invention is referred to as the customized connecting rod model in the following text unless otherwise specified. Figure 8 (a) is an oblique view of the customized connecting rod model; Figure 8 (b) is the front view of the customized connecting rod model.

[0072] Fig. 9 A customized femoral model and a customized connecting rod model were manufactured using stereolithography 3D printing technology. Fig. 9 (a) is a printed sample of a customized femur model; Fig. 9 (b) is the printed sample of the customized connecting rod model.

[0073] Fig.10 A simple TPMS structure is realized by utilizing the simple filling function in the direct filling module proposed by the present invention. Fig.10 (a) in the figure is the Sheet-Schware-P structure; Fig.10 (b) The Skeletal-Schware-P structure.

[0074] Fig.11 The circular ring-shaped TPMS structure is realized by utilizing the radial filling function in the direct filling module proposed by the present invention. DETAILED DESCRIPTION

[0075] The present invention is further explained below with reference to the accompanying drawings and specific embodiments.

[0076] The present invention discloses an efficient design system for three-periodic minimal surface structures for multiple application scenarios, including two filling modules, namely a direct filling module based on a signed distance field and a conformal filling module based on isoparametric element method mapping; the design requirements are determined according to different application scenarios, and the direct filling module based on a signed distance field or the conformal filling module based on isoparametric element method mapping suitable for the task is selected;

[0077] The direct filling module based on the signed distance field is used for the creation of discretized grid / target model distance field, the creation of three-periodic minimal surface distance field and distance field Boolean operation;

[0078] The conformal filling module based on isoparametric element method mapping is used for the creation of hexahedral meshing of the target model, the creation of basic cells of three-periodic minimal surfaces and isoparametric element method mapping. The following two embodiments are respectively the cases where one filling module is used.

[0079] Embodiment 1

[0080] The present embodiment describes an efficient design system for three-periodic minimal surface structures for multiple application scenarios, which uses a direct filling module based on a signed distance field. The specific implementation process is shown in the present embodiment:

[0081] like Figure 2 As shown, this embodiment provides a femoral head model. The femur is the most important bone of the human body, and the femoral head is even more important. People's upright walking and activities rely on the support of the femoral head. Therefore, the femoral head is also the most vulnerable part of the human body, and the most common femoral head disease is avascular necrosis. Artificial joint placement is considered to be an important medical technology to relieve the pain of patients with femoral head diseases and ensure their normal life and work. With the continuous understanding and exploration of the performance of three-period minimal surfaces, bone implants based on three-period minimal surface structures are receiving unprecedented attention.

[0082] The maximum size (bounding box size) of the femoral head model is 38*37*25mm, and its internal space is divided into 4 sub-filling domains, such as Figure 2 (b). Among them, sub-filling domains ① and ③ are both filled with Sheet-Gyroid structure with a cell size of 5mm and a C value of 0.3, and the C value is 0.3; sub-filling domain ② is filled with Sheet-Diamond structure with a cell size of 5mm and a C value of 0.3; sub-filling domain ④ is set as a solid, that is, φ4=1. The entire customized model is manufactured using 3D printing technology (photocuring LCD) and is integrally formed with a photosensitive resin to verify the printability of the customized model designed by the direct filling module of the present invention. Specifically comprising the following steps:

[0083] S1. According to the distribution characteristics of bone density, it is determined that the filling core must meet the design requirements of sparse center and dense outside, and thus the direct filling module based on signed distance field is selected.

[0084] S2. Import the femoral head model into the CAD software and cut it into blocks according to the filling requirements, thereby obtaining a series of sub-models. The internal space of these sub-models is the sub-filling domain, such as Figure 2 (b) These sub-models are converted into triangular facets, and the facet quality is adjusted to avoid excessive aspect ratio. The femoral head model and its sub-models are then exported in STL format.

[0085] S3. Import the STL files of the femoral head model and its sub-models into Matlab in order of volume size, from small to large, and store them in the form of cell arrays. Create a bounding box to completely enclose the femoral head model, and the internal space of the bounding box is the maximum filling domain. Then, the bounding box (maximum filling domain) is discretized uniformly. The cutoff distance is introduced to quickly calculate the signed distance field from the discrete grid points to the femoral head model. The femoral head model is used to accurately capture geometric features; the sub-model is used to quickly determine the discrete grid points located inside it. (Using the ray method).

[0086] S4. Select complex filling (gradient structure, hybrid structure and multi-scale structure) according to the design requirements described in step S1, and select Sheet-Gyroid and Sheet-Diamond as the filling core of the femur. The cell size and C value of Sheet-Gyroid and Sheet-Diamond are 5mm and 0.3 respectively. Construct the implicit equation of TPMS in the sub-filling domain, and introduce the weighting coefficient to define the complex filling core φ TPMS .

[0087] S5. For complex filling core φ TPMS and femoral head model φ GEO Distance field Boolean operations were performed to obtain a customized femoral head model φ filled with three TPMS structures. OBJ .

[0088] In this embodiment, the specific steps of introducing the truncation distance in step S3 to quickly calculate the signed distance field from the discrete grid point to the target model are:

[0089] S31. Uniformly discretize the maximum filling domain to obtain three-dimensional discrete grid point coordinates Calculate the number and distance d (including the maximum distance d) of the discrete grid points closest to each vertex of the triangle face max ), and extract the satisfying (Cutoff distance Set to the coordinates of the adjacent discrete grid point of the triangle face) (i.e., discretized grid points within a small range near the target model). Therefore, It is further subdivided into the internal coordinates of the femur model Coordinates of external points of femur model and the coordinates of the adjacent discrete grid points Right now

[0090] S32. Initialization Signed distance field to the femoral head model Will Initially set to be greater than the maximum distance d max Any value of , in this embodiment, is set to 100. Calculate Signed distance field to the femoral head model and will Update to the corresponding coordinates get like Figure 3 (a) shown.

[0091] S33. Set temporary variables Obviously, Then will Convert to logical matrix like Figure 3 (b). Therefore, and is also equal to 0. Calling the infill function will Set to 1, so the coordinates of the remaining logical 0 are like Figure 3 (c) as shown.

[0092] S34. Set to -d max ,like Figure 3 (d) shows that the signed distance field φ of the target model can be reconstructed quickly and efficiently. GEO .

[0093] In this embodiment, S3 quickly determines the discrete grid points in the sub-filling domain. The specific steps are as follows:

[0094] S35. Internal point coordinates of the sub-model The set relationship between them determines the geometric relationship between the sub-models, thereby determining the point set of each sub-filling domain Figure 4 To quickly determine the discrete grid points in the sub-filling domain For example, if sub-model B It is the sub-model A A proper subset of This means that sub-model B is inside sub-model A. Therefore, the internal point coordinates of sub-model B are This is the fill field of B. The filling domain of sub-model A Equivalent to Submodel C With sub-model B The intersection is an empty set This means that sub-model C and sub-model B are separated. Therefore, the filling domain of sub-model C and sub-model B are their respective internal point coordinates

[0095] In this embodiment, the specific method of constructing the implicit equation of the TPMS in the sub-filling domain and the complex filling core in S4 is:

[0096] Through the set-geometry relationship described in step S35, the point sets in sub-filling domain ①, sub-filling domain ② and sub-filling domain ③ can be obtained respectively. and The Sheet-Gyroid and Sheet-Diamond structures are assigned to the sub-filling domains respectively. To ensure a smooth transition between adjacent sub-filling structures and keep the overall operation simple, a weighting coefficient is introduced to define the complex filling core φ TPMS . It is described by the formula as follows:

[0097]

[0098]

[0099]

[0100] In the formula, is the signed distance field of the TPMS in the ith sub-filling domain; C i TPMS wall thickness, porosity and topology for controlling the i-th sub-filling domain; is the weight coefficient of the ith sub-filling structure, defined by the radial basis function:

[0101]

[0102] In the formula, γ i is the transition gradient coefficient, which is used to adjust the smoothness between adjacent sub-filling structures; refers to the coordinates of the jth point in the ith sub-filling domain; m refers to the number of discrete grid points in the ith sub-filling domain.

[0103] In this embodiment, the step S5 comprises the following specific steps:

[0104] S51. The complex filling core φ TPMS and femoral head model φ GEO Implementing distance field Boolean operations to obtain a customized femoral head model φ filled with three TPMS structures OBJ The signed distance field of . The formula is as follows:

[0105] φ OBJ =φ GEO ∩φ TPMS =min(φ GEO ,φ TPMS )

[0106] S52. Using the Marching Cubes algorithm to generate a one-sided file of the customized femoral head model, such as Figure 5 As can be seen in the close-up, the transition between sub-fill structures of different cell types is very smooth.

[0107] In the specific implementation process, the customized model was printed and verified using light-curing 3D printing technology. Fig. 9 The results show that the customized model based on TPMS structure filling designed by the direct filling module of the present invention has good printability.

[0108] This embodiment uses the direct filling module based on the signed distance field and the complex filling function proposed in the present invention to realize a customized femoral head model based on the TPMS filling core. The porosity of the customized femoral model is close to the actual human bone density distribution, that is, sparse in the center and dense on the outside.

[0109] In this embodiment, because the target model is complex and the filling core is also complex, step S4 is to select a complex filling module according to the design requirements described in step S1. In practical applications, simple filling or radial filling can also be selected according to requirements, the geometry or complexity of the target model.

[0110] like Fig.10 As shown, the simple filling refers to a filling method in which the cell type and geometric parameters of the TPMS remain unchanged within the maximum filling domain. Taking the Schware-P surface as an example, it is described by the following formula:

[0111]

[0112]

[0113] Where l represents the basic cell length, which is a constant in simple filling; x, y, and z are the coordinate component values ​​of discrete grid points; C1 and C2 are used to control the wall thickness, porosity, and topological structure of the TPMS structure, which are constant in simple filling; Sheet and Sketchetal refer to sheet-like and skeleton-like TPMS structures, respectively.

[0114] like Fig.11 As shown, the radial filling refers to a circular TPMS structure with radial gradient distribution. Taking the Gyroid surface as an example, the concept of coordinate transformation is used to transform the regular TPMS structure in the Cartesian coordinate system into a radial structure in the polar coordinate system. The specific steps are as follows:

[0115] (1) Determine the inner and outer diameters, filling height, rotation axis, rotation angle, and circumferential arrangement number of radial filling according to design requirements; then construct a suitable three-periodic minimal surface structure in the corresponding rectangular filling domain before transformation;

[0116] (2) Extract the vertex coordinates [x, y, z] and connection order of the triangular facets of the regular TPMS structure, and transform the vertex coordinates into real polar coordinates to obtain the radially transformed three-periodic minimal surface structure. Take the rotation around the z-axis as an example:

[0117]

[0118] In the formula, l represents the basic cell length; m is the circumferential arrangement number, that is, the number of basic cells of the three-periodic minimal surface in the circumferential direction;

[0119] (3) A customized model based on radial filling technology can be constructed by performing Boolean operations on the radially transformed annular TPMS structure and the target geometry.

[0120] Embodiment 2

[0121] The present embodiment describes an efficient design system for three-periodic minimal surface structures for multiple application scenarios, which uses a conformal filling module based on isoparametric element method mapping. The specific implementation process is shown in the present embodiment:

[0122] like Figure 6 As shown, this embodiment provides a connecting rod model for a vehicle engine. The engine connecting rod is used to connect the piston and the crankshaft, and transmit the force acting on the piston to the crankshaft, converting the reciprocating motion of the piston into the rotational motion of the crankshaft. Affected by multiple factors such as the global energy crisis and persistent climate change, governments and enterprises in various countries have put forward more stringent requirements for automotive fuel engines, and the demand for reducing fuel consumption is also increasing. Engine parts designed with lightweight technology can not only meet the use requirements, but also significantly reduce the weight, which is of great significance to reducing the vibration of the whole machine and improving the fuel consumption of the engine.

[0123] The maximum size of the connecting rod model is 50*20*132mm, and the conformal filling core selects the Sheet-Schware-P structure with a C value of 0.25. The entire customized model is manufactured using 3D printing technology (light-cured LCD) and is integrally formed. The material is photosensitive resin to verify the printability of the customized model designed by the conformal filling module of the present invention. Specifically, the following steps are included:

[0124] S1. From the working process of the engine, it can be seen that the connecting rod is always subjected to alternating loads such as compression and tension. Conformal filling can ensure that the filling core of the customized model is composed of complete cells. Therefore, the mechanical properties and service life of the component will be better (compared with the direct filling module based on the signed distance field), so the direct filling module based on the signed distance field is selected.

[0125] S2. Use CAD software, such as FreeCAD, to cut the connecting rod model into several sub-models with simpler shapes. Import all sub-models into a meshing tool, such as Hypermesh. Select a suitable mesh size according to the design requirements. This size determines the size of the cells involved in the filling. The mesh size of this embodiment is 4mm. Then perform hexahedral meshing and export the mesh in inp format. It is worth noting that the mesh on the interface of the sub-model must remain continuous.

[0126] S3. Import the inp file into Matlab and read the hexahedral unit and node information.

[0127] S4. According to the design requirements, a TPMS structure is created in a unit cube. In this embodiment, a Sheet-Schware-P structure with a C value of 0.25 is selected. The basic cell of the TPMS is constructed using a marching cube algorithm, and the vertices and connection lists of the triangular faces constituting the cell are extracted.

[0128] S5. The regular basic cell is mapped into each hexahedral unit by shape function isoparametric transformation, and finally Boolean operation is performed on the mapped complex core and connecting rod model to obtain a customized model based on conformal filling technology.

[0129] In this embodiment, the specific method of step S4, using shape function isoparametric transformation to map the regular cell to each hexahedral unit is:

[0130] S51. The shape function is used to transform the regular cell in the natural coordinate system into the irregular cell in the Cartesian coordinate system. The shape function equation is as follows:

[0131]

[0132]

[0133] Where (x, y, z) is the coordinate point inside the hexahedral unit in the Cartesian coordinate system, that is, the Cartesian coordinates of the vertices of each triangular face of the cell after the isoparametric transformation; (x i ,y i ,z i ) are the coordinate values ​​of the eight vertices of the hexahedral unit in the Cartesian coordinate system; N i is the node shape function; is the coordinate point inside the regular cube unit in the natural coordinate system, that is, the natural coordinate of the vertex of each triangular face of the cell before the isoparametric transformation; are the coordinate points of the eight vertices of the regular cube unit in the natural coordinate system; Figure 7 Schematic diagram of the shape function transformation process.

[0134] S52. Import the mapped complex core into CAD software and perform Boolean operations with the connecting rod model. Then perform geometric repair on the model that has completed the Boolean operation to generate a one-sided file of the customized connecting rod model, such as Figure 8 shown.

[0135] In the specific implementation process, the customized model was printed and verified using light-curing 3D printing technology. Fig. 9 The results show that the customized model based on TPMS structure filling designed with the conformable filling module of the present invention has good printability.

[0136] This embodiment uses the conformal filling module based on isoparametric element method mapping proposed in the present invention to realize a customized connecting rod model based on the TPMS filling core, and the filling core of the customized connecting rod model has a complete cellular structure.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. An efficient design system for three-periodic minimal surface structures for multiple application scenarios, characterized by: It includes two filling modules, namely a direct filling module based on signed distance field and a conformal filling module based on isoparametric element method mapping; The direct filling module based on the signed distance field is used for the creation of discretized grid / target model distance field, the creation of three-periodic minimal surface distance field and distance field Boolean operation; The conformal filling module based on isoparametric element method mapping is used for the creation of hexahedral meshing of the target model, the creation of basic cells of three-periodic minimal surfaces and isoparametric element method mapping; Determine the design requirements according to different application scenarios, and select the direct filling module based on the signed distance field or the conformal filling module based on the isoparametric element method mapping that is suitable for the task; The function operation of the direct filling module based on the signed distance field includes the following steps: S1a, import the triangle patch file of the target model, extract the vertex coordinate matrix [x, y, z] of all triangle patches, and create a bounding box based on the coordinate information to completely cover the target model. The internal space of the bounding box is the maximum filling domain. The maximum filling domain of the bounding box is evenly discretized, and the truncation distance is introduced to quickly calculate the discrete grid points. The signed distance field φ to the target model GEO ; S2a, select the design module, cell type and geometric parameters according to the design requirements, and construct the implicit equation φ of the TPMS structure in the maximum filling domain TPMS ; S3a, perform distance field Boolean operations on the TPMS structure and target model, and then obtain a TPMS customized model φ that meets the design requirements OBJ ,Then, the marching cubes algorithm is used to generate the one-sided file of the customized model; In step S1a, the cutoff distance is introduced to quickly calculate the signed distance field φ from the discrete grid point to the target model. GEO The specific method is: (1) Uniformly discretize the maximum filling domain to obtain the coordinates of three-dimensional discrete grid points Calculate the number and distance d of the discrete grid point closest to each vertex of the triangle patch, including the maximum distance d max ; and extract the content The coordinates of the adjacent discrete grid points That is, the discretized grid points in a small range near the target model, the cutoff distance therefore, It is further subdivided into the internal point coordinates of the target model Coordinates of external points of the target model and the coordinates of the adjacent discrete grid points Right now (2) Initialization Signed distance field to target model Will Initially set to be greater than the maximum distance d max For any value of Signed distance field to target model and will Update to the corresponding coordinates get (3) Setting temporary variables Obviously, Then will Convert to logical matrix therefore, and Also equal to 0; calling the infill function will Set to 1, so the coordinates of the remaining logical 0 are (4) Set to -d max , the signed distance field φ of the target model can be reconstructed quickly and efficiently GEO .

2. According to claim 1, an efficient design system for three-periodic minimal surface structures for multiple application scenarios is characterized in that: In step S2a, a design module is selected according to the design requirements, and the design modules include simple filling, complex filling and radial filling; The simple filling refers to a filling method in which the cell type and geometric parameters of the TPMS remain unchanged within the maximum filling domain. Taking the Schware-P surface as an example, it is described by the following formula: Where l represents the basic cell length, which is a constant in simple filling; x, y, z are the coordinate component values ​​of the discrete grid points; C1 and C2 are used to control the wall thickness, porosity and topological structure of the TPMS structure, which are constant in simple filling; Sheet and Sketchetal refer to sheet-like and skeleton-like TPMS structures, respectively; The radial filling refers to a circular TPMS structure distributed along the radial gradient. The concept of coordinate transformation is used to transform the regular TPMS structure in the Cartesian coordinate system into a radial structure in the polar coordinate system. The specific steps are as follows: (1) Determine the inner and outer diameters, filling height, rotation axis, rotation angle, and circumferential arrangement number of radial filling according to design requirements; then construct a suitable three-periodic minimal surface structure in the corresponding rectangular filling domain before transformation; (2) Extract the vertex coordinates [x, y, z] and connection order of the triangular facets of the regular TPMS structure, and transform the vertex coordinates into real polar coordinates to obtain the radially transformed three-periodic minimal surface structure. Take the rotation around the z-axis as an example: In the formula, l represents the basic cell length; m is the circumferential arrangement number, that is, the number of basic cells of the three-periodic minimal surface in the circumferential direction; (3) A customized model based on radial filling technology can be constructed by performing Boolean operations on the radially transformed annular TPMS structure and the target geometry.

3. The efficient design system for three-periodic minimal surface structures for multiple application scenarios according to claim 2 is characterized in that: The complex filling refers to a filling method that performs personalized design within a specified sub-filling domain of the target model, can fill TPMS structures of any type and geometric parameters, and realizes smooth connection of adjacent sub-filling structures. The specific steps are as follows: Step (1), importing the target model into CAD software, and cutting and dividing the target model into blocks according to the filling requirements, thereby obtaining a series of sub-models, the internal space of these sub-models is the sub-filling domain, converting these sub-models into triangular facets, and adjusting the facet quality to avoid excessive aspect ratio, and then exporting all sub-models and their original models in STL format; Step (2), import the STL files of the target model and the sub-model into Matlab in order of volume size from small to large, and store them in the form of cell arrays; create a bounding box to completely cover the target model, and the internal space of the bounding box is the maximum filling domain; Step (3), the internal point coordinates of the sub-model The set relationship between them determines the geometric relationship between the sub-models, thereby determining the point set of each sub-filling domain Step (4), through all the points in the sub-filling domain The TPMS structures that meet the design requirements are allocated to the sub-filling domains. To ensure a smooth transition between adjacent sub-filling structures and keep the overall operation simple, weighting coefficients are introduced to define the complex filling core φ TPMS , described by the formula as follows: In the formula, is the signed distance field of the TPMS structure of the ith sub-filling domain; yes Variables for customizing the wall thickness, porosity, and topology of TPMS structures; is the weight coefficient of the ith sub-filling structure, defined by the radial basis function: In the formula, γ i is the transition gradient coefficient, which is used to adjust the smoothness between adjacent sub-filling structures; refers to the coordinates of the jth point in the ith sub-filling domain; m refers to the number of discrete grid points in the ith sub-filling domain.

4. The efficient design system for three-periodic minimal surface structures for multiple application scenarios according to claim 1 is characterized in that: In step S2a, the cell types include Gyroid surface, Diamond surface, I-WP surface, Schware-P surface, common TPMS or custom implicit surface; the controllable geometric parameters include cell size and C value, and C value refers to the wall thickness, porosity and topology used to control the TPMS structure.

5. The efficient design system for three-periodic minimal surface structures for multiple application scenarios according to claim 1 is characterized in that: In step S3a, distance field Boolean operation is performed on the TPMS and the target model, and the calculation formula is:

6. The efficient design system for three-periodic minimal surface structures for multiple application scenarios according to claim 1 is characterized in that: The specific functional operation of the conformal filling module based on isoparametric element method mapping includes the following steps: S1b, cutting the target model into sub-models of multiple shapes, performing hexahedral meshing on the sub-models after the block processing, and then extracting the mesh unit and node information; S2b, select the cell type and geometric parameters according to the design requirements, construct the basic cell of TPMS in the unit cube, and extract the vertices and connection list of the triangular facets constituting the cell; S3b, using shape function isoparametric transformation to map the regular cell into each hexahedral unit; finally, performing Boolean operations on the mapped conformal core and the target model, a customized model based on conformal filling technology can be obtained.

7. The efficient design system for three-periodic minimal surface structures for multiple application scenarios according to claim 6 is characterized in that: The specific method of dividing the target model into hexahedral grids in step S1b is: (1) Determine whether the geometric features of the target model are relatively simple. If the conditions are met, proceed to the subsequent steps; otherwise, the target model needs to be cut into several sub-models with simpler shapes through CAD software, and then the subsequent meshing process is performed; (2) Import all sub-models into the meshing tool; select the appropriate mesh size according to the design requirements, which determines the size of the cells involved in the filling; then perform hexahedral meshing and export the mesh in inp format. If the target model consists of a series of sub-models, the mesh on the interface of the sub-models must remain continuous; (3) Import the inp file into Matlab and read the hexahedral unit and node information.

8. The efficient design system for three-periodic minimal surface structures for multiple application scenarios according to claim 6 is characterized in that: In step S3b, shape function isoparametric transformation is used to map the regular cell to each hexahedral unit, and the specific method is as follows: (1) According to the design requirements, create the basic cell of TPMS in the unit cube, construct it using the marching cube algorithm, and extract the vertices and connection list of the triangle face of the cell; (2) The shape function is used to transform the regular-shaped cell in the natural coordinate system into the irregular-shaped cell in the Cartesian coordinate system. The shape function equation is as follows: Where (x, y, z) is the coordinate point inside the hexahedral unit in the Cartesian coordinate system, that is, the Cartesian coordinates of the vertices of each triangular face of the cell after the isoparametric transformation; (x i ,y i ,z i ) are the coordinate values ​​of the eight vertices of the hexahedral unit in the Cartesian coordinate system; N i is the node shape function; is the coordinate point inside the regular cube unit in the natural coordinate system, that is, the natural coordinate of the vertex of each triangular face of the cell before the isoparametric transformation; are the coordinate points of the eight vertices of the regular cube unit in the natural coordinate system; (3) The mapped complex core is imported into CAD software, and Boolean operations are performed on the target model. Then, geometric repair is performed on the model that has completed the Boolean operation, thereby realizing a customized model based on conformal filling technology.

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