Volume fraction comprehensive evaluation model for Zener ratio of mixed TPMS structure

Abstract

The invention provides a volume fraction comprehensive evaluation model for the Zener ratio of a mixed TPMS structure, and belongs to the technical field of dot matrix structure design. The method comprises the following steps: firstly, designing various TPMS basic structures by utilizing implicit function modeling; then, carrying out anisotropy research on the TPMS configuration by utilizing finite element simulation; secondly, based on a simulation result of axial elastic modulus complementation, software nTopology is utilized to carry out Boolean combination on an elastic modulus complementation structure; and then, finite element simulation is utilized to carry out anisotropy research on the Boolean bonding structure. And finally, proposing an isotropy and lightweight comprehensive evaluation model according to a Boolean bonding structure simulation result, and realizing the comprehensive evaluation of the isotropy and lightweight capability of the TPMS Boolean bonding structure. And a supplement is provided for research of Ti2AlNb in the field of lattice structures. A means for rapidly screening an excellent structure is provided for the mixed TPMS structure, and a theoretical foundation is laid for manufacturability and effectiveness of the mixed TPMS structure.

Description

Technical Field

[0001] The invention belongs to the technical field of lattice structure design, and in particular relates to a volume fraction comprehensive evaluation model of a Zener ratio of a hybrid TPMS structure. Background Art

[0002] "Making the best use of everything" is the simplest idea of ​​lightweight design and the eternal pursuit of the development of aerospace vehicles. With the rapid development of aerospace vehicles, the importance of lightweight aircraft has become increasingly prominent. Its lightweight is mainly achieved through lightweight structure and lightweight materials.

[0003] Material lightweighting mainly involves replacing dense steel materials with lightweight materials with higher specific strength (such as titanium alloys, aluminum alloys, engineering plastics, etc.). High-performance titanium alloys have excellent performance at 600°C and below, and their density is about 3 / 5 of that of engineering steel and 1 / 2 of that of Ni-based alloys, which has a specific strength advantage. However, above 600°C, due to the proliferation of the non-protective oxide layer (rutile TiO2), interstitial atoms diffuse rapidly in the oxide layer, causing embrittlement in the subsurface area, which seriously limits the engineering application of titanium alloys in high temperature environments. The oxidation behavior of titanium-based alloys can be improved by optimizing the composition, such as adding a large amount of Al elements to form intermetallic compounds Ti3Al and TiAl, but their low toughness and plasticity have become a bottleneck restricting their development. Compared with traditional Ti3Al-based alloys, Ti2AlNb alloy exhibits better high-temperature performance and room-temperature plasticity, breaking through the "thermal barrier" problem of titanium alloy applications at 600°C, allowing it to be used for a long time in the temperature range of 650-750°C. It is particularly suitable for manufacturing hot end parts of aerospace engines, such as engine blades, turbine disks, etc.

[0004] Structural lightweighting uses topological calculation methods to obtain lightweight structures with higher structural efficiency. In the topological calculation of part structures, the final structure is usually determined by a density threshold. A higher density threshold can significantly reduce part materials, but removing too much material will inevitably reduce part performance; on the contrary, setting a lower material threshold will lead to insufficient weight reduction, and the service stress of some materials will remain at a low level. With the development of additive manufacturing technology, new process technology approaches have been provided for the design and manufacture of high-performance aerospace components. Among them, laser additive manufacturing technology has the process characteristics of free lamination manufacturing, which can realize the direct forming of high-melting-point difficult-to-process metals, alloys and metal-based composite materials, giving complex lightweight structures extremely high design and forming freedom, and can form lightweight complex lattice structures that are difficult to form with traditional processing methods. By replacing the solid structure with a lower stress level in the topological structure with a relatively low density porous structure, the weight of the part can be further reduced while ensuring the performance of the component. Common porous structures include lattice structures, honeycomb structures, and minimal surfaces. Among them, the triply periodic minimal surfaces, also known as TPMS (Triply Periodic Minimal Surfaces) structures, have attracted more and more attention from scholars and universities in recent years. Due to their unique geometric characteristics, they can significantly reduce weight while maintaining structural strength, making them an ideal structural choice in the aerospace field. Zhang et al. designed a lightweight airborne reflector. By establishing the elastic and thermal conductivity performance model of the TPMS structure, they accurately described the performance of the TPMS structure and matched it with the actual manufactured structural performance (CQ Zeng, W. Wang, K. Hai, et. al. Lightweight airborne TPMS-filled reflective mirror design for low thermal deformation [J]. Composite Structures, 2024, 327: 117665.). Therefore, it is urgent to focus on the dual weight reduction of materials and structures of hot end components of aerospace engines and to study the TPMS structure with Ti2AlNb as the target material.

[0005] However, TPMS structures usually exhibit anisotropic mechanical properties, making it difficult to capture the damage evolution law of the structure during service, and traditional metal aircraft design methods cannot effectively predict and evaluate it. In recent years, researchers have mixed TPMS structures in different ways to solve the anisotropy problem of TPMS. Zhang et al. proposed an isotropic design strategy for TPMS structure based on an accurate elastic modulus compensation mechanism through homogenization simulation and finite element analysis, combining the two structures by Boolean combination, significantly reducing the anisotropy of the original structure (J. Zhang, S. Xie, KK Jing, et. al. Study on isotropic design of triply periodic minimal surface structures under an elastic modulus compensation mechanism [J]. Composite Structures, 2024, 342: 118266.). At the same time, Yan et al. realized the multi-dimensional mixing of TPMS by means of functions, making full use of the complementary effects between different structural components to adjust the mechanical properties of the structure, and solving the problem that the performance of the three-periodic minimal surface lattice structure with a single configuration in the prior art is limited by anisotropic mechanical behavior (Yan Shilin, Zhang Xiaonan, Xie Xiangyu et al. Structural multi-dimensional mixing method, device and medium based on three-periodic minimal surfaces [P]. Publication No. CN 117116395A).

[0006] Although the range, curvature and period of TPMS can be easily controlled due to its implicit characteristics. But its implicit equations are too numerous to enumerate, and the ways to obtain isotropic structures through hybrid TPMS structures are becoming increasingly abundant. Therefore, how to screen hybrid TPMS structures is a problem that needs to be solved urgently. At the same time, there is a lack of relevant research on Ti2AlNb lattice structures. In summary, it is necessary to propose an isotropic and lightweight comprehensive evaluation model for hybrid TPMS structures. The present invention takes Ti2AlNb as the target material for finite element simulation, and takes the hybrid method of Boolean combination as an example. Two Boolean combination structures with Ti2AlNb as the target material are designed, and the anisotropy index (Zener ratio, A value) and volume fraction (Relative density, RD value) of the Boolean combination structure are evaluated at the same time. On the one hand, the isotropy of the structure is guaranteed, and on the other hand, the structure meets the lightweight requirements. Summary of the invention

[0007] The technical problem solved by the present invention is: Aiming at the comprehensive consideration of volume fraction and isotropy after Boolean combination of TPMS structure, a volume fraction comprehensive evaluation model of Zener ratio of hybrid TPMS structure is proposed. Firstly, a variety of TPMS basic structures are designed by implicit function modeling; then, the anisotropy of TPMS configuration is studied by finite element simulation; secondly, based on the simulation results of axial elastic modulus complementation, the elastic modulus complementary structure is Boolean combined by software nTopology; then, the anisotropy of Boolean combination structure is studied by finite element simulation. Finally, according to the simulation results of Boolean combination structure, an isotropy and lightweight comprehensive evaluation model is proposed, which realizes the comprehensive evaluation of isotropy and lightweight capacity of TPMS Boolean combination structure. It supplements the research of Ti2AlNb in the field of lattice structure. It provides a means for rapid screening of excellent structures for hybrid TPMS structure, and lays a theoretical foundation for the manufacturability and effectiveness of hybrid TPMS structure.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A volume fraction comprehensive evaluation model of the Zener ratio of a hybrid TPMS structure is established. The establishment of the volume fraction comprehensive evaluation model of the Zener ratio of a hybrid TPMS structure is specifically divided into three parts:

[0010] (I) TPMS anisotropy research, the specific process is:

[0011] Step 1: Implicit function modeling of TPMS configuration: Use implicit function modeling to design various TPMS basic structures;

[0012] Select typical TPMS surfaces, including Lindinoid, F-RD and Dprime, and use nTopology software to perform implicit function modeling to obtain an implicit body model of a lattice structure.

[0013] Step 2: Homogenization simulation of TPMS configuration: Use finite element simulation to study the anisotropy of TPMS configuration;

[0014] Based on the implicit body model of the TPMS structure designed in step 1, the lattice structure is meshed with the help of nTopology software; homogenization method and finite element simulation are used to apply periodic boundary conditions on unit cells with different TPMS structures and different volume fraction RD values, so as to obtain the elastic properties of the lattice structure;

[0015] (II) Design of isotropic TPMS Boolean combination structure; the specific process is as follows:

[0016] Step 3: Establish TPMS Boolean combination structure model:

[0017] Based on the elastic properties of the lattice structure obtained in step 2, a structure with complementary modulus in the axial direction is selected, and the selected TPMS structure is Boolean combined using the nTopology software to obtain an implicit body model of the Boolean combined structure;

[0018] Step 4: Homogenization simulation of TPMS Boolean bonding structure: Use finite element simulation to study the anisotropy of the Boolean bonding structure;

[0019] Based on the implicit body model of the Boolean combination structure established in step 3, the lattice structure is meshed using nTopology software; homogenization method and finite element simulation are used to apply periodic boundary conditions on the unit cells of different Boolean combination structures, so as to obtain the elastic properties of the Boolean combination structure;

[0020] Step 5: Establish an isotropic TPMS Boolean binding structure;

[0021] Based on the elastic properties of the Boolean combination structure obtained in step 4, the RD value is changed by changing the structure C value, thereby changing the A value and RD value of the Boolean combination structure; by implementing the above process, a Boolean combination structure with an A value close to 1 is obtained; wherein the C value is a threshold constant of the three-periodic minimal surface;

[0022] (III) Establishing a comprehensive evaluation model of the Zener ratio and volume fraction of the Boolean combination structure: Based on the simulation results of the Boolean combination structure, an isotropy and lightweight comprehensive evaluation model is proposed to achieve a comprehensive evaluation of the isotropy and lightweight capabilities of the TPMS Boolean combination structure; the specific process is as follows:

[0023] Step 6: Establish a mathematical model of A value and RD value

[0024] Based on the implementation process of step 5, the Origin software is used to draw the thermal label graphs of the RD values ​​of the two basic surfaces with respect to the A value and RD value of the Boolean combination structure, and the thermal label graphs are abstracted into a 5×5 square matrix;

[0025] Step 7: Establish an isotropic and lightweight comprehensive evaluation model

[0026] Based on the matrix in step 6, an isotropic and lightweight comprehensive evaluation model is proposed, which describes the ability of Boolean combination structure to obtain isotropic and lightweight structure.

[0027] Further limitation of the above scheme: In the above step 1, the implicit expression of the three-periodic minimal surface TPMS is:

[0028]

[0029] Among them, X = 2πx / l, Y = 2πy / l, Z = 2πz / l, 2X = 4πx / l, 2Y = 4πy / l, 2Z = 4πz / l, l is the unit length in the x, y, and z directions; Specific parameter information of the TPMS lattice structure in the above implicit body model: the unit cell size is 1×1×1mm 3 , the number of unit cells in the x, y and z directions is 1×1×1.

[0030] Further limitation of the above scheme: in the above step 2, the A value of the Lindinoid surface is greater than 1 on the above RD value scale; the A value of the Dprime surface is less than 1 on the above RD value scale; the A value of the F-RD surface is less than 1 on the above RD value scale;

[0031] The mesh division shape is a tetrahedron with a size of 0.03 mm; the RD value scales are 7.5, 15, 22.5, 30, and 37.5.

[0032] Further limitation of the above scheme: In the above step 3, the Lindinoid-F-RD and Lindinoid-Dprime Boolean binding structures were constructed.

[0033] Further limitation of the above scheme: in the above step 4, the obtained Boolean combination structure can achieve the complementarity of elastic modulus in the axial direction.

[0034] Further limitation of the above scheme: In the above step 5, under the parameters of Lindinoid surface RD value of 30 and F-RD surface RD value of 7.5, a Lindinoid-F-RD Boolean combination structure with an A value of 0.9892 was constructed; under the parameters of Lindinoid surface RD value of 30 and Dprime surface RD value of 7.5, a Lindinoid-Dprime Boolean combination structure with an A value of 1.0258 was constructed.

[0035] Further limitation of the above scheme: In the above step 6, within the range of the substructure RD value scale of 7.5, 15, 22.5, 30, and 37.5, a heat-labeled graph of the substructure RD value with respect to the Boolean combination structure RD value and the A value corresponding to the mixing is made, and a matrix is ​​introduced to describe the relationship between the substructure RD value and the A value and RD value of the Boolean combination structure; the mathematical expression of the above matrix is:

[0036]

[0037] Among them, a 5×5 square matrix is ​​denoted as M, and the other 5×5 square matrix is ​​denoted as N. In order to facilitate the generalization of the model, elementary row transformations are performed on the matrices M and N so that the row order of the matrices M and N is reversed, and they are recorded as matrices P and Q. Each element in the matrices M and N corresponds to each element in the hot-labeled graph of the Boolean combination structure RD value and A value obtained by mixing the substructures.

[0038] Further limitation of the above scheme: In the above step 7, based on the matrix of step 6, the mathematical expression of the isotropic and lightweight comprehensive evaluation model is:

[0039]

[0040] Among them, m ij is each element in the square matrix M, n ij For each element in the square matrix N, p ij For each element in the square matrix P, q ij are the elements in the square matrix Q; for the Describes the ability to achieve lightweight structures, It describes whether the ability to obtain an isotropic structure can be achieved. Its comprehensive ability is represented by the symbol Z, which describes the isotropic and lightweight ability of the Boolean combination structure within its entire RD value range. The larger the Z value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure. For formula (9) Describes the ability to achieve lightweight structures, " describes the ability to obtain an isotropic structure, and its comprehensive ability is represented by the symbol Z'. The same is that the larger the Z' value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure. The difference is that it describes the isotropic and lightweight ability of the Boolean combination structure at the RD value required by the researchers.

[0041] The present invention is different from the prior art in that:

[0042] 1. The present invention controls the change of the three-dimensional structure shape based on implicit surface equations, carries out isotropic design of Boolean combination structure, takes Ti2AlNb as the target material, explores the elastic performance of Boolean combination structure through finite element simulation, and proposes a comprehensive evaluation model for the lightweight and isotropic Boolean combination structure of TPMS based on the analysis of A value and RD of Boolean combination structure. It provides a means for rapid screening of substructures for hybrid TPMS and multi-cell TPMS structures, including but not limited to KM function, sigmoid function, directional mixing, Boolean combination and other hybrid and transitional TPMS structure methods, laying a theoretical foundation for the effectiveness of hybrid and transitional TPMS structures; BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1is a flow chart of the design strategy of the present invention;

[0044] Figure 2 It is a Lindinoid surface configuration diagram with an RD value of 0.30 according to the present invention;

[0045] Figure 3 It is the F-RD surface configuration diagram of the present invention with an RD value of 0.075;

[0046] Figure 4 It is the Dprime surface configuration diagram with an RD value of 0.075 of the present invention;

[0047] Figure 5 The three-dimensional elastic modulus diagram of Lindinoid with an RD value of 0.30 according to the present invention;

[0048] Figure 6 It is the F-RD three-dimensional elastic modulus diagram of the present invention with an RD value of 0.075;

[0049] Figure 7 It is the Dprime three-dimensional elastic modulus diagram of the present invention with an RD value of 0.075;

[0050] Figure 8 is a Lindinoid-F-RD Boolean binding strategy diagram with an A value close to 1 of the present invention;

[0051] Fig. 9 is a Lindinoid-Dprime Boolean binding strategy diagram with an A value close to 1 of the present invention;

[0052] Fig.10 is a labeled heat map of the Lindinoid-F-RD Boolean binding structure of the present invention with respect to A value;

[0053] Fig.11 is a labeled heat map of the Lindinoid-Dprime Boolean binding structure of the present invention with respect to A values;

[0054] Fig.12 is a labeled heat map of the Lindinoid-F-RD Boolean binding structure of the present invention with respect to RD values;

[0055] Fig.13 It is a labeled heat map of the Lindinoid-Dprime Boolean binding structure of the present invention with respect to RD values. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] The present invention discloses a volume fraction comprehensive evaluation model of the Zener ratio of a hybrid TPMS structure. The model uses Ti2AlNb alloy as the target material, and obtains the elastic properties of Lindinoid, F-RD and Dprime surfaces through homogenization and finite element simulation. Then, according to the principle of axial complementarity of elastic properties and the method of changing the volume fraction (Relative density, RD value) of the surface by changing the C value of the surface, a Lindinoid-F-RD and Lindinoid-Dprime Boolean combination structure with a Zener ratio (A value) close to 1 is constructed. Finally, through mathematical induction, the connection between the A value of the Boolean combination structure and the RD value of the substructure is established, and a model is obtained to evaluate the ability of two subsurfaces with complementary moduli to obtain an isotropic and lightweight hybrid structure. For details, please refer to Figure 1-13 , describe the embodiments of the present invention in detail.

[0058] Embodiment 1

[0059] In view of the comprehensive consideration of volume fraction and isotropy after Boolean combination of TPMS structure, the present invention proposes a comprehensive evaluation model for isotropy and lightness of hybrid TPMS structure. First, a variety of TPMS basic structures are designed by implicit function modeling; then, the anisotropy of TPMS configuration is studied by finite element simulation; secondly, based on the simulation results of axial elastic modulus complementarity, the elastic modulus complementary structure is Boolean combined by software nTopology; then, the anisotropy of the Boolean combined structure is studied by finite element simulation. Finally, based on the simulation results of Boolean combined structure, an isotropy and lightness comprehensive evaluation model is proposed, which realizes the comprehensive evaluation of isotropy and lightness of TPMS Boolean combined structure. A comprehensive evaluation of isotropy and lightness of TPMS Boolean combined structure is realized. A means for rapid screening of substructures is provided for hybrid TPMS and polyhedral TPMS structures, including but not limited to KM function, sigmoid function, directional mixing, Boolean combination and other hybrid TPMS structure methods, laying a theoretical foundation for the manufacturability and effectiveness of hybrid TPMS structure;

[0060] The present invention involves the establishment of a hybrid TPMS structure Zener ratio and volume fraction comprehensive evaluation model, which is specifically divided into three parts:

[0061] (I) TPMS anisotropy research. The specific process is:

[0062] Step 1: Implicit function modeling of TPMS configuration.

[0063] Select the lattice structure of TPMS (for example, Lindinoid, F-RD and Dprime), use nTopology commercial software to perform implicit function modeling, and generate an implicit body model of the required size through the Boolean Intersect module. Figure 2 , 3, 4. The selected lattice structure can be described by the following expression:

[0064]

[0065] Among them, X = 2πx / l, Y = 2πy / l, Z = 2πz / l, 2X = 4πx / l, 2Y = 4πy / l, 2Z = 4πz / l, l is the unit length in the x, y, z directions. Specific parameter information of the TPMS lattice structure in the above implicit body model: the unit cell size is 1×1×1mm 3 , the number of unit cells in the x, y and z directions is 1×1×1.

[0066] Step 2: Homogenization simulation of TPMS configuration.

[0067] Based on the implicit body model of the TPMS structure designed in step 1, the implicit body is meshed by the Mesh from Implicit Body module, the surface mesh is converted into a volume mesh by the Volume Mesh module, the volume mesh of the previous step is converted into a finite element volume mesh by the FE Volume Mesh, the finite element volume mesh is converted into a finite element model by the FE Model, and the finite element model is homogenized by the Homogenize Unit Cell module; the elastic properties of the selected structure are obtained by applying periodic boundary conditions on the unit cells of different TPMS lattice structures, such as Figure 5 , as shown in Figures 6 and 7.

[0068] The mesh is divided into tetrahedrons with a size of 0.03 mm. The performance parameters of Ti2AlNb used for finite element simulation are as follows: elastic modulus, yield strength and tensile strength are 104.2 GPa, 943.0 MPa and 992.6 MPa respectively, Poisson's ratio is 0.3, and density is 5.3 g / cm 3 .

[0069] (II) Design of isotropic TPMS Boolean combination structure. The specific process is as follows:

[0070] Step 3: Establish the TPMS Boolean combination structure model.

[0071] Based on the elastic properties of the lattice structure obtained in step 2, a structure with complementary modulus in the axial direction is selected, namely, the Lindinoid structure is complementary to the F-RD structure, and the Lindinoid structure is complementary to the Dprime structure. The selected structure is Boolean combined by the Boolean Union module in the commercial software nTopology to generate a new lattice structure, and the Lindinoid-F-RD Boolean combined structure implicit body and the Lindinoid-Dprime Boolean combined structure implicit body are obtained. In this embodiment, the selected Boolean combined structure is a Lindinoid-F-RD type.

[0072] Step 4: TPMS Boolean binding structure homogenization simulation.

[0073] Based on the Lindinoid-F-RD implicit body model designed in step 3, the implicit body is meshed through the Mesh from ImplicitBody module, the surface mesh is converted into a volume mesh through the Volume Mesh module, the volume mesh of the previous step is converted into a finite element volume mesh through the FE VolumeMesh, the finite element volume mesh is converted into a finite element model through the FE Model, and the finite element model is homogenized through the Homogenize Unit Cell module. By applying periodic boundary conditions on the unit cell of the Lindinoid-F-RD Boolean combination structure, its elastic properties, A value and RD value are obtained.

[0074] The mesh is divided into tetrahedrons with a size of 0.03 mm. The performance parameters of Ti2AlNb used for finite element simulation are as follows: elastic modulus, yield strength and tensile strength are 104.2 GPa, 943.0 MPa and 992.6 MPa respectively, Poisson's ratio is 0.3, and density is 5.3 g / cm 3 .

[0075] Step 5: Establish the isotropic TPMS Boolean binding structure.

[0076] By changing the C value of the Lindinoid, F-RD, Dprime structure, the RD value of the Lindinoid, F-RD, Dprime structure is changed, thereby changing the RD value of the structure to change the A value and RD value of the Lindinoid-F-RD type Boolean binding structure, the Lindinoid-Dprime type Boolean binding structure. In this embodiment, the selected Boolean binding structure is the Lindinoid-F-RD type. By implementing the above process, a Lindinoid-F-RD type Boolean binding structure with an A value close to 1 is obtained, such as Figure 8 shown.

[0077] The RD value scale of the present invention takes 7.5, 15, 22.5, 30, and 37.5 as examples.

[0078] Among them, the C value is the threshold constant of the three-periodic minimal surface, which is used to control the parameters of the periodic surface offset and to determine the position of the isosurface. In the mathematical expression of TPMS, the C value determines the isosurface of the trigonometric function, that is, each point on the surface has a constant C value. The surface with this property is also called an isosurface. By changing the C value, the shape of the isosurface can be changed, thereby affecting the pore morphology of the TPMS unit body.

[0079] (III) Establish a Boolean combined structural isotropy and lightweight comprehensive evaluation model. The specific process is:

[0080] Step 6: Establish a mathematical model of A value and RD value

[0081] Based on the implementation process of step 5, the commercial software Origin is used to draw the hot label graphs of the RD values ​​of the two basic surfaces with respect to the A value and RD value of the Boolean binding structure. The hot label graphs of the RD values ​​of the Lindinoid and F-RD structures with respect to the A value of the Lindinoid-F-RD type Boolean binding structure and the Lindinoid-Dprime type Boolean binding structure are shown in Fig.10 , as shown in 11; the RD values ​​of Lindinoid and F-RD structures are respectively related to the RD values ​​of Lindinoid-F-RD type Boolean binding structure and Lindinoid-Dprime type Boolean binding structure with hot labeling as shown in Fig.11 , as shown in 13. By observing each heat label graph, it is found that the A value and RD value increase with the increase of the substructure RD value, and the three have a clear linear relationship. Therefore, the present invention introduces a matrix to describe the relationship between the A value and the RD value of the Boolean combination structure. Fig.10 , 11 is abstracted into a 5×5 square matrix M, Fig.12 , 13 is abstracted as a 5×5 square matrix N. In order to facilitate the generalization of the model, the square matrices M and N are transformed by elementary rows, so that the order of the rows of the square matrices M and N is reversed, and they are counted as square matrices P and Q. The mathematical expression of the square matrices M, N, P, Q is:

[0082]

[0083]

[0084] Step 7: Establish an isotropic and lightweight comprehensive evaluation model

[0085] Based on the matrix M, N, P, Q in step 6, an isotropic and lightweight comprehensive evaluation model is proposed, which describes the ability of Boolean combination structure to obtain isotropic and lightweight structure. Its mathematical expression is:

[0086]

[0087] Among them, m ij is each element in the square matrix M, n ij For each element in the square matrix N, p ij For each element in the square matrix P, q ij are the elements in the square matrix Q; for formula (8) Describes the ability to achieve lightweight structures, It describes the ability to obtain an isotropic structure. Its comprehensive ability is represented by the symbol Z, which describes the isotropic and lightweight ability of the Boolean combination structure within its entire RD value range. The larger the Z value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure; for formula (9) Describes the ability to achieve lightweight structures, It describes the ability to obtain an isotropic structure. Its comprehensive ability is represented by the symbol Z'. The same is that the larger the Z' value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure. The difference is that it describes the isotropic and lightweight ability of the Boolean combination structure at the RD value required by the researchers.

[0088] Embodiment 2

[0089] In view of the comprehensive consideration of volume fraction and isotropy after Boolean combination of TPMS structure, the present invention proposes a comprehensive evaluation model for isotropy and lightness of hybrid TPMS structure. First, a variety of TPMS basic structures are designed by implicit function modeling; then, the anisotropy of TPMS configuration is studied by finite element simulation; secondly, based on the simulation results of axial elastic modulus complementarity, the elastic modulus complementary structure is Boolean combined by software nTopology; then, the anisotropy of the Boolean combined structure is studied by finite element simulation. Finally, based on the simulation results of Boolean combined structure, an isotropy and lightness comprehensive evaluation model is proposed, which realizes the comprehensive evaluation of isotropy and lightness of TPMS Boolean combined structure. A comprehensive evaluation of isotropy and lightness of TPMS Boolean combined structure is realized. A means for rapid screening of substructures is provided for hybrid TPMS and polyhedral TPMS structures, including but not limited to KM function, sigmoid function, directional mixing, Boolean combination and other hybrid TPMS structure methods, laying a theoretical foundation for the manufacturability and effectiveness of hybrid TPMS structure;

[0090] The present invention involves the establishment of a hybrid TPMS structure Zener ratio and volume fraction comprehensive evaluation model, which is specifically divided into three parts:

[0091] (I) TPMS anisotropy research. The specific process is:

[0092] Step 1: Implicit function modeling of TPMS configuration.

[0093] Select the lattice structure of TPMS (for example, Lindinoid, F-RD and Dprime), use nTopology commercial software to perform implicit function modeling, and generate an implicit body model of the required size through the Boolean Intersect module. Figure 2 , 3, 4. The selected lattice structure can be described by the following expression:

[0094]

[0095] Among them, X = 2πx / l, Y = 2πy / l, Z = 2πz / l, 2X = 4πx / l, 2Y = 4πy / l, 2Z = 4πz / l, l is the unit length in the x, y, z directions. Specific parameter information of the TPMS lattice structure in the above implicit body model: the unit cell size is 1×1×1mm 3 , the number of unit cells in the x, y and z directions is 1×1×1.

[0096] Step 2: Homogenization simulation of TPMS configuration.

[0097] Based on the implicit body model of the TPMS structure designed in step 1, the implicit body is meshed by the Mesh from Implicit Body module, the surface mesh is converted into a volume mesh by the Volume Mesh module, the volume mesh of the previous step is converted into a finite element volume mesh by the FE Volume Mesh, the finite element volume mesh is converted into a finite element model by the FE Model, and the finite element model is homogenized by the Homogenize Unit Cell module; the elastic properties of the selected structure are obtained by applying periodic boundary conditions on the unit cells of different TPMS lattice structures, such as Figure 5 , as shown in Figures 6 and 7.

[0098] The mesh is divided into tetrahedrons with a size of 0.03 mm. The performance parameters of Ti2AlNb used for finite element simulation are as follows: elastic modulus, yield strength and tensile strength are 104.2 GPa, 943.0 MPa and 992.6 MPa respectively, Poisson's ratio is 0.3, and density is 5.3 g / cm 3 .

[0099] (II) Design of isotropic TPMS Boolean combination structure. The specific process is as follows:

[0100] Step 3: Establish the TPMS Boolean combination structure model.

[0101] Based on the elastic properties of the lattice structure obtained in step 2, a structure with complementary modulus in the axial direction is selected, namely, the Lindinoid structure is complementary to the F-RD structure, and the Lindinoid structure is complementary to the Dprime structure. The selected structure is Boolean combined by the Boolean Union module in the commercial software nTopology to generate a new lattice structure, and the Lindinoid-F-RD Boolean combined structure implicit body and the Lindinoid-Dprime Boolean combined structure implicit body are obtained. In this embodiment, the selected Boolean combined structure is a Lindinoid-Dprime type.

[0102] Step 4: TPMS Boolean binding structure homogenization simulation.

[0103] Based on the Lindinoid-Dprime implicit body model designed in step 3, the implicit body is meshed through the Mesh from Implicit Body module, the surface mesh is converted into a volume mesh through the Volume Mesh module, the volume mesh of the previous step is converted into a finite element volume mesh through the FEVolume Mesh, the finite element volume mesh is converted into a finite element model through the FE Model, and the finite element model is homogenized through the Homogenize Unit Cell module. By applying periodic boundary conditions on the unit cell of the Lindinoid-Dprime Boolean combination structure, its elastic properties, A value and RD value are obtained.

[0104] The mesh is divided into tetrahedrons with a size of 0.03 mm. The performance parameters of Ti2AlNb used for finite element simulation are as follows: elastic modulus, yield strength and tensile strength are 104.2 GPa, 943.0 MPa and 992.6 MPa respectively, Poisson's ratio is 0.3, and density is 5.3 g / cm 3 .

[0105] Step 5: Establish the isotropic TPMS Boolean binding structure.

[0106] By changing the C value of the Lindinoid, F-RD, Dprime structure, the RD value of the Lindinoid, F-RD, Dprime structure is changed, thereby changing the RD value of the structure to change the A value and RD value of the Lindinoid-F-RD type Boolean binding structure, the Lindinoid-Dprime type Boolean binding structure. In this embodiment, the selected Boolean binding structure is the Lindinoid-Dprime type. By implementing the above process, a Lindinoid-Dprime type Boolean binding structure with an A value close to 1 is obtained, such as Fig. 9 shown.

[0107] The RD value scale of the present invention takes 7.5, 15, 22.5, 30, and 37.5 as examples.

[0108] Among them, the C value is the threshold constant of the three-periodic minimal surface, which is used to control the parameters of the periodic surface offset and to determine the position of the isosurface. In the mathematical expression of TPMS, the C value determines the isosurface of the trigonometric function, that is, each point on the surface has a constant C value. The surface with this property is also called an isosurface. By changing the C value, the shape of the isosurface can be changed, thereby affecting the pore morphology of the TPMS unit body.

[0109] (III) Establish a Boolean combined structural isotropy and lightweight comprehensive evaluation model. The specific process is:

[0110] Step 6: Establish a mathematical model of A value and RD value

[0111] Based on the implementation process of step 5, the commercial software Origin is used to draw the hot label graphs of the RD values ​​of the two basic surfaces with respect to the A value and RD value of the Boolean binding structure. The hot label graphs of the RD values ​​of the Lindinoid and F-RD structures with respect to the A value of the Lindinoid-F-RD type Boolean binding structure and the Lindinoid-Dprime type Boolean binding structure are shown in Fig.10 , as shown in 11; the RD values ​​of Lindinoid and F-RD structures are respectively related to the RD values ​​of Lindinoid-F-RD type Boolean binding structure and Lindinoid-Dprime type Boolean binding structure with hot labeling as shown in Fig.11 , as shown in 13. By observing each heat label graph, it is found that the A value and RD value increase with the increase of the substructure RD value, and the three have a clear linear relationship. Therefore, the present invention introduces a matrix to describe the relationship between the A value and the RD value of the Boolean combination structure. Fig.10 , 11 is abstracted into a 5×5 square matrix M, Fig.12 , 13 is abstracted as a 5×5 square matrix N. In order to facilitate the generalization of the model, the square matrices M and N are transformed by elementary rows, so that the order of the rows of the square matrices M and N is reversed, and they are counted as square matrices P and Q. The mathematical expression of the square matrices M, N, P, Q is:

[0112]

[0113] Step 7: Establish an isotropic and lightweight comprehensive evaluation model

[0114] Based on the matrix M, N, P, Q in step 6, an isotropic and lightweight comprehensive evaluation model is proposed, which describes the ability of Boolean combination structure to obtain isotropic and lightweight structure. Its mathematical expression is:

[0115]

[0116] Among them, m ij is each element in the square matrix M, n ij For each element in the square matrix N, p ij For each element in the square matrix P, q ij are the elements in the square matrix Q; for formula (8) Describes the ability to achieve lightweight structures, It describes the ability to obtain an isotropic structure. Its comprehensive ability is represented by the symbol Z, which describes the isotropic and lightweight ability of the Boolean combination structure within its entire RD value range. The larger the Z value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure; for formula (9) Describes the ability to achieve lightweight structures, It describes the ability to obtain an isotropic structure. Its comprehensive ability is represented by the symbol Z'. The same is that the larger the Z' value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure. The difference is that it describes the isotropic and lightweight ability of the Boolean combination structure at the RD value required by the researchers.

[0117] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0118] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A volume fraction comprehensive evaluation model of the Zener ratio of a hybrid TPMS structure, characterized by: The establishment of the volume fraction comprehensive evaluation model of the Zener ratio of the hybrid TPMS structure is specifically divided into three parts: (I) TPMS anisotropy research, the specific process is: Step 1: Implicit function modeling of TPMS configuration: Use implicit function modeling to design various TPMS basic structures; Select typical TPMS surfaces, including Lindinoid, F-RD and Dprime, and use nTopology software to perform implicit function modeling to obtain an implicit body model of a lattice structure. Step 2: Homogenization simulation of TPMS configuration: Use finite element simulation to study the anisotropy of TPMS configuration; Based on the implicit body model of the TPMS structure designed in step 1, the lattice structure is meshed with the help of nTopology software; homogenization method and finite element simulation are used to apply periodic boundary conditions on unit cells with different TPMS structures and different volume fraction RD values, so as to obtain the elastic properties of the lattice structure; (ii) Design of isotropic TPMS Boolean binding structure; The specific process is: Step 3: Establish TPMS Boolean combination structure model: Based on the elastic properties of the lattice structure obtained in step 2, a structure with complementary modulus in the axial direction is selected, and the selected TPMS structure is Boolean combined using the nTopology software to obtain an implicit body model of the Boolean combined structure; Step 4: Homogenization simulation of TPMS Boolean bonding structure: Use finite element simulation to study the anisotropy of the Boolean bonding structure; Based on the implicit body model of the Boolean combination structure established in step 3, the lattice structure is meshed using nTopology software; homogenization method and finite element simulation are used to apply periodic boundary conditions on the unit cells of different Boolean combination structures, so as to obtain the elastic properties of the Boolean combination structure; Step 5: Establish an isotropic TPMS Boolean binding structure; Based on the elastic properties of the Boolean bonding structure obtained in step 4, the RD value is changed by changing the structure C value, thereby changing the anisotropy index A value and the volume fraction RD value of the Boolean bonding structure; By implementing the above process, a Boolean associative structure with an A value close to 1 is obtained; wherein the C value is a threshold constant of a three-periodic minimal surface; (III) Establishing a comprehensive evaluation model of the Zener ratio and volume fraction of the Boolean combination structure: Based on the simulation results of the Boolean combination structure, an isotropy and lightweight comprehensive evaluation model is proposed to achieve a comprehensive evaluation of the isotropy and lightweight capabilities of the TPMS Boolean combination structure; the specific process is as follows: Step 6: Establish a mathematical model of anisotropy index A value and volume fraction RD value Based on the implementation process of step 5, the Origin software is used to draw the thermal label graphs of the RD values ​​of the two basic surfaces with respect to the A value and RD value of the Boolean combination structure, and the thermal label graphs are abstracted into a 5×5 square matrix; Step 7: Establish an isotropic and lightweight comprehensive evaluation model Based on the matrix in step 6, an isotropic and lightweight comprehensive evaluation model is proposed, which describes the ability of Boolean combination structure to obtain isotropic and lightweight structure.

2. The volume fraction comprehensive evaluation model of the Zener ratio of a hybrid TPMS structure according to claim 1, characterized in that: In the above step 6, within the range of substructure RD value scale of 7.5, 15, 22.5, 30, 37.5, a heat labelled graph of the substructure RD value with respect to the Boolean combination structure RD value and A value corresponding to the mixture is drawn, and a matrix is ​​introduced to describe the relationship between the substructure RD value and the A value and RD value of the Boolean combination structure. The mathematical expression of the square matrix is: Among them, a 5×5 square matrix is ​​denoted as M, and the other 5×5 square matrix is ​​denoted as N. In order to facilitate the generalization of the model, elementary row transformations are performed on the matrices M and N so that the row order of the matrices M and N is reversed, and they are recorded as matrices P and Q. Each element in the matrices M and N corresponds to each element in the hot-labeled graph of the Boolean combination structure RD value and A value obtained by mixing the substructures.

3. The volume fraction comprehensive evaluation model of the Zener ratio of a hybrid TPMS structure according to claim 1, characterized in that: In the above step 7, based on the matrix in step 6, the mathematical expression of the isotropic and lightweight comprehensive evaluation model is: Among them, m ij are the elements in the square matrix M, n ij For each element in the square matrix N, p ij For each element in the square matrix P, q ij are the elements in the square matrix Q; for the Describes the ability to achieve lightweight structures, It describes whether the ability to obtain an isotropic structure can be achieved. Its comprehensive ability is represented by the symbol Z, which describes the isotropic and lightweight ability of the Boolean combination structure within its entire RD value range. The larger the Z value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure. For formula (9) Describes the ability to achieve lightweight structures, It describes the ability to obtain an isotropic structure, and its comprehensive ability is represented by the symbol Z'. The same thing is that the larger the Z' value, the stronger the ability to obtain a lightweight, isotropic hybrid TPMS structure. The difference is that it describes the isotropic and lightweight ability of the Boolean combination structure at the RD value required by the researchers.

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