A lattice connector matching the coefficient of thermal expansion and a lattice filling method thereof

Abstract

This invention belongs to the field of additive design technology and proposes a lattice connector with a matching coefficient of thermal expansion and its lattice filling method. The connector matches the same coefficient of thermal expansion at the connection points with the preceding and following parts, and the intermediate part adopts a transition structure with an asymptotically changing coefficient of thermal expansion. Based on this, through parametric modeling of the transition structure while preserving the geometric relationship of the lattice unit cells, the lattice filling model of the connector is designed according to the conformal mesh information of the connector, realizing the automatic filling of unit cells within the complex geometric connector. This method solves the problem of excessive thermal stress on the connection surface of heterogeneous high-low temperature connection structures, largely ensuring the mechanical performance of the structure under temperature loads. Simultaneously, the automatic lattice filling technology of the lattice-filled connector ensures the integrity of the unit cells and the continuity of unit cells within the part, achieving conformal lattice filling of complex geometric parts.

Description

Technical Field

[0001] This invention relates to the field of additive design, and more particularly to a lattice connector with a matching coefficient of thermal expansion and a lattice filling method thereof. Background Technology

[0002] In aerospace and other fields, significant temperature differences exist between different parts of a structure, and the materials themselves undergo changes upon heating. Temperature gradients can lead to thermal stress within the structure, affecting its geometric stability and functionality. For high- and low-temperature heterogeneous connection structures, due to temperature variations or the use of different thermal expansion materials in different parts, the connectors need to have thermal expansion matching capabilities to reduce thermal stress. Therefore, designing a specific heterogeneous high- and low-temperature connection structure is essential. Invention patent CN202010788090.0 discloses a method for preparing ceramic material components with adjustable thermal expansion. This method achieves negative expansion, zero expansion, and large-value positive expansion designs by adjusting the ceramic component, and uses photopolymerization 3D printing to fabricate the ceramic structure. Invention patent CN200880012220.9 discloses a material with thermal expansion coefficient matching functionality. This method mixes other ceramic materials with lower thermal expansion coefficients with a ceramic substrate material with a high thermal expansion coefficient, resulting in a material whose thermal expansion coefficient matches that of the metallic material.

[0003] However, the current method for matching the coefficient of thermal expansion still has the following problems:

[0004] (1) Since the heterogeneous high and low temperature structure itself has a large temperature difference, it is necessary to design a connector with matching thermal expansion so that the mechanical properties of the two structural components can be guaranteed and the mutual influence caused by the temperature difference between the two components can be avoided. However, when the structural components adopt a hollow lattice material structure to reduce weight, there is no specific method to achieve matching of thermal expansion coefficients.

[0005] (2) Lack of lattice material filling methods for complex structural components. Due to the complexity of unit cell configurations, the dimensions of rods and the angles between rods are difficult to achieve in actual operation of commercial software. This makes it impossible to fully realize the complex configuration of lattice unit cell filling designs, thus reducing the efficiency of 3D lattice structure design and manufacturing. Moreover, transitional part structures are often irregular and cannot be constructed solely by periodic arrays of unit cells. Therefore, for complex geometric lattice-filled connectors, commercial software can only periodically arrange individual unit cells or cut off curved arrays, unable to flexibly change the configuration of each unit cell in the solid, thereby reducing the mechanical performance of the structure and failing to achieve the expected goals. Summary of the Invention

[0006] This invention addresses the problems encountered in practical engineering by providing a lattice connector with matched thermal expansion coefficients and its lattice filling method. The main reason for the high stress at the connection between two parts in high-temperature environments is the mismatch in their thermal expansion coefficients. Therefore, the connector at the connection point needs to match the thermal expansion coefficients of the two parts. Thus, the equivalent thermal expansion coefficient of the lattice material in the contact area with the transition part is designed to match the thermal expansion coefficient of the corresponding part, gradually transitioning from one side to the other. Furthermore, a zero-expansion lattice material can be used for the transition. By introducing a lattice-filled connector with matched thermal expansion coefficients, direct contact between two parts with significantly different thermal expansion coefficients is avoided. This invention is achieved in two ways: firstly, for complex geometric connection structures with heterogeneous components at high and low temperatures, the front and rear parts of the lattice connector are matched with the thermal expansion coefficients of the connected parts; secondly, for the structural design of the connector, a corresponding conformal lattice filling method is used to apply the lattice material structure to the complex parts. Ultimately, a macro-micro integrated design of a lattice-filled structure with matched thermal expansion coefficients is achieved.

[0007] The technical solution of the present invention:

[0008] A lattice connector with matching thermal expansion coefficient is used to connect two heterogeneous high and low temperature parts. It is divided into a front part, a rear part and a middle part. The front part and the rear part are connected to the parts respectively, and the unit cell structure ensures that the materials of the connected parts have the same equivalent thermal expansion coefficient. The middle part is a transition structure, which is filled with transition unit cells.

[0009] The transition unit cell in the transition structure is obtained by an optimization method. By optimizing the thermal expansion coefficient of the transition unit cell in the transition structure, the thermal expansion coefficient is used as the optimization target to achieve an asymptotic transition of the thermal expansion coefficient of the transition unit cell. Furthermore, by filling the transition unit cell in the transition structure, the transition structure becomes a thermal expansion structure in which the thermal expansion coefficient transitions from the distribution of the parts on one side to the distribution of the parts on the other side.

[0010] The basic unit of the transitional unit cell is formed by connecting the base surfaces of two bimaterial curved quadrangular pyramid structures. The bimaterial curved quadrangular pyramid structure is a structure with a designable coefficient of thermal expansion. The geometric relationship of the bimaterial curved quadrangular pyramid is shown in formula (1.1):

[0011]

[0012] Where L1, L2, and h are the dimensions of the lateral edge, base, and height of the curved pyramid, respectively, and β is the angle between the lateral edge of the pyramid and the center line; then, differentiating L1 and L2 respectively yields:

[0013]

[0014] Where dL1, dL2, dh, dβ, and dT are the differential forms of L1, L2, h, β, and temperature T, respectively; according to the definition of the coefficient of thermal expansion, the approximate coefficient of thermal expansion of the four rods at the base of the bimaterial curved pyramid is... The approximate coefficient of thermal expansion for the four lateral members of a square pyramid is... Therefore, an approximate relationship can be obtained between the equivalent thermal expansion coefficient of a single cell and the thermal expansion coefficients of the two materials: It can be seen that selecting two different materials or the magnitude of the design angle β can change the approximate equivalent thermal expansion coefficient α of the transition unit cell. h The size. By connecting the base surfaces of two bimaterial curved quadrangular pyramidal structures, a basic unit with a designable coefficient of thermal expansion is formed;

[0015] Eight basic units are connected in a front-to-back symmetrical and cross-symmetrical manner, with the vertices of the eight basic units connected at a single point to form a transition unit cell. Using the included angle β of the basic units within the transition unit cell as the design variable and the thermal expansion coefficient of the transition unit cell as the objective function, optimization is performed to obtain a transition unit cell with an asymptotic transition in thermal expansion coefficient, realizing the changes in positive, zero, and negative expansion coefficients of the transition unit cell. Finally, transition unit cells with different configurations are filled into the transition structure to form a lattice connector with a matching thermal expansion coefficient.

[0016] The specific configuration of the transition unit cell is derived from optimization design. One form is that the transition structure is entirely filled with zero-expansion unit cells. The zero-expansion unit cell achieves its thermal expansion coefficient of zero by adjusting the angle β in the basic unit within the unit cell.

[0017] A lattice filling method for lattice connectors matching thermal expansion coefficients is proposed. The overall structure of the transition structure is divided into eight-node solid units, which correspond to the eight vertices contained in the transition unit cell. A three-dimensional model of the transition unit cell is established according to different transition unit cell configurations and vertex positions. Finally, the automatic filling function of the three-dimensional software is used to fill the transition unit cells of different configurations into the corresponding positions of the transition structure to form a lattice filling model of the transition structure.

[0018] The front and rear portions of the lattice connectors with matching coefficients of thermal expansion are filled in the same way as the middle portion.

[0019] The specific steps of the lattice filling method for lattice connectors that match the coefficient of thermal expansion are as follows:

[0020] Step 1: Perform eight-node solid element meshing on the filled transition structure and obtain the corresponding mesh node location information, mesh node number information and mesh quantity information;

[0021] Step 2: Establish the body center and eight vertex positions of the transition unit cell; calculate the center point coordinates of the transition unit cell using the obtained mesh node position information; obtain the coordinates of the four points on the base of the bimaterial curve pyramid in the basic unit cell using the center point coordinates, vertex coordinates, and angle β of the basic unit cell, thus obtaining the various parameters for drawing the transition unit cell.

[0022] Step 3: Establish the transition unit cell model; based on the parameters of the obtained transition unit cell, connect the pre-established endpoints to form a line segment or curve. Establish a reference plane perpendicular to the connecting line at the endpoints of the line segment, and draw a circle with radius r centered on the endpoint of the line segment within the reference plane. Scan the circle along the line segment to establish the transition unit cell rod model. The cross-sectional area of ​​the rod changes according to the value of the control parameter r, and the cross-sectional shape is varied through the sketch shape. To achieve manufacturability of the unit cell, connect the rod vertices by establishing spherical corner points of the transition unit cell. Draw a semicircle centered on the endpoint of the line segment within the reference plane where the rod cross-section was previously established, with a radius slightly larger than the rod radius. Rotate the semicircle around its diameter using a rotation command to establish a spherical corner point. This completes the 3D model of each transition unit cell.

[0023] Step 4: Using a loop statement, repeat the process of step 3 so that each transition cell has different grid node position information and grid number information, thereby forming transition cells with different configurations, and save each transition cell to a specified location.

[0024] Step 5: Insert the previously established transition unit cells with different configurations into the corresponding positions of the transition structure. The transition structure is combined with the front and rear parts of the lattice connector with matching thermal expansion coefficients to obtain the lattice connector with matching thermal expansion coefficients.

[0025] The beneficial effects of this invention are:

[0026] 1) A lattice connector with matching thermal expansion coefficient was designed. The connector structure is composed of a transition unit cell with asymptotically changing thermal expansion coefficient. By connecting two heterogeneous high and low temperature parts, the generation of thermal stress is avoided, which largely ensures the mechanical performance of the structure under temperature load.

[0027] 2) Parametric modeling: By introducing parameters to change the cross-sectional area of ​​unit cells and the angles between cells, parametric modeling is achieved. A filling program is used to fill the unit cells of the part. Furthermore, this method has the advantages of being fast, efficient, and convenient compared to traditional 3D modeling software methods.

[0028] 3) This invention achieves the filling of unit cells by dividing the part into conformal meshes, avoiding the irregularity of unit cell arrangement caused by the traditional direct periodic array of unit cells, such as gaps and breaks between unit cells. At the same time, it ensures the integrity of unit cells and the continuity of unit cells inside the part. The boundary shape of the filled part can also be closer to the original boundary shape of the part as the mesh is densified. Attached image description:

[0029] Figure 1 This is a geometric relationship diagram of a dual-material curved quadrangular pyramid according to the present invention;

[0030] Figure 2 This is a diagram of a transitional unit cell basic unit of the present invention, (a) is a traditional basic unit, and (b) is a circular arc basic unit;

[0031] Figure 3 This is a complete diagram of a transitional unit cell structure according to the present invention;

[0032] Figure 4 These are the different thermal expansion lattice unit cell diagrams of the present invention: (a) is a body-centered cubic unit cell diagram, (b) is a face-centered cubic unit cell diagram, and (c) is a transition unit cell diagram.

[0033] Figure 5 (a) is an overall view of the connection between the lattice connector and the part in an embodiment of the present invention, which matches the coefficient of thermal expansion. Figure 5 (b) is a partial view of a lattice connector matching the coefficient of thermal expansion according to an embodiment of the present invention. In the figure, 1-part one, 2-part two, 3-lattice connector matching the coefficient of thermal expansion.

[0034] Figure 6 This is a diagram showing the filling structure of a lattice connector matching the coefficient of thermal expansion according to an embodiment of the present invention. In the diagram, 4 represents the front part of the connector, 5 represents the transition structure of the connector, and 6 represents the rear part of the connector. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and examples. However, the embodiments of this invention are not limited thereto.

[0036] Specific Implementation Method 1: This example uses filling a complex connector as an example. A lattice connector with a matching coefficient of thermal expansion needs to be designed between two heterogeneous high-low temperature components, Part 1 and Part 2. The unit cell configuration constituting Part 1 is as follows: Figure 4 As shown in (b), the unit cell configuration constituting part two is as follows: Figure 4 As shown in (a). Using the filling method of this invention, a dot matrix filling structure of the part is obtained, with the filling configuration as follows. Figure 6 As shown. The specific steps are as follows:

[0037] 1. Matching thermal expansion coefficient connection structure design:

[0038] like Figure 5 The three parts shown, from right to left, are Part 1, a lattice connector with a matching coefficient of thermal expansion, and Part 2. In a specific working environment, Part 1 and Part 2 have a significant difference in temperature load. If Part 1 is directly connected to Part 2, a large stress will be generated at the connection surface between the two parts. Therefore, a lattice connector with a matching coefficient of thermal expansion needs to be designed between the two parts to reduce thermal stress and achieve the effect of matching the coefficients of thermal expansion.

[0039] In this embodiment, the main reason for the high stress at the connection between the two parts is the mismatch in their coefficients of thermal expansion. Therefore, the connector needs to match the coefficients of thermal expansion of the two parts. The front and rear parts of the lattice connector with matched coefficients of thermal expansion have the same equivalent coefficients of thermal expansion as the materials in the contact areas of parts one and two, respectively. The middle part of the lattice connector with matched coefficients of thermal expansion uses a zero-expansion lattice for transition, thus forming a lattice connector with matched coefficients of thermal expansion.

[0040] 2. Dot matrix filling method for connectors with matching coefficients of thermal expansion:

[0041] Combination Figure 5 and Figure 6 Note that, based on the geometry of the intermediate connector structure, the front and rear parts of the connector respectively adopt unit cell structures with the same coefficient of thermal expansion as parts one and two, corresponding to... Figure 4 (a)(b), the middle part is the transition structure 5, which is filled with zero expansion lattice. Here we will focus on the filling method of the zero expansion part of the transition structure.

[0042] Step 1: Establish the geometric model of the transition structure, import the transition structure into the finite element tool for eight-node solid element mesh generation, and extract and save the mesh node position information, mesh node number information and mesh quantity information.

[0043] Step 2: Establish a zero-expansion unit cell structure, because as... Figure 2 In the traditional square pyramid structure shown in (a), angular changes also occur at the points where the rods connect, leading to stress concentration. To reduce the stress in the unit cell, a smoothing treatment is applied at the joints of the two rods, modifying these straight rods into arc-shaped rod structures, forming a structure like... Figure 2 The new basic unit structure shown in (b) is called the circular arc basic unit. Applying this new basic unit to a unit cell structure forms a new unit cell configuration. By setting the material and angle β of the basic unit, the thermal expansion coefficient of the transition unit cell is set to zero, forming a zero-expansion unit cell overall structure, such as... Figure 3 As shown.

[0044] Step 3: Using VBA, based on the solid unit mesh information extracted in Step 1, establish a 3D model of the transition unit cell. Using loop statements, each transition unit cell has different mesh node position information and mesh number information, thus forming transition units cells with different configurations.

[0045] Step 4: Insert the transition unit cell established in Step 3 into the corresponding position of the transition structure according to the grid node position information, thereby forming the connector transition structure 5.

[0046] Finally, after completing the zero-expansion unit cell filling of the transition structure, the front part of the connector, the rear part of the connector, and the transition structure are combined to obtain a lattice connector with a matching coefficient of thermal expansion.

Claims

1. A lattice connector matching the coefficient of thermal expansion, characterized in that, The lattice connector with matching thermal expansion coefficient is used to connect two heterogeneous high and low temperature parts. It is divided into a front part, a rear part and a middle part. The front part and the rear part are connected to the parts respectively, and the unit cell structure ensures that the materials of the connected parts have the same equivalent thermal expansion coefficient. The middle part is a transition structure, which is filled with transition unit cells. The basic unit of the transitional unit cell is formed by connecting the bottom surfaces of two bimaterial curved quadrangular pyramid structures. The bimaterial curved quadrangular pyramid structure is a structure with a designable coefficient of thermal expansion. The equivalent thermal expansion coefficient of the transition unit cell can be changed by selecting two different materials or designing the angle of the quadrangular pyramid; and by connecting the base surfaces of two bimaterial curved quadrangular pyramid structures, a basic unit with a designable thermal expansion coefficient is formed. Eight basic units are connected in a front-to-back symmetrical and cross-symmetrical manner, with the vertices of the eight basic units connected at a single point to form a transition unit cell. Using the included angle of the quadrangular pyramids within the transition unit cell as the design variable and the thermal expansion coefficient of the transition unit cell as the objective function, optimization is performed to obtain a transition unit cell with an asymptotic transition in thermal expansion coefficient, realizing the changes in positive, zero, and negative expansion coefficients of the transition unit cell. Finally, transition unit cells with different configurations are filled into the transition structure to form a lattice connector with a matching thermal expansion coefficient. The specific configuration of the transition unit cell is obtained through optimization. One form is that the transition structure is entirely filled with zero-expansion unit cells. The zero-expansion unit cell achieves its thermal expansion coefficient as zero by adjusting the included angles of the basic units within the unit cell.

2. The lattice connector with matched thermal expansion coefficient according to claim 1, characterized in that, The transition unit cell in the transition structure is obtained by an optimization method. By optimizing the thermal expansion coefficient of the transition unit cell in the transition structure, the thermal expansion coefficient is used as the optimization target to achieve an asymptotic transition of the thermal expansion coefficient of the transition unit cell. Furthermore, by filling the transition structure with unit cells, the transition structure becomes a thermal expansion structure in which the thermal expansion coefficient transitions from the distribution of the parts on one side to the distribution of the parts on the other side.

3. A method for filling a lattice with a lattice connector that matches the coefficient of thermal expansion, characterized in that, The transition structure is divided into eight-node solid units, which correspond to the eight vertices contained in the transition unit cell. Based on different transition unit cell configurations and vertex positions, a three-dimensional model of the transition unit cell is established. Finally, the automatic filling function is used to fill the transition unit cells of different configurations into the corresponding positions of the transition structure to form a lattice-filled model of the transition structure. The filling method of the front and rear parts of the lattice connector with the matching coefficient of thermal expansion is the same as that of the middle part; The specific steps are as follows: Step 1: Perform eight-node solid element meshing on the filled transition structure and obtain the corresponding mesh node location information, mesh node number information and mesh quantity information; Step 2: Establish the body center and eight vertex positions of the transition unit cell; calculate the center point coordinates of the transition unit cell using the obtained mesh node position information; obtain the coordinates of the four points on the base of the bimaterial curve pyramid in the basic unit cell by using the center point coordinates of the transition unit cell, the vertex coordinates of the transition unit cell, and the angle between the basic unit cell and the basic unit cell, thus obtaining the various parameters for drawing the transition unit cell. Step 3: Establish the transition unit cell model; based on the parameters of the obtained transition unit cell, connect the pre-established endpoints to form a line segment or curve. Establish a reference plane perpendicular to the connecting line at the endpoints of the line segment, and draw a circle with radius r centered on this endpoint within the reference plane. Scan the circle along the line segment to establish the transition unit cell rod model. The cross-sectional area of ​​the rod changes according to the value of the control parameter r, and the cross-sectional shape can also be varied. To achieve manufacturability of the unit cell, connect the rod vertices by establishing a spherical corner in the transition unit cell. Draw a semicircle centered on the endpoint within the reference plane where the rod cross-section was previously established, with a radius slightly larger than the rod radius. Using a rotation command, rotate the semicircle one revolution around its diameter to establish the spherical corner. This completes the 3D model of each transition unit cell. Step 4: Using a loop statement, repeat the process of step 3 so that each transition cell has different grid node position information and grid number information, thereby forming transition cells with different configurations, and save each transition cell to a specified location. Step 5: Insert the previously established transition unit cells with different configurations into the corresponding positions of the transition structure. The transition structure is combined with the front and rear parts of the lattice connector with matching thermal expansion coefficients to obtain the lattice connector with matching thermal expansion coefficients.

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