A design method of multi-material lattice structure with adjustable low thermal expansion coefficient

Abstract

The application discloses a kind of adjustable low thermal expansion coefficient multi-material lattice structure design method, belong to material structure design field, comprising: the connection relationship between the physical modeling of lattice structure is characterized, the initial material of each rod is set;Fixed geometric constraint boundary condition is applied at the key node of model, suppress all degrees of freedom;Uniform temperature field load is applied in the whole domain of model, simulate the overall temperature rise environment experienced by structure;Solve the thermal stress generated in the structure under the action of thermal load and the displacement field caused thereby, the displacement of each node on outer surface is calculated;Through material grade thermal expansion coefficient differentiation matching, realize cross-temperature domain deformation compensation, with the displacement of outer surface node as constraint, the material of each rod is determined by optimization method, obtain near-zero expansion lattice structure;Parameterized design platform is constructed, for realizing the optimization design of multi-configuration lattice structure, realize low thermal expansion characteristics.The application has the advantages of wide application range.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of material structure design, and more particularly to a multi-material lattice structure design method with adjustable low thermal expansion coefficient. BACKGROUND

[0002] For high-temperature working conditions of precision structures (such as spacecraft optical platforms and semiconductor lithography equipment), thermal expansion deformation will directly affect the stability and measurement accuracy of the equipment. For example, in a satellite remote sensing system, the support structure produces a large thermal deformation due to the periodic temperature changes in the orbit, resulting in misalignment of the optical elements and a decrease in imaging quality.

[0003] Controlling the thermal expansion coefficient is a key requirement for achieving high-precision systems. The advantage of lattice structure is its programmable topological configuration design capability, that is, by reasonably designing the material properties and spatial arrangement of the rods, the deformation behavior under thermal load can be actively controlled, and a negative thermal expansion effect opposite to the intrinsic expansion of the base material can be produced on a macroscopic scale. This makes it unique in the field of thermal deformation compensation in a wide temperature range, especially when traditional homogeneous materials cannot meet the requirements of lightweight, high strength, and low thermal expansion. Lattice structures can provide efficient and reliable solutions. Currently, there is a dual demand for low thermal expansion and lightweight of precision equipment in extreme temperature environments. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a multi-material lattice structure design method with adjustable low thermal expansion coefficient, which has a wide range of applications, especially for scenarios that require strict thermal stability, such as aerospace titanium alloy support frames, silicon carbide ceramic optical pedestals, and semiconductor silicon-based bonding platforms.

[0005] The purpose of the present application is achieved by the following scheme:

[0006] A multi-material lattice structure design method with adjustable low thermal expansion coefficient, comprising the following steps:

[0007] First, a physical model of the lattice structure is established, the connection relationship between the rods is characterized by the model, and the initial material of each rod is set. Fixed geometric constraint boundary conditions are applied at the key nodes of the model to suppress all degrees of freedom. A uniform temperature field load is applied to the entire model to simulate the overall temperature rise environment experienced by the structure. Through thermal-mechanical coupling static analysis, the thermal stress generated inside the structure under thermal load and the displacement field induced thereby are solved, and the displacement of each node on the outer surface is calculated.

[0008] Next, through differential matching of the material level thermal expansion coefficient, deformation compensation across the temperature range is achieved. The material of each rod is determined through an optimization method with the displacement of the outer surface nodes as a constraint, and a near-zero expansion lattice structure is obtained.

[0009] Finally, a parameterized design platform is constructed to realize the optimization design of the lattice structure of multiple configurations and realize the low thermal expansion characteristics.

[0010] Further, the physical modeling of the lattice structure specifically adopts finite element software to physically model the lattice structure.

[0011] Further, the key node is the left lower corner node of the model.

[0012] Further, the deformation compensation across the temperature domain is realized by differentiating the matching of the material level thermal expansion coefficient, and the material of each rod is determined by an optimization method with the displacement of the outer surface node as a constraint to obtain a near-zero expansion lattice structure, including the following sub-steps:

[0013] A digital material database covering a plurality of materials with different thermal expansion coefficients and elastic moduli is established, the material used by the structure is determined by an optimization method, and the material properties of each rod are defined as design variables, and the optimization target is the displacement of all nodes on the outer surface of the structure, and the constraint is the maximum stress that the material can withstand.

[0014] Further, the establishment of the digital material database covering a plurality of materials with different thermal expansion coefficients and elastic moduli, and the determination of the material used by the structure by the optimization method specifically includes the following sub-steps:

[0015] A gradient thermal expansion coefficient material database is constructed, and the material is selected according to the functional requirements of each rod in the lattice structure; wherein, the synergistic effect of the high thermal expansion coefficient rod and the negative thermal expansion coefficient rod is utilized: in a wide temperature range, the expansion amount of the metal rod and the contraction amount of the ceramic rod offset each other under high temperature working conditions, and finally the net expansion coefficient of the overall structure reaches the expected value range.

[0016] Further, the gradient thermal expansion coefficient material database specifically includes positive expansion metal, negative expansion ceramic and near-zero expansion alloy.

[0017] Further, the optimization method specifically includes an improved genetic algorithm NSGA-II.

[0018] The beneficial effects of the present application include:

[0019] Unlike traditional low-expansion alloys and composite laminated structures, the near-zero expansion structure designed by the method of the present application has good specific stiffness, specific strength, light weight, excellent design performance and high design freedom.

[0020] Unlike single and double material composed lattice structures, the method of the present application can effectively realize the structure demand of high-precision equipment for wide temperature range, full-direction near-zero expansion, realize the two-dimensional expansion coefficient ≤ ± 1.5 × 10 -6 / K is suitable for extreme working conditions such as aerospace titanium alloy components and silicon carbide ceramic optical bases. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the dot matrix structure in an embodiment of the present invention;

[0023] Figure 2 This is a flowchart of a method according to an embodiment of the present invention;

[0024] Figure 3a This is a structural finite element model containing coordinate system positions in this embodiment of the invention; it should be noted that the coordinate system is a default color set by the finite element simulation software and is a necessary identifier color for the structural finite element model;

[0025] Figure 3b This is a structural finite element model in this embodiment of the invention, including the fixed constraint application position and node number; wherein, the lower left corner symbol represents the displacement and rotation of constraint node 1 in the x and y directions;

[0026] Figure 4 This is a comparison of the overall deformation cloud map (deformation magnified 20 times) between 300°C and the undeformed state in an embodiment of the present invention. Detailed Implementation

[0027] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.

[0028] In view of the current situation, this invention aims to address the dual requirements of low thermal expansion and lightweight for precision equipment under extreme temperature variations. Based on a multi-material lattice structure with an adjustable low coefficient of thermal expansion, it proposes an active thermal deformation compensation design method. This method compensates for the deformation caused by the different coefficients of thermal expansion of different materials, achieving a thermal expansion coefficient ≤ ±1.5 × 10⁻⁶ within the range of 0–300 °C. -6 / K is suitable for applications with stringent requirements for thermal stability, such as aerospace titanium alloy support frames, silicon carbide ceramic optical substrates, and semiconductor silicon-based bonding platforms.

[0029] In the inventive concept, the low thermal expansion property of the structure is obtained mainly based on the material design of the near-zero expansion lattice structure rods. The lattice structure is an artificial metamaterial with a periodic spatial topological configuration, and its thermal expansion behavior can be actively regulated by microstructure design. The negative thermal expansion effect is generated by the deformation of the rod curvature under high temperature working conditions, which offsets the intrinsic positive expansion of the base material. The change of temperature causes the change of thermal strain of the lattice unit, and shows a predictable regularity. Based on this, in the preferred embodiment of the present application, a multi-material lattice structure design method with adjustable low thermal expansion coefficient is provided, as shown in Figure 2 The specific steps are as follows:

[0030] First, the finite element software is used to model the physical model of the lattice structure, and the model represents the connection relationship between the rods (as shown in Figure 1 The fixed geometric constraint boundary condition is applied to the key nodes at the lower left corner of the model to suppress all degrees of freedom. A uniform temperature field load is applied to the whole model to simulate the overall temperature rise environment experienced by the structure. Through thermal-mechanical coupled static analysis, the thermal stress and displacement field caused by the thermal load in the structure are solved, and the displacement of each node on the outer surface is calculated.

[0031] Then, the material of each rod is determined. A digital material database covering a variety of materials with different thermal expansion coefficients and elastic moduli is established. The material of the structure is determined by optimization method, and the material properties of each rod are defined as design variables. The optimization target is the displacement of all nodes on the outer surface of the structure, and the constraint is the maximum stress that the material can withstand.

[0032] More specifically, one of the design cores of the near-zero expansion lattice structure is to realize deformation compensation across the temperature range by differentiating the matching of the material level thermal expansion coefficient, and one of the key points is: by constructing a gradient thermal expansion coefficient material database (covering positive expansion metals, negative expansion ceramics and near-zero expansion alloys), the material selection is carried out according to the functional requirements of each rod in the lattice structure. The synergistic effect of high thermal expansion coefficient rods (such as titanium alloy with thermal expansion coefficient α≥8.6×10 -6 / K) and negative thermal expansion coefficient rods (such as ZrW2O8 ceramic with α≈-9.0×10 -6 / K): in a wide temperature range, the expansion of the metal rod and the shrinkage of the ceramic rod offset each other under high temperature working conditions, and finally realize the net expansion coefficient of the structure ≤±1.5×10 -6K, the thermal expansion coefficient of which is less than the thermal expansion coefficient of the aluminum alloy, titanium alloy and other materials commonly used in spacecraft, and breaks through the design limitation of traditional dependence on hinged structure, and directly achieves the thermal stability target through the combination of intrinsic properties of the material. The structure established by the method of deformation compensation of different thermal expansion coefficients is not limited to one configuration, but can be designed for near-zero expansion for any lattice structure. Subsequently, low thermal expansion is achieved at a higher temperature (> 500℃) by the variable property of the material, and low thermal expansion characteristics in a wider temperature range are obtained.

[0033] Finally, by constructing a universal intelligent parameterized design platform, the optimization design of other configuration lattice structures can be realized, and the low thermal expansion characteristics can be realized.

[0034] In other embodiments of the present application, based on the above embodiments, the following implementation is further adopted: Figures 3a-3b All are finite element models of lattice structures, and the lower left corner node is fixed. Each beam element of the model is numbered (number range: 1~20), and the optimization algorithm for material selection is an improved genetic algorithm (NSGA-II), and the optimization formula is as follows:

[0035] Optimization variable: m n1 , m n2 , …, m n20 , m n1 , m n2 , …, m n20 is the material number in the material library;

[0036] Optimization goal: u i , v i tends to 0, u i is the deformation amount of node i in the x direction, v i is the deformation amount of node i in the y direction, i is the outer surface node number, i = 2, 3, …, 8;

[0037] Constraint: σ i < σ * , σ i is the stress of the beam element, and σ * is the allowable stress.

[0038] The final results are shown in Table 1 and Figure 4 . Figure 4 is the overall deformation cloud chart (deformation amount is enlarged 20 times) of 300℃ in the embodiment of the present application compared with the undeformed state; different colors represent different deformation amounts, such as dark blue representing displacement of 0~3.31×10 -4 m, and the dark red part represents displacement of 2.65×10 -3 ~2.98×10 -3m. Thermal expansion coefficients in x and y directions in the temperature range of 0-300℃ . Figure 4 The overall deformation (i.e. overall displacement) of the structure after the temperature is raised by 300℃ is shown, and since the lower left corner is a fixed node, the overall deformation is zero; the maximum structural deformation is 2.976x10 -3 m, at the position of node 10; in addition, the deformation of the three nodes 9, 11 and 12 inside the structure is large, and the essence of the structure is that the internal region of the structure bears the main deformation coordination function, i.e. when the temperature of the structure is raised, the internal region absorbs and coordinates the deformation demand of the structure through a large deformation, so that the displacement of the outer surface part can be kept at a low level, meeting the design requirement of near-zero expansion.

[0039] Table 1. Thermal expansion coefficient data table of the structure at different temperatures

[0040]

[0041] The units described in the embodiments of the present application can be implemented in the form of software, or can be implemented in the form of hardware, and the described units can also be arranged in a processor. In some cases, the name of the unit does not constitute a limitation on the unit itself.

[0042] According to an aspect of the embodiments of the present application, a computer program product or computer program is provided, which includes computer instructions stored in a computer readable storage medium. The processor of the computer device reads the computer instructions from the computer readable storage medium, and the processor executes the computer instructions, so that the computer device executes the method provided in the various optional implementation manners described above.

[0043] As another aspect, the embodiments of the present application also provide a computer readable medium, which can be included in the electronic device described in the above embodiments; or can exist independently without being assembled into the electronic device. The computer readable medium carries one or more programs, and when the one or more programs are executed by the electronic device, the electronic device implements the method described in the above embodiments.

Claims

1. A method of designing a multi-material lattice structure with tunable low thermal expansion coefficient, characterized in that, The method comprises the following steps: First, the lattice structure is physically modeled, the connection relationship between the rods is represented by a model, the initial material of each rod is set, a fixed geometric constraint boundary condition is applied at the key nodes of the model to suppress all degrees of freedom, a uniform temperature field load is applied to the whole model to simulate the overall temperature rise environment experienced by the structure, and the thermal stress generated inside the structure under the action of the thermal load and the displacement field caused thereby are solved through thermal-mechanical coupled static analysis to calculate the displacement of each node on the outer surface; Then, cross-temperature domain deformation compensation is achieved by differentiating and matching the material level thermal expansion coefficient, and the material of each rod is determined by an optimization method with the displacement of the outer surface nodes as a constraint to obtain a near-zero expansion lattice structure; Finally, a parameterized design platform is constructed to realize the optimization design of lattice structures of multiple configurations and realize the low thermal expansion characteristic; The near-zero expansion lattice structure obtained by differentiating and matching the material level thermal expansion coefficient to achieve cross-temperature domain deformation compensation, and determining the material of each rod by an optimization method with the displacement of the outer surface nodes as a constraint, comprises the following sub-steps: A digital material database covering multiple materials with different thermal expansion coefficients and elastic moduli is established, the material used by the structure is determined by an optimization method, the material properties of each rod are defined as design variables, and the optimization target is the displacement of all nodes on the outer surface of the structure, and the constraint is the maximum stress that the material can withstand; The digital material database covering multiple materials with different thermal expansion coefficients and elastic moduli is established, and the material used by the structure is determined by an optimization method, which specifically comprises the following sub-steps: A gradient thermal expansion coefficient material database is constructed, and the materials are selected according to the functional requirements of each rod in the lattice structure; wherein, the collaborative action of the high thermal expansion coefficient rod and the negative thermal expansion coefficient rod is utilized: in a wide temperature range, the expansion amount of the metal rod and the shrinkage amount of the ceramic rod offset each other under high temperature working conditions, and finally the overall net expansion coefficient of the structure reaches the expected value range.

2. The multi-material lattice structure design method for tunable low coefficient of thermal expansion of claim 1, wherein, The physical modeling of the lattice structure is specifically performed by using a finite element software.

3. The multi-material lattice structure design method for tunable low coefficient of thermal expansion of claim 1, wherein, The key node is the lower left corner node of the model.

4. The multi-material lattice structure design method for tunable low coefficient of thermal expansion of claim 1, wherein, The gradient thermal expansion coefficient material database specifically includes positive expansion metal, negative expansion ceramic, and near-zero expansion alloy.

5. The multi-material lattice structure design method for tunable low coefficient of thermal expansion of claim 1, wherein, The optimization method specifically includes an improved genetic algorithm NSGA-II.

Images