A metal lattice structure with a customizable coefficient of thermal expansion and its design method

Abstract

This invention relates to the field of aerospace materials technology, and discloses a metal lattice structure with a customizable coefficient of thermal expansion and its design method. Each lattice unit cell of the structure is an isosceles triangle composed of two waist elements and a base element. Each element consists of a rhombic frame and a diagonal. Each element is composed of two metal materials: one for the rhombic frame and another for the diagonal. By adjusting the length ratio of the sides and the diagonal of the rhombic frame and the material type, the lattice unit cell can exhibit one of the following characteristics: a negative coefficient of thermal expansion, a zero coefficient of thermal expansion, a positive coefficient of thermal expansion, or an anomalous coefficient of thermal expansion. This allows for a sudden change in the coefficient of thermal expansion near the Curie temperature of a low-expansion alloy, satisfying the customizable thermal expansion requirements of the metal lattice structure.

Description

Technical Field

[0001] This invention relates to the field of aerospace materials technology, and discloses a metal lattice structure with a customizable coefficient of thermal expansion and its design method. Background Technology

[0002] The coefficient of thermal expansion, as a physical quantity that quantifies the thermal deformation behavior of materials, is used to measure the degree of change in the volume and shape of a material / structure due to changes in external temperature. Traditional metallic materials have the physical property of thermal expansion and contraction. When two materials with different thermal expansion are combined (heterogeneous material structures), severe thermal stress concentration will occur due to thermal mismatch. Especially in the aerospace field, thermal deformation caused by temperature changes can destroy the original structural precision of high-precision heterogeneous material structures.

[0003] Clearance control components are widely used in aero-engines to control rotor-stator clearance, such as the rotor blades and outer ring / casing, and the ferrule and honeycomb inner ring. In aero-engines, the rotor-stator clearance of clearance control components is a critical parameter, significantly impacting engine performance and safety. Reduced clearance improves engine performance, increases efficiency, and lowers fuel consumption; conversely, excessively small clearance increases the risk of contact between components, leading to wear, overheating, and even failure. The radial clearance design of advanced aero-engine clearance control components must balance performance and safety, with the ultimate goal of minimizing radial clearance under all operating conditions and preventing severe rubbing under normal flight conditions.

[0004] In practical applications, a large negative thermal expansion coefficient, a large positive thermal expansion coefficient, or a zero thermal expansion coefficient are required. However, current research on customizable thermal expansion lattices mainly focuses on expanding their thermal expansion coefficients. Most of these lattices only have isotropic thermal expansion coefficients, or a large negative or large positive thermal expansion coefficient in a single direction, and cannot achieve large variations in the range of thermal expansion, especially abrupt changes in the thermal expansion coefficient. Summary of the Invention

[0005] The purpose of this invention is to provide a metal lattice structure with a customizable coefficient of thermal expansion and its design method, which can meet the customizable thermal expansion requirements of metal lattice structures.

[0006] To achieve the above-mentioned technical effects, the technical solution adopted by the present invention is as follows:

[0007] A metal lattice structure with a customizable coefficient of thermal expansion, the lattice structure being composed of multiple lattice unit cells arranged periodically in space; each lattice unit cell is formed by two waist primitives and a base primitive fixedly connected to form an isosceles triangle; each primitive consists of a rhombic frame and a diagonal.

[0008] Each primitive is composed of two metal materials. The sides of the rhombus frame of the waist primitive and the diagonal of the bottom primitive are made of one metal material, while the diagonal of the waist primitive and the sides of the rhombus frame of the bottom primitive are made of another metal material.

[0009] Furthermore, the rhomboid frame of the waist unit cell of the lattice structure is made of a first metal material, and the diagonal of the waist unit is made of a second metal material; and the rhomboid frame of the bottom unit is made of a second metal material, and the diagonal of the bottom unit is made of a first metal material; within the same temperature range, the coefficient of thermal expansion of the first metal material is less than the coefficient of thermal expansion of the second metal material.

[0010] Furthermore, the rhomboid frame of the waist unit cell of the lattice structure is made of a second metal material, and the diagonal of the waist unit is made of a first metal material; and the rhomboid frame of the bottom unit is made of a first metal material, and the diagonal of the bottom unit is made of a second metal material; within the same temperature range, the coefficient of thermal expansion of the first metal material is less than that of the second metal material.

[0011] Furthermore, the coefficient of thermal expansion of the second metallic material is more than 1.5 times that of the first metallic material.

[0012] Furthermore, the first metallic material includes one of titanium alloy, Invar alloy, and low-expansion high-temperature alloy; the second metallic material includes one of aluminum alloy, stainless steel, nickel-based high-temperature alloy, and cobalt-based high-temperature alloy.

[0013] Furthermore, the three basic elements in the isosceles triangle are connected by welding, pin connection, bolt connection or mortise and tenon inlay.

[0014] To achieve the above-mentioned technical effects, the present invention also provides a method for designing a metal lattice structure with a customizable coefficient of thermal expansion, for obtaining the aforementioned metal lattice structure, comprising:

[0015] An analytical model is constructed to establish the thermal expansion coefficients of the waist-element rhombic frame, the diagonal metal materials of the base-element, the diagonal metal materials of the waist-element, the base-element rhombic frame, and the rhombic frame of the waist-element and base-element, as well as the relationship between the size parameters of the waist-element, base-element rhombic frame and their corresponding diagonals and the thermal expansion coefficients of the lattice unit cells along the normal of the isosceles triangle base-element.

[0016] Based on the selected coefficients of thermal expansion of the waist element rhombic frame, the diagonal metal material of the bottom element, and the metal material of the waist element diagonal and bottom element rhombic frame, the analysis model is used to analyze and obtain the combination of waist element, bottom element rhombic frame and corresponding diagonal dimension parameters that satisfy the target coefficient of thermal expansion of the metal lattice structure.

[0017] Furthermore, the constructed analytical model is as follows: ,in Let be the coefficient of thermal expansion of the unit cell of the lattice along the normal direction of the base element of the isosceles triangle. The coefficient of thermal expansion is given by the rhomboid frame of the waist element and the diagonal metal material of the base element. Let be the coefficient of thermal expansion of the rhombic frame metal material of the waist element, diagonal, and base element. Let the side length of the waist-shaped rhombus frame be the basic element. The diagonal length of the waist element is... The side length of the bottom primitive rhombus frame. The length of the diagonal of the base element.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: Each unit cell of the metal lattice structure of the present invention is composed of two metal materials, the rhomboid frame is one metal material, and the diagonal is another metal material. By adjusting the length ratio of the sides and diagonals of the unit rhomboid frame and the material type, the lattice unit cell can have one of the characteristics of a sudden change in thermal expansion coefficient near the Curie temperature of a low-expansion alloy with negative thermal expansion coefficient, zero thermal expansion coefficient, positive thermal expansion coefficient, or anomalous thermal expansion phenomenon, thus meeting the customizable thermal expansion requirements of the metal lattice structure. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of a lattice unit cell of the metal lattice structure in the embodiment;

[0020] Figure 2 This is a schematic diagram of the waist or bottom edge elements in the embodiment;

[0021] Among them, 1. Rhombus frame; 2. Diagonal; 3. Waist element; 4. Base element. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0023] Example 1

[0024] See Figure 1 , Figure 2 A metal lattice structure with a customizable coefficient of thermal expansion, the lattice structure being composed of multiple lattice unit cells arranged periodically in space; each lattice unit cell is formed by two waist units 3 and a base unit 4 fixedly connected to form an isosceles triangle; each unit cell is composed of a rhombic frame 1 and a diagonal 2;

[0025] Each element is composed of two metal materials. The sides of the waist element 3 rhombus frame 1 and the diagonal 2 of the bottom element 4 are made of one metal material, while the diagonal 2 of the waist element 3 and the sides of the bottom element 4 rhombus frame 1 are made of another metal material.

[0026] In this embodiment, each lattice unit cell of the lattice structure is an isosceles triangle composed of two waist elements 3 and a base element 4. Each element consists of a rhombus frame 1 and a diagonal 2. Each element is composed of two metal materials: the rhombus frame 1 is one metal material, and the diagonal 2 is another metal material. By adjusting the length ratio of the sides of the rhombus frame 1 and the diagonal 2, as well as the material type, the lattice unit cell can exhibit one of the following characteristics: a negative thermal expansion coefficient, a zero thermal expansion coefficient, a positive thermal expansion coefficient, or an anomalous thermal expansion phenomenon. This allows for a sudden change in the thermal expansion coefficient near the Curie temperature of a low-expansion alloy, thus satisfying the customizable thermal expansion requirements of the metal lattice structure.

[0027] In this embodiment, the two metallic materials have different coefficients of thermal expansion within the same temperature range, and are labeled as a material with a low coefficient of thermal expansion and a material with a high coefficient of thermal expansion, respectively. The two materials can be combined in the following ways:

[0028] 1. The rhomboid frame 1 of the waist unit 3 is made of a material with a low coefficient of thermal expansion, and the diagonal 2 of the waist unit 3 is made of a material with a high coefficient of thermal expansion; and the rhomboid frame 1 of the bottom unit 4 is made of a material with a high coefficient of thermal expansion, and the diagonal 2 of the bottom unit 4 is made of a material with a low coefficient of thermal expansion; by adjusting the length ratio of the sides and diagonals 2 of each rhomboid frame 1 and the material type, the lattice unit cell can have the characteristics of a negative coefficient of thermal expansion, a zero coefficient of thermal expansion, or a low positive coefficient of thermal expansion.

[0029] 2. The rhomboid frame 1 of the waist unit 3 is made of a material with a high coefficient of thermal expansion, and the diagonal 2 of the waist unit 3 is made of a material with a low coefficient of thermal expansion; and the rhomboid frame 1 of the bottom unit 4 is made of a material with a low coefficient of thermal expansion, and the diagonal 2 of the bottom unit 4 is made of a material with a high coefficient of thermal expansion; by adjusting the length ratio of the sides and diagonals 2 of each rhomboid frame 1 and the material type, the lattice unit cell can have an ultra-high positive coefficient of thermal expansion.

[0030] 3. Select Invar alloys (including standard Invar alloy, super Invar alloy, stainless Invar alloy) and other low-expansion alloys with anomalous thermal expansion phenomena as the low thermal expansion coefficient material in 1 or 2; by adjusting the length ratio of the side and diagonal 2 of the basic rhombic frame 1 and the material type, the lattice unit cell can undergo a sudden change in the coefficient of thermal expansion near the Curie temperature of the low-expansion alloy with anomalous thermal expansion phenomena.

[0031] In this embodiment, the metal material with a low coefficient of thermal expansion includes one of titanium alloy, Invar alloy, and low-expansion high-temperature alloy; the metal material with a high coefficient of thermal expansion includes one of aluminum alloy, stainless steel, nickel-based high-temperature alloy, and cobalt-based high-temperature alloy.

[0032] In some other embodiments, the high coefficient of thermal expansion is more than 1.5 times that of the low coefficient of thermal expansion, which broadens the designable range of the custom coefficient of thermal expansion and makes it easier to design a custom coefficient of thermal expansion.

[0033] Based on the same inventive concept, this embodiment also provides a method for designing a metal lattice structure with a customizable coefficient of thermal expansion, including:

[0034] An analytical model is constructed to establish the thermal expansion coefficients of the metal materials of the waist element 3 rhombic frame 1, the base element 4, and the diagonal 2, as well as the thermal expansion coefficients of the metal materials of the waist element 3, the diagonal 2, and the base element 4 rhombic frame 1, and the dimensional parameters of the waist element 3 and the base element 4 rhombic frame 1 and the corresponding diagonal 2, and the thermal expansion coefficients of the lattice unit cell along the normal of the isosceles triangle base element 4.

[0035] Based on the thermal expansion coefficients of the selected waist element 3 rhombus frame 1, bottom element 4, and diagonal 2 metal materials, the analysis model is used to analyze and obtain the combination of dimensional parameters of the waist element 3, bottom element 4 rhombus frame 1, and corresponding diagonal 2 that satisfy the target thermal expansion coefficient of the metal lattice structure.

[0036] In this embodiment, the constructed analysis model is as follows: ,in Let be the coefficient of thermal expansion of the lattice unit cell along the normal direction of the isosceles triangle base element 4. The coefficient of thermal expansion of the metal material is given by the waist element 3 (rhomboid frame 1), the base element 4, and the diagonal element 2. The coefficient of thermal expansion of the metal material is given by the waist element 3, diagonal element 2, and base element 4 (rhomboid frame 1). The waist element is a 3-rhombus frame with a side length of 1. The waist element has a diagonal length of 2. The base element is a rhombus frame with a side length of 1. The base element has 4 units, and the diagonal has 2 units.

[0037] In this embodiment, by constructing an analytical model of the thermal expansion coefficient of the lattice unit cell along the normal direction of the isosceles triangular base element 4, the thermal expansion coefficient of the lattice unit cell along a specific direction can be calculated based on the thermal expansion coefficients of different metal materials and the dimensional parameters of each element. In practical applications, designers can flexibly select the metal materials used for the waist element 3 (rhombus frame 1), the base element 4 (diagonal 2), etc., according to actual needs, determine their thermal expansion coefficients, and then combine them with the target thermal expansion coefficient of the required metal lattice structure. Using this analytical model, reverse derivation can be performed to quickly determine the dimensional parameter combination of the waist element 3, the base element 4 (rhombus frame 1), and the corresponding diagonal 2, greatly improving design efficiency and accuracy, and meeting the diverse needs of different engineering fields for the thermal expansion performance of metal lattice structures.

[0038] Example 2

[0039] See Figure 1 , Figure 2 In this embodiment, taking the waist unit 3 and the base unit 4 as having the same shape, two sets of metal materials are used in different combinations to verify the thermal expansion coefficient of the lattice unit cell along the normal direction of the isosceles triangle base unit 4. The thermal expansion coefficients of each material are shown in Table 1.

[0040] Table 1. Coefficients of thermal expansion for each material

[0041]

[0042] Combination 1: Each basic element, the rhombus frame 1, has a side length of 2mm and a diagonal length of 1mm. The waist element 3 (rhombus frame 1) and the bottom element 4 (diagonal 2) are made of aluminum alloy, while the waist element 3 (diagonal 2) and the bottom element 4 (rhombus frame 1) are made of titanium alloy. Simulation analysis shows that the coefficient of thermal expansion of this structure at the operating temperature is 29.7 × 10⁻⁶. -6 ℃ -1 According to the above analytical model, the theoretically achievable coefficient of thermal expansion using an aluminum alloy and titanium alloy structure is 30.1 × 10⁻⁶. -6 ℃ -1 The difference between the two is small.

[0043] Combination 2: Each basic element, the rhombus frame 1, has a side length of 2mm and a diagonal length of 1mm. The waist element 3 (rhombus frame 1) and the bottom element 4 (diagonal 2) are made of titanium alloy, while the waist element 3 (diagonal 2) and the bottom element 4 (rhombus frame 1) are made of aluminum alloy. Simulation analysis shows that the coefficient of thermal expansion of this structure at the operating temperature is 0.7 × 10⁻⁶. -6 ℃ -1 The thermal expansion is close to zero; and according to the above analysis model, the theoretically achievable thermal expansion coefficient using an aluminum alloy and titanium alloy structure is 0.4 × 10⁻⁶. -6 ℃ -1 .

[0044] Combination 3: The rhombus frame 1 of waist element 3 has a side length of 4mm and a diagonal length of 3mm; the rhombus frame 1 of bottom element 4 has a side length of 5mm and a diagonal length of 2mm; and the rhombus frame 1 of waist element 3 and the diagonal length of bottom element 4 are made of aluminum alloy, while the diagonal length of waist element 3 and the rhombus frame 1 of bottom element 4 are made of Invar alloy. Simulation analysis shows that the coefficient of thermal expansion of this structure below the Curie temperature of Invar alloy is 46.1 × 10⁻⁶. -6 ℃ -1 According to the above analytical model, the theoretically achievable coefficient of thermal expansion using an aluminum alloy and Invar alloy structure is 46.7 × 10⁻⁶. -6 ℃ -1 When the temperature exceeds the Curie temperature of Invar alloy, the coefficient of thermal expansion will suddenly decrease significantly.

[0045] Combination 4: The rhombus frame 1 of waist element 3 has a side length of 4mm and a diagonal length of 3mm; the rhombus frame 1 of bottom element 4 has a side length of 5mm and a diagonal length of 2mm; and the rhombus frame 1 of waist element 3 and the diagonal length of bottom element 4 are made of Invar alloy, while the diagonal length of waist element 3 and the rhombus frame 1 of bottom element 4 are made of aluminum alloy. Simulation analysis shows that the coefficient of thermal expansion of this structure below the Curie temperature of Invar alloy is -21.3 × 10⁻⁶. -6 ℃ -1 According to the above analytical model, using an aluminum alloy and Invar alloy structure, at temperatures below the Curie temperature of Invar alloy, the theoretically achievable coefficient of thermal expansion is -22.0 × 10⁻⁶. -6 ℃ -1 Moreover, when the temperature exceeds the Curie temperature of Invar alloy, the coefficient of thermal expansion will suddenly increase significantly.

[0046] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A metal lattice structure with a customizable coefficient of thermal expansion, characterized in that, The lattice structure is composed of multiple lattice unit cells arranged periodically in space; each lattice unit cell is formed by two waist primitives and one base primitive fixedly connected to form an isosceles triangle; each primitive is composed of a rhombic frame and a diagonal. Each primitive is composed of two metal materials. The sides of the rhombus frame of the waist primitive and the diagonal of the bottom primitive are made of one metal material, while the diagonal of the waist primitive and the sides of the rhombus frame of the bottom primitive are made of another metal material.

2. The metal lattice structure according to claim 1, characterized in that, The rhomboid frame of the waist unit cell of the lattice structure is made of a first metal material, and the diagonal of the waist unit is made of a second metal material; and the rhomboid frame of the bottom unit is made of the second metal material, and the diagonal of the bottom unit is made of the first metal material; within the same temperature range, the coefficient of thermal expansion of the first metal material is less than that of the second metal material.

3. The metal lattice structure according to claim 1, characterized in that, The rhomboid frame of the waist unit cell of the lattice structure is made of a second metal material, and the diagonal of the waist unit is made of a first metal material; and the rhomboid frame of the bottom unit is made of a first metal material, and the diagonal of the bottom unit is made of a second metal material; within the same temperature range, the coefficient of thermal expansion of the first metal material is less than that of the second metal material.

4. The metal lattice structure according to claim 2 or 3, characterized in that, The coefficient of thermal expansion of the second metal material is more than 1.5 times that of the first metal material.

5. The metal lattice structure according to claim 2 or 3, characterized in that, The first metallic material includes one of titanium alloy, Invar alloy, and low-expansion high-temperature alloy; the second metallic material includes one of aluminum alloy, stainless steel, nickel-based high-temperature alloy, and cobalt-based high-temperature alloy.

6. The metal lattice structure according to claim 1, characterized in that, The three basic elements of an isosceles triangle are connected by welding, pinning, bolting, or mortise and tenon joints.

7. A method for designing a metal lattice structure with a customizable coefficient of thermal expansion, used to obtain the metal lattice structure according to any one of claims 1-6, characterized in that, include: An analytical model is constructed to establish the thermal expansion coefficients of the waist-based rhombic frame and the diagonal metal materials of the base-based rhombic frame, as well as the thermal expansion coefficients of the waist-based rhombic frame and the diagonal metal materials of the base-based rhombic frame, and the relationship between the rhombic frame and the corresponding diagonal dimension parameters of the waist-based and base-based rhombic frames and the thermal expansion coefficients of the lattice unit cells along the normal direction of the isosceles triangle base-based rhombic frame. Based on the selected coefficients of thermal expansion of the waist element rhombic frame and the diagonal metal materials of the bottom element, the analysis model is used to analyze and obtain the combination of waist element, bottom element rhombic frame and corresponding diagonal dimension parameters that satisfy the target coefficient of thermal expansion of the metal lattice structure.

8. The metal lattice structure design method according to claim 7, characterized in that, The constructed analysis model is as follows ,in Let be the coefficient of thermal expansion of the unit cell of the lattice along the normal direction of the base element of the isosceles triangle. The coefficient of thermal expansion is given by the rhomboid frame of the waist element and the diagonal metal material of the base element. Let be the coefficient of thermal expansion of the rhombic frame metal material of the waist element, diagonal, and base element. Let the side length of the waist-shaped rhombus frame be the basic element. The diagonal length of the waist element is... The side length of the bottom primitive rhombus frame. The length of the diagonal of the base element.

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