Thermal actuator for a satellite antenna support based on a metamaterial with adjustable thermal expansion coefficient

Abstract

This invention discloses a thermal actuator for a satellite antenna support based on a metamaterial with an adjustable coefficient of thermal expansion. The thermal actuator is composed of multiple bimaterial concave hexagonal units arranged in an array, installed below the platform of the satellite antenna support, and connected to the support arm. The low coefficient of thermal expansion beam (2) of the concave hexagonal unit is located within the frame of the high coefficient of thermal expansion beam (1) and is connected by mortise and tenon joints. The upper deformable rod (3) and the lower deformable rod (5) on the right end are mortised and tenoned to the right end of the high coefficient of thermal expansion beam (1), and the upper deformable rod (4) and the lower deformable rod (6) on the left end are mortised and tenoned to the left end of the high coefficient of thermal expansion beam (1). The concave hexagonal unit of this invention is driven to deform by flexible hinges, thereby obtaining a large rotation angle. By adjusting the beam length and hinge parameters of the concave hexagonal unit, different degrees of angular deformation can be achieved, resulting in a thermal actuator with adjustable positive / zero / negative coefficient of thermal expansion metamaterials.

Description

Technical Field

[0001] This invention relates to thermal actuators, and more particularly, to an actuator for adjusting the thermal stability of a satellite antenna support for use in environments with drastic temperature changes. The kinetic energy of the thermal actuator is mechanical energy, provided by a metamaterial with an adjustable coefficient of thermal expansion based on the operating temperature of the thermal actuator. Background Technology

[0002] Controlling the thermal expansion of materials has significant technical implications in scientific and engineering applications. Materials with high coefficients of thermal expansion can be used to construct thermal actuators for precision instrument components such as satellite antenna supports. Thermal dimensional stability is a crucial performance parameter for many space structures; environmental changes (including weightlessness, temperature, and vacuum) can affect the accuracy of large structures and satellite platforms. These Earth-orbiting satellites regularly transition from sunlight to shade and back; these transitions are typically accompanied by significant temperature variations. When adjacent components made of different materials are subjected to large temperature changes, the temperature variations and the difference in thermal expansion coefficients between the two materials generate thermal mismatch stresses. These thermal stresses are associated with undesirable deformations, which can degrade the operating environment of onboard instruments, for example, reducing the accuracy of optical telescopes or the positioning accuracy of space cameras. Furthermore, it can also cause structural fatigue and failure through long-term cycling.

[0003] The coefficient of thermal expansion of ordinary solid materials is limited and difficult to adjust due to the binding forces between particles in the lattice. A small number of materials with zero / negative coefficients of thermal expansion exist in nature, but these materials have limitations to varying degrees, such as high brittleness, narrow temperature range, and significant anisotropy. Guillaume first discovered Invar alloys with an exceptionally low coefficient of thermal expansion, but their low strength and high price limit their widespread application. Ceramic materials have low coefficients of thermal expansion, but they are brittle and prone to failure under varying environmental temperatures. In negative coefficient of thermal expansion metamaterials, the coefficient of thermal expansion can be effectively controlled by artificially designing and adjusting the geometry of micro-elements. These structures, acting as effective compensation for volume changes, can balance thermal stress under varying temperature conditions, maintaining good system stability. The principle of tunable coefficient of thermal expansion metamaterials is to use different combinations of materials to induce local bending / rotation within the structure's internal space by utilizing the differences in their thermal responses, thus generating an adjustable thermal expansion effect and providing a new approach to achieving zero / negative coefficients of thermal expansion.

[0004] Commonly used metamaterials with adjustable coefficient of thermal expansion are mainly of two types: double-beam bending-driven and tension-driven.

[0005] The foundation of a bending-driven structure is a double-layered beam composed of two materials. The straight double-layered beam transforms into an arc shape under a uniform temperature field, allowing for adjustable chord length with temperature variations. This theory was first proposed by Timoshenko. Because bending-driven structures achieve thermal contraction between two points, they require a large design space, and the stress is primarily bending stress. Furthermore, the interface between different materials is difficult to perfectly bond.

[0006] The deformation principle of tension-driven materials is based on the axial deformation of a rod as the ambient temperature changes. The most representative structure is a triangular unit cell composed of two materials, proposed by Miller et al. Subsequently, Lim and Lehman proposed three-dimensional bimaterial tetrahedral and octahedral truss lattices, respectively, to obtain customizable coefficients of thermal expansion in specific directions. Summary of the Invention

[0007] Currently, most metamaterials used in satellite antenna supports have limited thermal expansion coefficients and thus limited thermal deformation. This invention proposes a novel structural unit capable of large-angle deformation—a dual-material concave hexagonal unit, such as… Figure 1 The desired result is achieved by using a dual-material concave hexagonal unit cell, unlike traditional structural deformation principles, which employs flexible hinges to drive deformation, thus enabling the creation of large rotation angles. This dual-material concave hexagonal unit cell can be used to construct metamaterials with a significantly adjustable range of thermal expansion coefficients, and can also be applied to construct thermally responsive opening and closing windows. By controlling the beam length and hinge parameters, different degrees of angular deformation can be achieved, resulting in metamaterials with adjustable positive / zero / negative thermal expansion coefficients.

[0008] The dual-material concave hexagonal unit designed in this invention is a large-angle deformation unit composed of beams made of two materials with different coefficients of thermal expansion connected by flexible hinges, which converts differential linear thermal expansion into angular changes to amplify the thermal response. Beams of different materials, flexible hinges, and deformation amplification rods constitute the most basic thermal response angle deformation structure. The dual-material concave hexagonal unit is composed of a high coefficient of thermal expansion beam (1), a low coefficient of thermal expansion beam (2), an upper deformable rod (3) on the right end, an upper deformable rod (4) on the left end, a lower deformable rod (5) on the right end, and a lower deformable rod (6) on the left end; the low coefficient of thermal expansion beam (2) is located within the frame of the high coefficient of thermal expansion beam (1) and is connected by mortise and tenon joints; the upper deformable rod (3) on the right end and the lower deformable rod (5) on the right end are mortised and tenon jointed to the right end of the high coefficient of thermal expansion beam (1), and the upper deformable rod (4) on the left end and the lower deformable rod (6) on the left end are mortised and tenon jointed to the left end of the high coefficient of thermal expansion beam (1).

[0009] The dual-material concave hexagonal unit cell designed in this invention utilizes and amplifies the thermal deformation difference between different materials, enabling the dual-material concave hexagonal unit cell to achieve an exceptionally large amount of thermal deformation. Through simulation and experiments, a thermal actuator obtained by arranging multiple dual-material concave hexagonal unit cells in an array was found to have a lateral thermal expansion coefficient ranging from -2.7 × 10⁻⁶. -3 K -1 ~1.25×10 -3 K -1 The achievable range of thermal expansion coefficient in the longitudinal direction is -5.2 × 10⁻⁶. -3 K -1 ~1.97×10 - 2 K -1 The extremely wide range of adjustable thermal expansion allows the structure to be customized for use in precision instrument applications where environmental temperatures fluctuate drastically, such as satellite antenna supports. The design is tailored to the thermal expansion coefficient of the support material to compensate for thermal deformation of the original structure and to balance thermal stress under varying temperature conditions, ensuring the system maintains good stability.

[0010] The technical advantages of the dual-material concave hexagonal unit cell of this invention:

[0011] ① The coefficient of thermal expansion can be customized and adjusted to adjust structural parameters for different application scenarios. It can serve as an effective compensation for volume changes and balance thermal stress in environments with temperature changes, so that the satellite antenna support still has good stability.

[0012] ② The designed dual-material concave hexagonal unit configuration has a wide range of positive / negative thermal expansion coefficient adjustment range, -5.2×10 -3 K -1 ~1.97×10 -2 K -1 Its coefficient of thermal expansion far exceeds that of metamaterial array structures in existing research, making it applicable to a wider range of fields.

[0013] ③ The isotropic / anisotropic properties can be customized. By adjusting the axial length, angle and flexible hinge thickness ratio of the high and low thermal expansion coefficient beams, a dual-material concave hexagonal unit can be customized.

[0014] ④ Since the thermal expansion characteristics of the bimaterial concave hexagonal unit are independent of scale, it can be applied to macroscopic, microscopic and even nanoscale. With the development of micro-nano 3D printing technology, it will be easier to realize the transformation of structures to the micrometer level in the future. Attached Figure Description

[0015] Figure 1 This is a structural diagram of the concave hexagonal unit in the thermal actuator of the satellite antenna support based on the adjustable thermal expansion coefficient metamaterial of the present invention.

[0016] Figure 1A yes Figure 1 The exploded diagram.

[0017] Figure 1B yes Figure 1 Another perspective breakdown diagram.

[0018] Figure 2 This is a front view of the concave hexagonal unit body of the present invention.

[0019] Figure 2A yes Figure 2 Top view.

[0020] Figure 2B yes Figure 2 A three-dimensional image.

[0021] Figure 2C yes Figure 2 Another perspective stereoscopic view.

[0022] Figure 2D This is a structural diagram of the concave hexagonal unit body of the present invention without the deformable rods assembled.

[0023] Figure 2E yes Figure 2C A-A cross-section.

[0024] Figure 3 This is a front view of the array arrangement of multiple concave hexagonal units of the present invention.

[0025] Figure 3A This is another perspective of the array arrangement structure of multiple concave hexagonal units of the present invention.

[0026] Figure 3B This is a structural diagram of the concave hexagonal unit array of the present invention, which is then installed on the satellite antenna support platform below.

[0027] Figure 4 This is a top view of the beam with a high thermal expansion coefficient in the concave hexagonal unit cell of the present invention.

[0028] Figure 4A This is a bottom view of the beam with a high thermal expansion coefficient in the concave hexagonal unit cell of the present invention.

[0029] Figure 4B This is a front view and a partial enlarged view of the beam with a high thermal expansion coefficient in the concave hexagonal unit cell of the present invention.

[0030] Figure 4C This is a first-view structural diagram of the beam with a high thermal expansion coefficient in the concave hexagonal unit body of the present invention.

[0031] Figure 4DThis is a second-view structural diagram of the beam with a high thermal expansion coefficient in the concave hexagonal unit body of the present invention.

[0032] Figure 4E This is a third-view structural diagram of the beam with a high thermal expansion coefficient in the concave hexagonal unit cell of the present invention.

[0033] Figure 4F This is a fourth-view structural diagram of a beam with a high thermal expansion coefficient in the concave hexagonal unit cell of the present invention.

[0034] Figure 5 This is a structural diagram of a beam with a low coefficient of thermal expansion in the concave hexagonal unit cell of the present invention.

[0035] Figure 5A This is a first-view structural diagram of the beam with a low thermal expansion coefficient in the concave hexagonal unit body of the present invention.

[0036] Figure 5B This is a second-view structural diagram of the beam with a low thermal expansion coefficient in the concave hexagonal unit body of the present invention.

[0037] Figure 5C This is a structural diagram of the right end of the beam with a low thermal expansion coefficient in the concave hexagonal unit cell of the present invention.

[0038] Figure 5D This is a structural diagram of the left end of the beam with a low thermal expansion coefficient in the concave hexagonal unit body of the present invention.

[0039] Figure 6 This is a structural diagram of the upper and lower deformable rods on the right end of the concave hexagonal unit body of the present invention.

[0040] Figure 7 This is a structural diagram of the upper and lower deformable rods at the left end of the concave hexagonal unit body of the present invention.

[0041] Figure 8 This is a schematic diagram of the large-angle deformation structure of the thermal response of an array of concave hexagonal units during operation.

[0042] Figure 9 It is to change the initial angle of the concave structure Keeping l constant and the flexible hinge thickness 0.15mm, the graph shows the change in the coefficient of thermal expansion of the structure in the x and y directions.

[0043]

[0044] Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings. The examples of the parameters listed are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0046] See Figure 3 , Figure 3A , Figure 3B As shown, this invention discloses a thermal actuator for a satellite antenna support based on a metamaterial with an adjustable coefficient of thermal expansion. The thermal actuator is formed by arranging multiple bimaterial concave hexagonal unit cells in an array. Figure 3 , Figure 3A A thermal actuator, formed by an array of concave hexagonal units, is mounted below the upper platform of the satellite antenna support. Figure 3B Located between the upper platform and the support arm, the thermal actuator's upper mounting surface connects to the lower part of the upper platform, and its lower mounting surface connects to the support arm. When the ambient temperature of the satellite antenna support increases during service, the satellite antenna support will undergo significant axial thermal expansion, while the thermal actuator will undergo significant vertical contraction, becoming thinner, to counteract the platform rise caused by the thermal expansion of the satellite antenna support and maintain the thermal stability of the entire upper platform. Traditionally, an additional instrument or device is used to control the airborne ambient temperature. However, the temperature control device not only occupies a large amount of payload weight but also consumes a large amount of onboard energy, placing a heavy burden on the satellite.

[0047] See Figure 1 , Figure 1A , Figure 1B As shown, the dual-material concave hexagonal unit body designed in this invention is composed of a beam with a high thermal expansion coefficient 1, a beam with a low thermal expansion coefficient 2, an upper deformable member 3 at the right end, an upper deformable member 4 at the left end, a lower deformable member 5 at the right end, and a lower deformable member 6 at the left end.

[0048] Among them, the upper deformable member 3 on the right end and the lower deformable member 5 on the right end have the same structure.

[0049] Among them, the upper deformable member 4 on the left end and the lower deformable member 6 on the left end have the same structure.

[0050] There is a narrow gap C 23 between the AA frame 11 of the high thermal expansion coefficient beam 1 and the BA crossbeam 2A of the low thermal expansion coefficient beam 2; there is a narrow gap C 24 between the AD frame 14 of the high thermal expansion coefficient beam 1 and the BC crossbeam 2C of the low thermal expansion coefficient beam 2. There is a narrow gap A 21 between the BA crossbeam 2A and the BB crossbeam 2B of the low thermal expansion coefficient beam 2; there is a narrow gap B 22 between the BB crossbeam 2B and the BC crossbeam 2C. The narrow gap design between the high thermal expansion coefficient beam 1 and the low thermal expansion coefficient beam 2 is beneficial for the expansion avoidance of the thermal actuator when it is in operation in a high-temperature environment.

[0051] In this invention, the high thermal expansion coefficient beam (1) of the dual-material concave hexagonal unit is made of PE material, while the others are made of ABS material, all fabricated using 3D printing technology. The 3D printing technology is referenced from the article "Research Status and Development Trend of FDM-based 3D Printing Technology" published in the June 2015 issue, Vol. 43, No. 6 of *New Chemical Materials*. Figure 1 Authors include Tang Tongming, Zhang Zheng, Deng Jiawen, and others.

[0052] High thermal expansion coefficient beam 1

[0053] See Figure 1 , Figure 1A , Figure 1B , Figure 4 , Figure 4A , Figure 4B , Figure 4C , Figure 4D , Figure 4E , Figure 4F As shown, the high thermal expansion coefficient beam 1 is surrounded by AA border 11, AB border 12, AC border 13, AD border 14, AE border 15 and AF border 16; among them, AB border 12 and AC border 13 are arranged symmetrically from top to bottom, and AE border 15 and AF border 16 are arranged symmetrically from top to bottom.

[0054] See Figure 1B As shown, the left end of the AA frame 11 is provided with an AA through hole 11A, and a BA transverse pin 2F is installed in the AA through hole 11A; the right end of the AA frame 11 is provided with an AK through hole 11B, and a BA longitudinal pin 2D is installed in the AK through hole 11B.

[0055] See Figure 1B As shown, an AD through hole 14A is provided on the left end of the AD frame 14, and a BB transverse pin 2G is installed in the AD through hole 14A; an AI through hole 14B is provided on the right end of the AD frame 14, and a BB longitudinal pin 2E is installed in the AI ​​through hole 14B.

[0056] See Figure 4 , Figure 4A As shown, at the left end of the high thermal expansion coefficient beam 1, there are upper tenon block 1B (B), upper tenon block 1C (C), lower tenon block 10B (B), and lower tenon block 10C (C). Upper tenon block 1B and lower tenon block 10B are parallel vertically, and upper tenon block 1C and lower tenon block 10C are parallel vertically. At the right end of the high thermal expansion coefficient beam 1, there are tenon block 17, upper tenon block 1A (A), and lower tenon block 10A (A).

[0057] See Figure 2E As shown, the tenon 17 is installed in the mortise 2B3 near the left end of the BB crossbeam 2B of the low thermal expansion coefficient beam 2.

[0058] The upper tenon 1A is placed in the upper tenon 2B1 at the right end of the crossbeam 2B of the low thermal expansion coefficient beam 2.

[0059] The lower tenon 10A is placed in the lower tenon 2B2 at the right end of the BB crossbeam 2B of the low thermal expansion coefficient beam 2.

[0060] The upper tenon 1B is placed in the upper tenon groove 2C1 at the left end of the BC crossbeam 2C of the low thermal expansion coefficient beam 2.

[0061] The lower tenon 10B is placed in the lower tenon groove 2C2 at the left end of the BC crossbeam 2C of the low thermal expansion coefficient beam 2.

[0062] The tenon 1C is placed in the tenon groove 2A1 on the left end of the BA crossbeam 2A of the low thermal expansion coefficient beam 2.

[0063] The lower tenon 10C is placed in the lower tenon 2A2 at the left end of the BA crossbeam 2A of the low thermal expansion coefficient beam 2.

[0064] See Figure 4B , Figure 4C , Figure 4D , Figure 4E , Figure 4F As shown, the AB frame 12 is provided with AB through hole 12A and AC through hole 12B, and the bottom plate of the AB frame 12 is provided with AA rivet 12C.

[0065] CA rivet 3B1 of the C support plate 3B of the right-end upper deformable rod 3 is installed in the AB through hole 12A;

[0066] The AC through hole 12B contains the C support plate 3B of the right-end upper deformable rod 3 and the CB rivet 3B2.

[0067] The AA rivet 12C is placed in the C through hole 3B3 of the upper deformable member 3 on the right end.

[0068] See Figure 4B , Figure 4C , Figure 4D , Figure 4E , Figure 4F As shown, the AC frame 13 is provided with AG through hole 13A and AH through hole 13B, and the top plate of the AC frame 13 is provided with AB rivet 13C.

[0069] The EA rivet 5B1 of the E support plate 5B of the right end lower deformable rod 5 is installed in the AG through hole 13A.

[0070] The E support plate 5B of the right end lower deformable rod 5 is installed in the AH through hole 13B with EB rivet 5B2.

[0071] The AB rivet 13C is placed in the E through hole 5B3 of the right end lower deformable member 5.

[0072] See Figure 4B , Figure 4C , Figure 4D , Figure 4E , Figure 4F As shown, the AE frame 15 is provided with AE through hole 15A and AF through hole 15B, and the bottom plate of the AE frame 15 is provided with AC rivet 15C, EA tenon 15D and EB tenon 15E.

[0073] The AE through hole 15A contains the DA rivet 4B1 of the D support plate 4B of the left-end upper deformable rod 4.

[0074] DB rivet 4B2 of the D support plate 4B of the left-end upper deformable rod 4 is installed in the AF through hole 15B.

[0075] The AC rivet 15C is placed in the D through hole 4B3 of the deformable rod 4 on the left end;

[0076] The EA tenon block 15D is placed in the DA tenon groove 4B4 of the D support plate 4B of the left-end upper deformable rod 4.

[0077] The EB tenon 15E is placed in the DB tenon 4B5 of the D support plate 4B of the upper deformable rod 4 on the left end.

[0078] See Figure 4B , Figure 4C , Figure 4D , Figure 4E , Figure 4F As shown, the AF frame 16 is provided with AI through hole 16A and AJ through hole 16B, and the top plate of the AF frame 16 is provided with AD rivet 16C, FA tenon 16D and FB tenon 16E.

[0079] The AI ​​through hole 16A contains the FA rivet 6B1 of the F support plate 6B of the left end lower deformable rod 6;

[0080] The F support plate 6B of the left-end lower deformable rod 6 is installed in the AJ through hole 16B with FB rivet 6B2.

[0081] The AD rivet 16C is placed in the F through hole 6B3 of the F support plate 6B of the lower deformable member 6 at the left end;

[0082] The FA tenon block 16D is placed in the FA tenon groove 6B4 of the F support plate 6B of the lower deformable rod 6 at the left end;

[0083] The FB tenon 16E is placed in the FB tenon 6B5 of the F support plate 6B of the lower deformable rod 6 at the left end.

[0084] Low thermal expansion coefficient beam 2

[0085] See Figure 1 , Figure 1A , Figure 1B , Figure 5 , Figure 5A , Figure 5B , Figure 5C , Figure 5D As shown, the low thermal expansion coefficient beam 2 is provided with a BA crossbeam 2A, a BB crossbeam 2B, and a BC crossbeam 2C. There is a narrow gap A 21 between the BA crossbeam 2A and the BB crossbeam 2B, and a narrow gap B 22 between the BB crossbeam 2B and the BC crossbeam 2C. There is a narrow gap C 23 between the BA crossbeam 2A and the AA frame 11 of the high thermal expansion coefficient beam 1. There is a narrow gap D 24 between the BC crossbeam 2C and the AD frame 14 of the high thermal expansion coefficient beam 1. The narrow gap design between the high thermal expansion coefficient beam 1 and the low thermal expansion coefficient beam 2 is beneficial for preventing expansion of the thermal actuator when it operates in a high-temperature environment.

[0086] A longitudinal pin 2D is provided on the outer side of the right end of the BA beam 2A, and the longitudinal pin 2D passes through the AK through hole 11B of the AA frame 11 of the high thermal expansion coefficient beam 1. The left end of the BA beam 2A is provided with an upper mortise 2A1 and a lower mortise 2A2. The upper mortise 2A1 is used to place the upper tenon 1C of the left end of the high thermal expansion coefficient beam 1. The lower mortise 2A2 is used to place the lower tenon 10C of the left end of the high thermal expansion coefficient beam 1.

[0087] The right end of the BB beam 2B is provided with an upper tenon 2A1 and a lower tenon 2A2. The upper tenon 2A1 is used to place the upper tenon block 1A of the right end of the beam 1 with a high coefficient of thermal expansion. The lower tenon 2A2 is used to place the lower tenon block 10A of the right end of the beam 1 with a high coefficient of thermal expansion.

[0088] A longitudinal pin 2E (BB) is provided on the outer side of the right end of the BC beam 2C. The longitudinal pin 2E (BB) passes through the AL through hole 14B of the AD frame 14 of the high thermal expansion coefficient beam 1. The left end of the BC beam 2C has an upper mortise 2C1 (C) and a lower mortise 2C2 (C). The upper mortise 2C1 (C) is used to place the upper tenon 1B (B) of the left end of the high thermal expansion coefficient beam 1. The lower mortise 2C2 (C) is used to place the lower tenon 10B (B) of the left end of the high thermal expansion coefficient beam 1.

[0089] A longitudinal connecting plate 2H is provided below the left end of the low thermal expansion coefficient beam 2. The longitudinal connecting plate 2H is used to enhance the support force of the left end of the low thermal expansion coefficient beam 2. A BA transverse pin 2F is provided above one end of the longitudinal connecting plate 2H, and a BB transverse pin 2G is provided above the other end of the longitudinal connecting plate 2H. The BA transverse pin 2F passes through the AA through hole 11A of the AA frame 11 of the high thermal expansion coefficient beam 1. The BB transverse pin 2G passes through the AD through hole 14A of the AD frame 14 of the high thermal expansion coefficient beam 1.

[0090] In this invention, in order to enhance the stability of the right end of the thermal actuator, a mortise 2B3 for placing the tenon block 17 is provided on the BB crossbeam 2B at the left end of the low thermal expansion coefficient beam 2.

[0091] Right end upper deformable member 3

[0092] See Figure 1 , Figure 1A , Figure 6 As shown, the upper deformable member 3 on the right end has a C-deformation plate 3A and a C-support plate 3B. The C-support plate 3B has a C-through hole 3B3, and the inner side of the C-support plate 3B has a CA rivet 3B1 and a CB rivet 3B2.

[0093] The C-hole 3B3 contains the AA rivet 12C below the AB frame 12 of the high thermal expansion coefficient beam 1.

[0094] The CA rivet 3B1 is installed in the AB through hole 12A of the AB frame 12 of the high thermal expansion coefficient beam 1.

[0095] The CB rivet 3B2 is installed in the AC through hole 12B of the AB frame 12 of the high thermal expansion coefficient beam 1.

[0096] See Figure 1 , Figure 1A , Figure 1B , Figure 6 As shown, the lower deformable member 5 at the right end has an E-deformation plate 5A and an E-support plate 5B. The E-support plate 5B has an E-through hole 5B3, and the inner side of the E-support plate 5B has an EA rivet 5B1 and an EB rivet 5B2.

[0097] The AB rivet 13C above the AC frame 13 of the high thermal expansion coefficient beam 1 is placed inside the E through hole 5B3.

[0098] The EA rivet 5B1 is installed in the AG through hole 13A of the AC frame 13 of the high thermal expansion coefficient beam 1.

[0099] The EB rivet 5B2 is installed in the AH through hole 13B of the AC frame 13 of the high thermal expansion coefficient beam 1.

[0100] Left end upper deformable rod 4

[0101] See Figure 1 , Figure 1A , Figure 7 As shown, the upper deformable member 4 on the left end has a D deformable plate 4A and a D support plate 4B. The D support plate 4B is provided with a D through hole 4B3, a DA tenon 4B4, and a DB tenon 4B5. The inner side of the D support plate 4B is provided with a DA rivet 4B1 and a DB rivet 4B2.

[0102] The AC rivet 15C is placed below the AE frame 15 of the high thermal expansion coefficient beam 1 inside the D through hole 4B3.

[0103] The DA rivet 4B1 is installed in the AE through hole 15A of the AE frame 15 of the high thermal expansion coefficient beam 1.

[0104] The DB rivet 4B2 is installed in the AF through hole 15B of the AE frame 15 of the high thermal expansion coefficient beam 1.

[0105] The EA tenon block 15D is placed below the AE frame 15 of the high thermal expansion coefficient beam 1 inside the DA tenon 4B4.

[0106] The DB tenon 4B5 contains the EB tenon block 15E below the AE frame 15 of the high thermal expansion coefficient beam 1.

[0107] See Figure 1 , Figure 1A , Figure 1B , Figure 7 As shown, the lower deformable member 6 at the left end has an F deformable plate 6A and an F support plate 6B. The F support plate 6B is provided with an F through hole 6B3, an FA tenon 6B4, and an FB tenon 6B5. The inner side of the F support plate 6B is provided with an FA rivet 6B1 and an FB rivet 6B2.

[0108] The AD rivet 16C is placed above the AF frame 16 of the high thermal expansion coefficient beam 1 inside the F through hole 6B3.

[0109] The FA rivet 6B1 is installed in the AI ​​through hole 16A of the AF frame 16 of the high thermal expansion coefficient beam 1.

[0110] The FB rivet 6B2 is installed in the AJ through hole 16B of the AF frame 16 of the high thermal expansion coefficient beam 1.

[0111] The FA tenon block 16D is placed above the AF frame 16 of the high thermal expansion coefficient beam 1 within the FA tenon groove 6B4.

[0112] The FB tenon 16E is placed inside the FB tenon 6B5 above the AF frame 16 of the beam 1 with a high thermal expansion coefficient.

[0113] Concave hexagonal unit cell structure dimensions

[0114] See Figure 1 , Figure 2D As shown, due to the need for miniaturized and lightweight structures for satellite antenna supports, the structural dimensions of the dual-material concave hexagonal unit are designed based on the length, width, and height of the high thermal expansion coefficient beam 1. The length of the high thermal expansion coefficient beam 1 is denoted as a (unit, mm), the width as b (unit, mm), and the height as c (unit, mm). Figure 1 As shown, the included angle of the bimaterial concave hexagonal unit cell is denoted as . The distance between the upper and lower deformable parts is denoted as k (unit: mm).

[0115] The included angle It is equal to 4.0 degrees to 60 degrees. The value of k is 0.6 mm.

[0116] The c is equal to 3mm, a is equal to 21c~23c, and b is equal to 4.5c~6c.

[0117] See Figure 8 As shown, the design of the dual-material concave hexagonal unit of this invention considers two beams made of materials with high thermal expansion coefficients and one beam made of materials with low thermal expansion coefficients, enabling bilateral angular deformation. Symmetrical hinges are added in the vertical direction, each connecting to a deformable member, enabling four-way angular deformation. The high thermal expansion coefficient is denoted as C1, and the low thermal expansion coefficient as C2. At room temperature, both beams have an initial length of x0 (i.e., the lengths of beam 1 (high thermal expansion coefficient) and beam 2 (low thermal expansion coefficient) are the same). Flexible hinges are located at the ends of the beams, and the center-to-center distance between the two hinges is d (keeping the length l of the deformable member constant). After a temperature change ΔT, the angle changes of the two beams are similar. Based on the deformation principle, the effective angle change of the hinges is calculated as follows: The size of structural angular deformation and (C1-C2), ΔT, and flexible hinge thickness h b ,h a Highly relevant. Figure 8 In the middle, h b h represents the thickness of the flexible hinge on a beam with a low coefficient of thermal expansion. a x1 is the thickness of the flexible hinge on the beam with a high coefficient of thermal expansion, x2 is the length of the beam with a low coefficient of thermal expansion after heating, x1 is the length of the beam with a high coefficient of thermal expansion after heating, and θ is the effective angle of the hinge after heating.

[0118] Figure 8This is a schematic diagram of a large-angle deformation structure of a bimaterial concave hexagonal unit cell during operation, considering its thermal response. The outer beams and hinges are designed as beam 1 with a high coefficient of thermal expansion, while the inner beams are designed as beam 2 with a low coefficient of thermal expansion. The symmetrical structural design ensures more balanced stress on the hinges. As the temperature rises, the beams with higher coefficients of thermal expansion become longer, exerting pressure on the connected structure; the beams with lower coefficients of thermal expansion exert tension on the connected structure. Due to the different hinge positions of the beams and connectors made of different materials, bending moments can be generated on the end members, causing them to rotate around the flexible hinges. Based on this principle, the structure can be designed with five beams to obtain a unit cell with four-way synchronous angular deformation. The outermost beam is made of a material with a high coefficient of thermal expansion, and the middle three beams are made of a material with a low coefficient of thermal expansion. The ends of the central beam BB2B, beams BA2A and BC2C are fixed at both ends by upper and lower deformable members, as shown below. Figure 1 As shown, this method achieves a unit with synchronous deformation in two directions (X and Z). Furthermore, symmetrical hinges and members are added in the Z direction, allowing 14 hinges to rotate using 5 beams. All hinges are made of materials with a high coefficient of thermal expansion and are classified as flexible hinges a and b based on the material of the connected members. The direction of hinge rotation can be changed by altering the sign of the distance d between hinges a and b. The rotation amplitude of the hinges under the same temperature change can be altered by changing the beam length, the value of the hinge distance d, and the hinge thickness. Therefore, by designing different numbers of end members, the versatility of structural combinations is greatly enhanced.

[0119] Change the initial angle of the concave structure Simulation was performed. Keeping l constant and the flexible hinge thickness constant at 0.15mm, the initial angle of the concave structure was gradually changed. The coefficients of thermal expansion were obtained at different temperatures ranging from 20 to 60°C. Data from 22°C were used to plot the coefficients of thermal expansion in the x and y directions. It can be seen that when... As the length and angle increase, the thermal expansion coefficient of the structure becomes more pronounced in the x-direction, while it decreases significantly in the y-direction. This result can be explained by the principle of structural deformation. With a constant change in rod length and angle, the more compact the initial structure... The smaller the coefficient of thermal expansion (COP), the easier it is for the structure to achieve a large coefficient of thermal expansion in the y-direction. And when the initial structure is sufficiently porous... At that time, the increase in temperature causes the structure to expand significantly in all directions, such as Figure 9 As shown.

[0120] Example 1

[0121] This invention utilizes a dual-material concave hexagonal unit body manufactured using dual-material 3D printing, which simplifies the fabrication of dual-material structures. The 3D printer used for sample fabrication is an FDM dual-nozzle printer, Snapmaker J1S, using PE and ABS materials. The PE nozzle has a melting temperature of 220°C, while the ABS nozzle temperature is 250°C, and the base plate temperature is 85°C. Due to the different melting temperatures of the two materials, interlocking tenon and mortise structures (tenon and groove) are added at the joints to ensure stable connection of the parts requiring fixation in the 3D printed structure. Because of the high FDM molding temperature, the printed part, designed to be flat, will hinge and rotate after returning to room temperature. Therefore, the sample is in a state of large deformation at room temperature, and this initial state will be used for temperature testing.

[0122] The dual-material concave hexagonal unit cell used in the simulation performance test has a total length L = 81 mm, a total width B = 17 mm, and a total height H = 13 mm. Figure 2 , Figure 2A As shown. The initial beam length x0 = 70 mm for the low thermal expansion coefficient beam and the high thermal expansion coefficient beam, and the hinge thickness h. a =h b =0.3m, hinge neutral layer spacing d=0.5mm, included angle It is 4.4 degrees, such as Figure 8 As shown.

[0123] The properties of a bimaterial concave hexagonal element were calculated using finite element analysis (FEA). A steady-state temperature-displacement coupling module was used, and numerical simulations were performed in ABAQUS / Standard. The constituent materials were set to PE and ABS, with Young's moduli E and E, respectively. a =0.5GPa, E b =2GPa, Poisson's ratio μ a =μ b =0.3, and their coefficients of thermal expansion are respectively c a =2×10 -4 K -1 and c b =7.3×10 -5 K -1 Boundary conditions were set with the left end face of the beam fixed, assuming a temperature range from 20℃ to 100℃. Photographs of the sample at different temperatures were acquired using a camera (Canon M6 II). Throughout the experiment, the camera's focal length and the sample's position remained unchanged. Rotation angles at different temperatures were measured on the camera-acquired images using Photoshop software. The experiment yielded angular deformations of a novel structural unit similar to those obtained in simulations.

[0124] Change the initial angle of the concave structure Simulation was performed. Keeping l constant and the flexible hinge thickness constant at 0.15mm, the initial angle of the concave structure was gradually changed. The coefficients of thermal expansion were obtained at different temperatures ranging from 20 to 60°C. Data from 22°C were used to plot the coefficients of thermal expansion in the x and y directions. It can be seen that when... As the length and angle increase, the thermal expansion coefficient of the structure becomes more pronounced in the x-direction, while it decreases significantly in the y-direction. This result can be explained by the principle of structural deformation. With a constant change in rod length and angle, the more compact the initial structure... The smaller the coefficient of thermal expansion (COP), the easier it is for the structure to achieve a large coefficient of thermal expansion in the y-direction. And when the initial structure is sufficiently porous... At that time, the increase in temperature causes the structure to expand significantly in all directions.

[0125] See Figure 3B As shown, a metamaterial thermal actuator with an adjustable coefficient of thermal expansion is used in a satellite antenna support. The thermal actuator is formed by an array of bimaterial concave hexagonal units, which can provide -2.79 × 10⁻⁶ thermal expansion coefficients. -3 K -1 ~1.97×10 -2 K -1 An adjustable scheme for isotropic / anisotropic positive / negative thermal expansion coefficients within a given range is presented. By changing the rod length and the thickness and gap ratio of the flexible hinges, the anisotropy and thermal expansion coefficients of the array structure can be customized, and theoretical calculations are provided. Simulations verify that based on this principle, near-isotropic negative thermal expansion behavior and large anisotropic positive thermal expansion performance can be obtained over a wide range.

[0126] Simulations were performed on an array structure with an abnormally large negative coefficient of thermal expansion. The isotropic structure can achieve a coefficient of thermal expansion of -2.7 × 10⁻⁶ in the x-direction. -3 K -1 Anisotropic structures achieve -4.48 × 10⁻⁴ in the x-direction. -3 K -1 The coefficient of thermal expansion in the y-direction is -6.3 × 10⁻⁶. -4 K -1 Experiments were conducted on a prototype array structure with an abnormally large positive thermal expansion coefficient. Unit samples were fabricated using 3D printing, and the assembled test structure achieved large anisotropic positive thermal expansion performance similar to the simulation results. The lateral achievable thermal expansion coefficient of the array structure prototype was 1.25 × 10⁻⁶. -3 K -1 The achievable coefficient of thermal expansion in the longitudinal direction is 1.97 × 10⁻⁶. -2 K -1 The results are similar to those obtained from simulations of the positive thermal expansion coefficient. Finite element analysis and prototype experiments verified that the structure can effectively control thermal expansion and compensate for the thermal deformation of conventional materials in the antenna support legs.

[0127] By arraying the structure into thin-plate metamaterials with negative thermal expansion coefficients and applying them to the top of the satellite payload mounting platform support, the thermal expansion of the support legs can be compensated for during drastic changes in ambient temperature. Furthermore, the compensation parameters can be specifically designed and adjusted based on the thermal expansion coefficients of the component materials. This approach maintains structural stability without the need for additional equipment temperature control, significantly reducing the effective payload carried by the satellite while minimizing its energy consumption.

[0128] The thermal actuator of this satellite antenna mount can provide -2.79 × 10⁻⁶. -3 K -1 ~1.97×10 -2 K -1 An adjustable isotropic / anisotropic positive / negative thermal expansion coefficient scheme was developed. Finite element simulation and prototype experiments demonstrated the effectiveness of this method in controlling thermal deformation. Applied to the top of a satellite payload mounting platform support, it effectively isolates residual thermal expansion and improves overall structural stability. Because the thermal expansion coefficient characteristics of this structure do not require additional energy consumption, it offers a significant advantage over traditional energy-intensive thermal control technologies. Furthermore, this structure is scale-independent and can be applied to macroscopic, microscopic, and even nanoscale applications. With the development of micro / nano 3D printing technology, it will be easier to achieve the transformation of structures to the micrometer scale in the future, demonstrating exceptional potential for practical engineering applications.

Claims

1. A thermal actuator for a satellite antenna support based on a metamaterial with an adjustable coefficient of thermal expansion, said thermal actuator being fabricated from two materials with different coefficients of thermal expansion; characterized in that: A thermal actuator, formed by multiple concave hexagonal units arranged in an array, is mounted below the upper platform of the satellite antenna support. The thermal actuator is composed of multiple arrayed dual-material concave hexagonal units; The dual-material concave hexagonal unit is composed of a high thermal expansion coefficient beam (1), a low thermal expansion coefficient beam (2), a right-end upper deformable member (3), a left-end upper deformable member (4), a right-end lower deformable member (5), and a left-end lower deformable member (6). A low thermal expansion coefficient beam (2) is set within the frame of the high thermal expansion coefficient beam (1) and is connected by mortise and tenon joints; The upper deformable member (3) on the right end is tenon-jointed to the lower deformable member (5) on the right end of the high thermal expansion coefficient beam (1); The upper deformable member (4) on the left end is mortised and tenoned with the lower deformable member (6) on the left end to form the left end of the high thermal expansion coefficient beam (1); Among them, the upper deformable member (3) on the right end has the same structure as the lower deformable member (5) on the right end; Among them, the upper deformable member (4) on the left end has the same structure as the lower deformable member (6) on the left end; Among them, the low thermal expansion coefficient beam (2), the upper deformable member on the right end (3), the upper deformable member on the left end (4), the lower deformable member on the right end (5), and the lower deformable member on the left end (6) are made of the same material with the same thermal expansion coefficient. The thermal actuator obtained by arranging the dual-material concave hexagonal unit cells in an array has a transverse thermal expansion coefficient of [value missing]. The coefficient of thermal expansion of longitudinal energy is ; The high thermal expansion coefficient beam (1) includes a frame (11, 12, 13, 14, 15, 16) surrounding the perimeter; tenons (1B, 1C, 10B, 10C, 17, 1A, 10A) are provided at the left and right ends for mortise and tenon connection with the low thermal expansion coefficient beam (2); through holes (11A, 11B, 14A, 14B, 12A, 12B, 13A, 13B, 15A, 15B, 16A, 16B) and rivets (12C, 13C, 15C, 16C) for riveting with deformable members are provided on each frame, as well as tenons (15D, 15E, 16D, 16E) for mortise and tenon connection with deformable members. The low thermal expansion coefficient beam (2) includes three crossbeams (2A, 2B, 2C) arranged side by side, with small gaps between adjacent crossbeams; and there are small gaps between the crossbeams and the frame of the high thermal expansion coefficient beam (1); the small gaps facilitate the expansion avoidance of the thermal actuator when it is in operation in a high temperature environment; each crossbeam end is provided with a mortise (2A1, 2A2, 2B1, 2B2, 2B3, 2C1, 2C2) for tenon-mortise connection with the high thermal expansion coefficient beam (1); and it is also provided with longitudinal pins (2D, 2E) and transverse pins (2F, 2G) for positioning connection with the high thermal expansion coefficient beam (1); The upper deformable member (3) on the right end includes a deformable plate and a support plate. The support plate is provided with through holes and rivets on the inner side, which are used to connect with the corresponding through holes and rivets on the frame of the high thermal expansion coefficient beam (1). The upper deformable member (4) on the left end includes a deformable plate and a support plate. The support plate is provided with through holes, tenons and rivets on the inner side, which are used to connect with the corresponding through holes, rivets and tenons on the frame of the high thermal expansion coefficient beam (1). The right end lower deformable member (5) includes a deformable plate and a support plate. The support plate is provided with through holes and rivets on the inner side, which are used to connect with the corresponding through holes and rivets on the frame of the high thermal expansion coefficient beam (1). The lower deformable member (6) at the left end includes a deformable plate and a support plate. The support plate is provided with through holes, tenons and rivets on the inner side, which are used to connect with the corresponding through holes, rivets and tenons on the frame of the high thermal expansion coefficient beam (1).

2. The thermal actuator for a satellite antenna support based on an adjustable thermal expansion coefficient metamaterial according to claim 1, characterized in that: The thermal response angular deformation of the dual-material concave hexagonal unit body is a flexible hinge mode in which the tenon and mortise are engaged.

3. The thermal actuator for a satellite antenna support based on an adjustable thermal expansion coefficient metamaterial according to claim 1, characterized in that: The high thermal expansion coefficient beam (1) in the dual-material concave hexagonal unit is made of PE material, while the beams other than the high thermal expansion coefficient beam (1) are made of ABS material.

4. The thermal actuator for a satellite antenna support based on an adjustable thermal expansion coefficient metamaterial according to claim 1, characterized in that: The dual-material concave hexagonal unit is fabricated using 3D printing technology.

5. The thermal actuator for a satellite antenna support based on an adjustable thermal expansion coefficient metamaterial according to claim 1, characterized in that: The dimensions of the miniaturized high thermal expansion coefficient beam (1) are denoted as a, b, and c, respectively, and the included angle of the bimaterial concave hexagonal unit is denoted as . Let k be the distance between the two deformed parts, then there is an included angle. =4.0 degrees to 60 degrees, spacing k is 0.6 mm, c=3 mm, a=21c to 23c, b=4.5c to 6c.

6. The thermal actuator for a satellite antenna support based on an adjustable thermal expansion coefficient metamaterial according to claim 1, characterized in that: The thermal actuator is mounted between the upper platform and the support arm of the satellite antenna bracket.

7. The thermal actuator for a satellite antenna support based on an adjustable thermal expansion coefficient metamaterial according to claim 1, characterized in that: The thermal actuator mounted below the upper platform of the satellite antenna bracket is a multi-layer array of dual-material concave hexagonal units.

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