Composite laminate structure embedded with ni-ti alloy wire, and preparation method and application thereof

CN120003141BActive Publication Date: 2026-10-30SHENYANG AEROSPACE UNIVERSITY
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Patent Information

Application Number
CN202510159097.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-02-13
Publication Date
2026-10-30
Estimated Expiration
2045-02-13

AI Technical Summary

Technical Problem

对于振动阻尼装置,目前包括阻尼器在内的装置虽能满足减振需求,但其往往需要留有安装位置和额外供能,不能满足新能源飞机的空间要求和轻量化设计要求

Benefits of technology

[0024]1)本发明提出了一种嵌入NiTi形状记忆合金丝的抗振复合材料层压板结构设计,不但重量轻、耐疲劳性能优异,而且具有增强复合材料结构的抗振能力以及一体化加工特性。

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Abstract

The application belongs to the technical field of vibration control, and particularly relates to a composite laminate structure embedded with NiTi alloy wires and a preparation method and application thereof. The preparation method comprises the following steps: fixing two ends of a plurality of NiTi alloy wires on a wire embedding mold to form an alloy wire surface; symmetrically arranging a first layer plate part and a second layer plate part on the upper and lower surfaces of the alloy wire surface, arranging an initial pressure bottom plate below the first layer plate part, and arranging an initial pressure top plate above the second layer plate part; applying a first pressure to the initial pressure top plate and the initial pressure bottom plate to form a preform structure of the first layer plate part, the alloy wire surface and the second layer plate part; and high-temperature and high-pressure solidification molding. The composite laminate structure is prepared by the above method. The laminate structure can be applied to a wall plate of a new energy aircraft. The composite laminate structure provided by the application is light in weight, good in fatigue resistance, and can enhance the vibration resistance of the composite structure and can be integrally processed.
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Description

Technical Field

[0001] This invention belongs to the field of vibration control technology, specifically relating to the structure and application of composite laminates embedded with NiTi shape memory alloy wires. Background Technology

[0002] In recent years, with the widespread application of composite laminate structures in transportation fields such as aerospace, new energy vehicles, and new energy aircraft, their performance has been challenged when dealing with complex working conditions. In actual working environments, composite structures will vibrate under external impact or continuous excitation, leading to failure and damage. Previous solutions to this problem have included selecting high-performance composite materials, optimizing composite structure design, and thickening excessive vibration sections. However, these methods are often accompanied by difficulties in material selection, high processing costs, design complexity, and failure to meet lightweight structural design requirements, thus limiting their practical application.

[0003] To overcome this deficiency, designing a vibration damping reinforcement structure for composite materials that meets requirements such as strong applicability, low processing difficulty, and lightweight design has gradually become a focus of research and practice. While current vibration damping devices, including dampers, can meet vibration reduction needs, they often require installation space and additional power supply, which cannot meet the space requirements and lightweight design requirements of new energy aircraft. Summary of the Invention

[0004] This invention proposes a composite laminate structure embedded with NiTi shape memory alloy wire, which not only has strong mechanical properties and good vibration resistance, but also achieves structural-functional integration in processing and design.

[0005] The technical solution adopted by this invention to solve the technical problem is:

[0006] A method for preparing a composite laminate structure embedded with NiTi alloy wires, characterized by comprising the following steps:

[0007] Step 1: Fix the two ends of several NiTi alloy wires arranged along the first direction and / or the second direction onto the wire inserting mold to form an alloy wire surface;

[0008] Step 2: Lay a first layer plate under the alloy wire surface and lay a second layer plate on the alloy wire surface. The first layer plate and the second layer plate are symmetrically arranged. A preliminary pressure bottom plate is set below the first layer plate and a preliminary pressure top plate is set above the second layer plate.

[0009] Step 3: Apply a first pressure to the initial pressure top plate and the initial pressure bottom plate to form a prefabricated structure from the first layer plate, the alloy wire surface and the second layer plate.

[0010] Step 4: Cut off the exposed NiTi alloy wire between the prefabricated structure and the embedded mold, and then perform high temperature and high pressure curing to form a composite material laminate structure with embedded NiTi alloy wire.

[0011] In the above-mentioned method for preparing composite laminate structure, step 4 uses an autoclave for high-temperature and high-pressure curing.

[0012] In the above-mentioned method for preparing composite laminate structure, the high-temperature and high-pressure curing molding pressure is 4-5 standard atmospheres, the temperature is 100-150℃, and the processing time of the high-temperature and high-pressure curing molding is 4-6 hours.

[0013] In the above-mentioned method for preparing composite laminate structure, the first pressure is the weight of a 10-20 kg mass block, and the duration of applying the first pressure to the initial pressure top plate and the initial pressure bottom plate is ≥30 min.

[0014] In the above-mentioned method for preparing composite laminate structure, the first direction is transverse and the second direction is longitudinal;

[0015] In the above-mentioned method for preparing composite laminate structure, the spacing between adjacent NiTi alloy wires is 10~30 mm;

[0016] In the above-mentioned method for preparing composite laminate structure, the diameter of the NiTi alloy wire is 0.1~0.4 mm.

[0017] In the above-mentioned method for preparing composite material laminate structure, the first layer includes 2N layers of fiber composite material, and the second layer includes 2N layers of fiber composite material, wherein N=1, 2, 3, 4, 5.

[0018] In the above-mentioned method for preparing composite laminate structure, the fiber composite material layer is made of carbon fiber prepreg or glass fiber composite material.

[0019] In the above-mentioned method for preparing composite laminate structure, the wire insert mold includes a square frame, a clamping and fixing block is provided on the square frame, a semi-circular groove is provided on the square frame, and a semi-circular protrusion is provided on the clamping and fixing block. The shape and number of the semi-circular groove and the semi-circular protrusion are matched to fix the NiTi alloy wire.

[0020] In the above-mentioned method for preparing composite laminate structure, the shapes of the initial pressure top plate and the initial pressure bottom plate match the shape of the square frame and are slightly smaller than the space enclosed by the square frame.

[0021] A composite material laminate structure embedded with NiTi alloy wires is prepared by the above-described preparation method. The composite material laminate structure includes: an alloy wire surface, and a first layer portion and a second layer portion symmetrically arranged along the alloy wire surface; the first layer portion and the second layer portion are connected to the alloy wire surface by hot pressing and curing.

[0022] An application of a composite laminate structure embedded with NiTi alloy wires is described above, where the wall panels of a new energy aircraft are made of the aforementioned composite laminate structure embedded with NiTi alloy wires.

[0023] By employing the above technical solution, the present invention has at least the following advantages:

[0024] 1) This invention proposes a vibration-resistant composite material laminate structure design with embedded NiTi shape memory alloy wire, which is not only lightweight and has excellent fatigue resistance, but also enhances the vibration resistance of the composite material structure and has integrated processing characteristics.

[0025] 2) This invention provides a theoretical analysis method for vibration suppression schemes based on NiTi shape memory alloy wires, providing a theoretical research approach for the design of embedded wire layouts in reinforced structures.

[0026] 3) This invention discloses the application of reinforced vibration-resistant composite material laminate structure in the field of new energy aircraft, namely: using the processing method of this invention to manufacture vibration-resistant reinforced composite material laminate, and providing corresponding manufacturing molds.

[0027] 4) Vibration tests were conducted on the processed vibration-damping reinforced composite laminate to verify the feasibility of the method proposed in this invention.

[0028] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, the preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0029] Figure 1a This is a schematic diagram of the mold for preparing the composite material laminate structure embedded with NiTi alloy wire according to the present invention;

[0030] Figure 1b This is a top view of the wire-embedding mold used in the preparation of the composite laminate structure embedded with NiTi alloy wires according to the present invention;

[0031] Figure 1cThis is a partially enlarged view of the long fixed outer frame strip and clamping fixing block of the wire-inserting mold of the present invention;

[0032] Figure 2a This is an exploded structural diagram of the composite material laminate structure with embedded NiTi alloy wires of the present invention;

[0033] Figure 2b This is a cross-sectional schematic diagram of the composite material laminate structure embedded with NiTi alloy wires according to the present invention;

[0034] Figure 3 This is a dynamic model diagram of the vibration-resistant scheme of the composite laminate structure with embedded NiTi alloy wires of the present invention;

[0035] Figure 4a This is a diagram showing the theoretical analysis results comparing the vibration suppression effects of the vibration enhancement scheme of configuration 1 of the present invention;

[0036] Figure 4b This is a diagram showing the theoretical analysis results comparing the vibration suppression effects of the vibration enhancement scheme of configuration 2 of the present invention;

[0037] Figure 5a This is a schematic diagram of the structure of the vibration suppression experimental verification device of the present invention under the first boundary condition;

[0038] Figure 5b This is a schematic diagram of the vibration suppression experimental verification device of the present invention under the second boundary condition;

[0039] Figure 6a These are diagrams illustrating the vibration reduction effect of the unreinforced composite laminate of the present invention at different temperatures;

[0040] Figure 6b These are diagrams illustrating the vibration reduction effect of the longitudinally embedded composite laminate of the present invention at different temperatures.

[0041] Figure 6c These are diagrams illustrating the vibration reduction effect of the transversely embedded composite laminate of the present invention at different temperatures;

[0042] Figure 7a This is an experimental data graph showing the vibration reduction effect of the transverse embedding scheme of the present invention on vibration damping reinforced composite laminate;

[0043] Figure 7b This is an experimental data graph showing the vibration reduction effect of the longitudinal embedding scheme of the present invention on vibration damping reinforced composite laminate;

[0044] Figure 7c This is an experimental data graph showing the vibration reduction effect of the staggered embedding scheme of the present invention on vibration damping reinforced composite laminate;

[0045] Figure 8aThis is an experimental data graph showing the vibration reduction effect of the multi-resonance peak of the vibration damping reinforced composite laminate under an acceleration excitation of 0.2g according to the present invention;

[0046] Figure 8b This is an experimental data graph showing the vibration reduction effect of the multi-resonance peak of the vibration damping reinforced composite laminate under an acceleration excitation of 0.3g according to the present invention;

[0047] Figure 8c This is an experimental data graph showing the vibration reduction effect of the multi-resonance peak of the vibration damping reinforced composite laminate under an acceleration excitation of 0.5g according to the present invention. Detailed Implementation

[0048] To further illustrate the technical means and effects of the present invention in achieving the intended purpose, the following detailed description of the specific implementation methods, structures, features and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0049] Preparation method examples

[0050] This embodiment discloses a method for preparing a composite laminate structure embedded with NiTi alloy wires, including the following steps:

[0051] Step 1: Fix the two ends of several NiTi alloy wires arranged along the first direction and / or the second direction onto the wire inserting mold to form an alloy wire surface;

[0052] Step 2: Lay a first layer plate under the alloy wire surface and lay a second layer plate on the alloy wire surface. The first layer plate and the second layer plate are symmetrically arranged. A preliminary pressure bottom plate is set below the first layer plate and a preliminary pressure top plate is set above the second layer plate.

[0053] Step 3: Apply a first pressure to the initial pressure top plate and the initial pressure bottom plate to form a prefabricated structure from the first layer plate, the alloy wire surface and the second layer plate.

[0054] Step 4: Cut off the exposed NiTi alloy wire between the prefabricated structure and the embedded mold, and then perform high temperature and high pressure curing (in this embodiment, a hot autoclave is specifically used for high temperature and high pressure curing). The resulting composite plate structure is a composite material laminate structure with embedded NiTi alloy wire.

[0055] The composite laminate structure prepared by the method for preparing a composite laminate structure embedded with NiTi alloy wire proposed in this invention is not only lightweight and has excellent fatigue resistance, but also has enhanced vibration resistance and integrated processing characteristics.

[0056] In the preparation method of this invention, an alloy wire surface is first prepared, and then a laminate portion is symmetrically arranged on the upper and lower surfaces of the alloy wire surface. The laminate portion is initially fixed to the alloy wire surface by pressure. Since the diameter of the NiTi alloy wires constituting the alloy wire surface is between 0.1 and 0.4 mm, they are very prone to curling during the preparation of the composite laminate structure. This results in the prepared composite laminate structure not matching the theoretical modeling and analysis, causing the predictions in the theoretical analysis to fail. In addition, it can also lead to stress concentration at the curling points, thereby causing the composite laminate structure to lose dynamic stability and reducing vibration reduction efficiency.

[0057] In the preparation method of the present invention, by first forming a prefabricated structure, the alloy wire surface between the first layer plate and the second layer plate can be embedded into the flexible first layer plate and the second layer plate by the first pressure applied by the initial pressure top plate and the initial pressure bottom plate. Thus, even after the exposed NiTi alloy wire is cut, the planar structure is basically maintained. In addition, it can also ensure that the cut NiTi alloy wire remains straight.

[0058] Through the combined action of the insert mold and pressure plate provided by this invention, the alloy wire layer is positioned in the middle of the two composite layers and parallel to them. Since the NiTi alloy wire and the composite prepreg are two different materials with different densities, if the NiTi wire layer is not in the middle position (i.e., the composite layer is not symmetrical along the alloy wire mesh), it will cause a shift in the center of gravity of the laminate, affecting the dynamic stability of the structure. Furthermore, the NiTi wire layer cannot move in accordance with the shape of the laminate, resulting in a displacement difference between the NiTi wire and the composite structure. In severe cases, this may cause delamination of the laminate, affecting its service life.

[0059] This invention, through high-temperature and high-pressure curing, enables the composite laminate structure embedded with NiTi alloy wires to maintain the mechanical properties of the laminate.

[0060] In order to better shape the composite laminate structure embedded with NiTi alloy wire, this embodiment further limits the pressure and temperature of the autoclave and the processing time. The high temperature and high pressure curing molding pressure is 4 standard atmospheres, the temperature is 120°C, and the processing time is 5 hours.

[0061] The first pressure is the weight of a 10kg mass block, and the duration of applying the first pressure to the initial pressure top plate and the initial pressure bottom plate is 30 minutes.

[0062] As a possible implementation method, the pressure for high-temperature and high-pressure curing can also be 5 standard atmospheres.

[0063] As a possible implementation method, the temperature of the high-temperature and high-pressure curing molding can be any value between 100-150°C.

[0064] As a possible implementation method, the processing time for the high-temperature and high-pressure curing molding can be any value between 4 and 6 hours.

[0065] As a possible implementation, the first pressure is the gravity provided by a mass block of any weight, ranging from 10 to 20 kg.

[0066] As a possible implementation, the duration for which the first pressure is applied to the initial pressure top plate and the initial pressure bottom plate is >30 minutes.

[0067] In order to achieve the initial fixation of the alloy wire, this embodiment specifically uses a wire-inserting mold to fix both ends of the alloy wire.

[0068] The wire-embedding mold includes a square frame, a clamping block on the square frame, a semi-circular groove on the square frame, and a semi-circular protrusion on the clamping block. The shape and number of the semi-circular groove and the semi-circular protrusion are matched to fix the NiTi alloy wire. The shape of the initial pressure top plate and the initial pressure bottom plate matches the shape of the square frame and is slightly smaller than the space enclosed by the square frame.

[0069] The fixed outer frame has a hollowed-out section for placing the clamping block, and a semi-circular groove is provided in the hollowed-out section.

[0070] The fixed outer frame includes two short fixed outer frame strips 101 and two long fixed outer frame strips 102. The two long fixed outer frame strips 102 are arranged parallel to each other, and the two short fixed outer frame strips 101 are also arranged parallel to each other. The shape formed by connecting the two short fixed outer frame strips 101 and the two long fixed outer frame strips 102 is rectangular. The number and position of the hollow parts and semi-circular grooves provided on the long fixed outer frame strips 102 are matched, so that the steel wire rope fixed thereon is parallel and straight. Similarly, the number and position of the hollow parts and semi-circular grooves provided on the short fixed outer frame strips 101 are matched.

[0071] The shapes of the initial pressing top plate and the initial pressing bottom plate match the internal space of the support frame and are slightly smaller than the internal space of the frame, thereby enabling the initial pressing of the initial pressing top plate and the initial pressing bottom plate onto the laminate portion. During the initial pressing process of the initial pressing top plate and the initial pressing bottom plate onto the laminate portion, the support base of the wire insert mold will not obstruct the initial pressing process, thereby enabling full pressing of the laminate and the alloy wire surface.

[0072] The square frame includes a support base and four fixed outer frame strips. The support base has studs, and the fixed outer frame strips have threaded holes. No additional bolts are needed; the height of the square frame can be adjusted by adjusting the connection height between the studs and the threaded holes. The specific assembly process of the alloy wire is as follows: First, fix the support base and fixed outer frame to form a 'U' shape. Then, place the base plate inside the 'U' shape, then place the lower half of the composite material plate, and then perform the wire embedding operation.

[0073] The assembly process of the alloy wire is as follows: First, place the alloy wire into the hollow part in the middle of the fixed outer frame strip, that is, into the recessed semi-circular groove inside the hollow part. Then, place the clamping block on top, so that the semi-cylindrical protrusion inside the clamping block fits into the semi-cylindrical groove inside the hollow part. Then, use a bolt to hold the fixing block in place through the threaded hole on the fixing strip, thus clamping one end of the NiTi alloy wire. After fixing one end of the NiTi alloy wire, straighten the NiTi alloy wire, and then place the straightened other end into the hollow part of the fixed outer frame strip on the other side. Repeat the operation of clamping the fixing block to fix the NiTi wire.

[0074] The composite material laminate structure prepared by the method of the present invention embedding NiTi alloy wire includes, from top to bottom: a first layer plate part, an alloy wire surface and a second layer plate part, as shown in Figure 1.

[0075] The alloy wire surface is spatially located in the middle of the laminate, equidistant from the top and bottom layers of the laminate. This alloy wire surface is the embedded area of ​​the reinforcing vibration-damping material, which is a NiTi shape memory alloy wire. Preferably, a wire-type NiTi shape memory alloy damping reinforcement device with strong hysteretic damping effect is selected to improve the vibration reduction effect. Further, the diameter of the NiTi shape memory alloy wire ranges from 0.1 to 0.4 mm. Preferably, a 0.2 mm diameter NiTi shape memory alloy wire is selected to ensure the vibration reduction effect and prevent shearing or breakage of the prepreg carbon fiber filaments in the laminate due to excessively large wire diameter.

[0076] In specific implementation, the first direction is transverse, and the second direction is longitudinal; that is, the NiTi alloy wire laying method can include the following: 1) a gold wire surface composed only of multiple transversely laid NiTi alloy wires; 2) a gold wire surface composed only of multiple longitudinally laid NiTi alloy wires; 3) a gold wire surface composed of multiple transversely laid NiTi alloy wires and multiple longitudinally laid NiTi alloy wires. Specifically: the alloy wire surface includes several longitudinally arranged NiTi shape memory alloy wires; or the alloy wire surface includes several transversely arranged NiTi shape memory alloy wires; or the alloy wire surface includes several transversely and longitudinally interwoven NiTi shape memory alloy wires.

[0077] In practical implementation, the spacing between adjacent NiTi alloy wires laid horizontally or vertically is 10-30 mm; the diameter of the NiTi alloy wire is 0.1-0.4 mm. In practical implementation, the NiTi alloy wire is a NiTi shape memory alloy wire. The NiTi alloy wire used in this embodiment is a black 0.1 mm or 0.2 mm NiTi alloy wire purchased from Guangdong Southeast Nickel-Titanium Alloy Materials Co., Ltd.

[0078] Furthermore, the NiTi shape memory alloy wires are embedded in various ways, including transverse embedding, longitudinal embedding, and crisscross embedding, with a spacing of 10mm between each wire. In the case of crisscross embedding, the NiTi shape memory alloy wires are embedded in a crisscross pattern, with a spacing of 20mm between wires in the same direction.

[0079] In this embodiment, the processing dimensions of the composite material laminate structure are selected as 250mm in length and 150mm in width. The spacing of the NiTi alloy wires is 10mm. Alternatively, the processing dimensions of the fiber composite material layer can range from 50 to 1000mm.

[0080] In this embodiment, when the NiTi shape memory alloy wire is embedded in the transverse direction, the number of embedded wires is 14; when the NiTi shape memory alloy wire is embedded in the longitudinal direction, the number of embedded wires is 24. Further, the NiTi shape memory alloy wire is embedded in a staggered transverse and longitudinal manner, with a spacing of 30mm between alloy wires in the same direction. When the NiTi shape memory alloy wire is embedded in a staggered transverse and longitudinal manner, the number of embedded wires is 8 in the transverse direction and 13 in the longitudinal direction.

[0081] In a specific implementation, the first layer plate includes 2N layers of fiber composite material, and the second layer plate includes 2N layers of fiber composite material, wherein N = 1, 2, 3, 4, 5.

[0082] The fiber composite material layer is made of carbon fiber prepreg or glass fiber composite. The prepreg material is soft during initial pressing and embedding, but hardens after hot pressing.

[0083] In specific implementation, the fiber composite material layer described in this embodiment is made of unidirectional carbon fiber prepreg purchased from Shanghai Xin'ao Composite Materials Technology R&D Center, with specific specifications of T700-12K / 100g / resin 36%.

[0084] Both the first and second layer plates include 2N layers of fiber composite material. In specific implementations, the specific value of N can be any value among 1, 2, 3, 4, or 5, depending on the processing requirements. In this way, the number of composite material layers in both the first and second layer plates is even and symmetrically arranged.

[0085] Because of the fiber composite layer, the layup angle of the fiber composite layer can be determined according to the fiber direction. In specific implementations, to ensure the symmetry of the first and second layer plates, the layup angle of the fiber composite layer in the symmetrical layers of the first and second layer plates is the same, and the layup angle is determined according to the fiber direction. The layup angle can be 0°, 90°, or ±45°. The material selected for the second layer plate must be the same as that selected for the first layer plate.

[0086] In this embodiment, the processing material for the fiber composite material layer is T700 carbon fiber composite prepreg, with a single layer thickness of 0.1 mm. The first layer has 10 layers, and the layup angle is [0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°]. When the layup angle is different, attention should be paid to the symmetry of the first and second layers, and the layup angles of the first and second layers should also be symmetrical along the alloy wire plane. The number of layers in the second layer should be the same as the number of layers in the first layer. Therefore, in this embodiment, the number of layers in the second layer is 10. The layup angle of the second layer should be symmetrical with respect to the alloy wire plane of the first layer, and the layup angle of the second layer is [90°, 0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°, 0°].

[0087] In this way, the alloy wire surface can be positioned between the first and second layer plates, and the first and second layer plates are symmetrically arranged along the alloy wire surface. Therefore, it can directly replace existing composite laminates without embedded alloy wires. The composite laminate needs to be symmetrical about the neutral layer during processing, mainly to avoid warping, deformation, or cracking of the laminate due to thermal residual stress or external forces, thereby ensuring its mechanical properties and structural stability. Specifically, this is to avoid deformation caused by thermal residual stress, ensure consistency of mechanical properties, improve dimensional stability, and simplify design and analysis.

[0088] Figure 2 shows the layer distribution diagram and cross-sectional schematic diagram of the composite laminate structure embedded with NiTi alloy wire.

[0089] To further verify the vibration reduction effect of the composite laminate structure embedded with NiTi alloy wire prepared by the method of this invention, the vibration resistance of a transverse embedding scheme with 14 transverse wires, a longitudinal embedding scheme with 24 longitudinal wires, and a staggered embedding scheme with 8 transverse and 13 longitudinal wires were further tested. This invention provides a theoretical analysis method for vibration suppression schemes based on NiTi shape memory alloy wires, offering a theoretical research approach for the design of embedding layouts in reinforced structures.

[0090] The dynamic model diagram of the vibration-resistant scheme of the reinforced composite laminate with embedded NiTi shape memory alloy wire of the present invention is shown below. Figure 3 Based on the aforementioned dynamic model, the displacement equation for the composite laminate is established:

[0091] (1)

[0092] Where u, v, and w represent the displacements of the plate structure about the x, y, and z directions, respectively. The stress-strain relationship between the plates is as follows:

[0093] (2)

[0094] (3)

[0095] The kinetic equations for the reinforced composite laminate with embedded NiTi shape memory alloy wires are established using Hamilton's principle:

[0096] (4)

[0097] Where T is the kinetic energy of the structure, U is the potential energy of the structure, δ is the variational sign, and δW f It is the virtual work done by external forces on the laminated plate structure, δW smaThis is the virtual work done by the damping component, composed of NiTi shape memory alloy wires, to resist vibration. Furthermore, let's analyze the terms in the equation:

[0098] (5)

[0099] and These are the dimensionless components of the laminated plate structure in the x and y directions. The stiffness matrix [R] is established based on the classical ABD theory:

[0100] (6)

[0101] Temperature potential energy U T writing:

[0102] (7)

[0103] Structural kinetic energy T writing:

[0104] (8)

[0105] Virtual work δW f and δW sma writing:

[0106] (9)

[0107] Where f(t) represents the external force; m and a b Let f represent the structural mass and the external force acceleration, respectively, and δw be the virtual displacement of the structure; sma This represents the damping force provided by the NiTi-SMA shape memory alloy wire; χ is the damping coefficient; Δ hori Δ vert and Δ cross The Dirac function represents different embedding enhancement schemes, and its magnitude is related to the embedding position and number of NiTi shape memory alloy wires; k1 and k3 are the stiffness terms of the NiTi shape memory alloy wires; c1 and r 21 and r 12 The damping term for NiTi shape memory alloy wire is given in Table 1.

[0108] Table 1 Material parameters of NiTi shape memory alloy wire

[0109]

[0110] The dynamic equations of a vibration suppression scheme based on NiTi shape memory alloy wires were theoretically analyzed, and the theoretical frequency sweep results of the amplitude of the reinforced composite laminate with embedded NiTi shape memory alloy wires were compared with those of a conventional composite laminate (without embedded alloy wires). A comparison of the amplitude at the midpoint of the laminate was conducted to obtain a comparison of the effects of three vibration-resistant reinforcement schemes, such as... Figure 4a and Figure 4b As shown.

[0111] As shown in the figure, theoretically speaking, the reinforcement schemes calculated using the mechanical parameters of NiTi shape memory alloy wires with configurations F1 and F2 (transverse embedding: 14 wires; longitudinal embedding: 24 wires; cross-embedded embedding: 8 wires in the transverse direction and 13 wires in the longitudinal direction) can significantly suppress vibration in composite laminates in all three embedding states.

[0112] To verify the vibration suppression performance of composite laminates, this invention establishes a vibration suppression experimental verification platform for reinforced vibration-resistant composite laminates. The vibration suppression experimental verification platform includes experimental specimens and fixtures, a loading system, an environmental simulation device, and a data acquisition system. Further, the experimental specimens and fixtures include both reinforced vibration-resistant and general-type composite laminates, and the experimental fixtures are vibration suppression experimental devices, such as... Figure 5a and Figure 5b As shown. The loading system refers to the system that provides the external force to the experimental specimen to induce vibration. It can be composed of a vibration table, a vibrator, or other force-applying devices. Preferably, the present invention uses a vibration table system as the loading system. The environmental simulation device refers to the system that provides a simulation of the external environment experienced by the cockpit front panel of a new energy aircraft during operation. Preferably, the present invention uses a temperature chamber to provide an experimental environment with different temperatures and humidity levels for the vibration suppression experiment. The experimental temperature range is -20℃ to 120℃, and the humidity range is 30% to 98% RH. The data acquisition system refers to the system that, during the experiment, the accelerometer on the experimental specimen receives the acceleration signal generated by the vibration, and the data acquisition system converts a series of signals into visualized experimental results. Preferably, the present invention uses an LMS data processing system.

[0113] The vibration suppression experimental verification device includes a base plate, a support plate, fixed angle brackets, a support frame, fixed blocks, and a composite material laminate. The base plate is bolted to the vibration table platform and can be adjusted by different mounting hole positions to simulate different force directions on the composite material laminate. Furthermore, adjusting the base plate's mounting position allows the laminate to experience force at 0°, ±45°, and 90°. The support plate is mounted on the base plate and connected by the fixed angle brackets. One end of the support frame is bolted to the support plate, and the other end is connected to the fixed blocks and the composite material laminate. Eight fixed blocks are installed at each of the four corners on both the front and rear sides of the composite material laminate and are bolted to the support frame.

[0114] This invention also discloses a vibration suppression experimental verification platform and method, comprising the following steps:

[0115] Step 1: First, fabricate an experimental specimen of reinforced vibration-resistant composite laminate and a control group experimental specimen, i.e., a composite laminate without embedded wire reinforcement.

[0116] Step 2: Then design and fabricate the components of the vibration suppression experimental device;

[0117] Step 3: Install the vibration suppression experimental device on the vibration table loading system and adjust its working frequency range and excitation range. Further, the working frequency range is 10-2000Hz and the excitation range is 0.1-2.0g, where g refers to gravitational acceleration.

[0118] Step 4, the environmental simulation device includes an adjustable temperature chamber and a humidity control module, which are installed on the vibration suppression experimental device to realize simulation experiments under different temperatures and humidity levels. The chamber can isolate the influence of environmental noise and other factors on the vibration test results during the vibration test. Further, a temperature chamber is selected as the environmental simulation device described above.

[0119] Step 5: Install the high-precision sensor and determine its installation position on the experimental piece to obtain accurate measurement data. Furthermore, this invention selects a high-precision lightweight accelerometer for vibration suppression experimental testing.

[0120] Step 6: Following the installation procedure of the vibration suppression experimental verification device, after adjusting the installation status of the experimental piece, start the vibration table, record and analyze the vibration response of the system.

[0121] Figure 1 shows a schematic diagram of the processing mold used in the preparation method of the composite laminate structure embedded with NiTi alloy wires provided in this embodiment. The NiTi alloy wires can enhance the vibration damping performance of the composite laminate, i.e., suppress the vibration of the composite laminate. The processing mold for the composite laminate structure embedded with NiTi alloy wires includes an embedding mold and a pressure plate (including a primary pressure base plate 105 and a primary pressure top plate 106). The embedding mold includes four fixed outer frame strips (two short fixed outer frame strips 101 and two long fixed outer frame strips 102), a support base 103, a clamping block 104, and mounting bolts 107. The embedding positions are as follows... Figure 2b As shown.

[0122] In the processing mold for the composite material laminate structure embedded with NiTi alloy wire, the installation quantity and installation relationship of each component are as follows: The two short fixed outer frame strips 101 and the two long fixed outer frame strips 102 are connected by bolts to complete the construction of the square outer frame (the internal space and hollow part of the square outer frame), thereby establishing the wire embedding space of the composite material laminate structure; the support base 103 is connected to the short fixed outer frame strips 101 by its own studs, and its height can be adjusted to achieve the horizontality of the wire embedding mold. Furthermore, this example requires 4 support bases; the clamping and fixing block 104 is installed between the short fixed outer frame strips 101 and the long fixed outer frame strips 102 according to the specific wire embedding requirements. In the mounting groove, the semi-cylindrical protrusion on each clamping block is aligned with the semi-cylindrical groove in the mounting groove. The upper end of the clamping block is tightened by mounting bolts installed on the fixed outer frame, thereby fixing the lower end of the clamping block to the groove of the mounting groove. Furthermore, NiTi shape memory alloy wire is fixed between the clamping block and the groove of the mounting groove. The initial pressure base plate 105 is placed in the middle of the fixed outer frame, with its upper end level with the bottom end of the mounting groove between the short fixed outer frame strip 101 and the long fixed outer frame strip 102. The initial pressure top plate 106 is placed horizontally on the second layer plate 302 of the composite material to press the composite material laminate.

[0123] In specific implementation, the processing flow of the processing mold for the composite material laminate structure embedded with NiTi alloy wire can be carried out according to the following steps:

[0124] Step 1: Place the first layer plate 301 horizontally on the initial pressing base plate 105;

[0125] Step 2: Connect the short fixed outer frame strip 101 and the long fixed outer frame strip 102 in sequence using the mounting bolts 107, and adjust the height of the support base 103 to ensure that the fixed outer frame is horizontal;

[0126] Step 3: According to the requirements of the embedded wire reinforcement scheme, place the NiTi shape memory alloy wire 201 in the semi-cylindrical groove of the mounting slot of the fixed outer frame, and then place the clamping and fixing block 104 on it and tighten it with the mounting bolts.

[0127] Step 4: It should be noted that after fixing one end of the NiTi shape memory alloy wire 201, the other end needs to be fixed after tightening to ensure that the NiTi shape memory alloy wire in the embedding space is embedded in the neutral layer of the composite laminate in a straight line.

[0128] Step 5: After the above-mentioned wire embedding work is completed, place the second layer plate 302 of the composite material on the bottom layer 301 and the NiTi shape memory alloy wire 201 that has been embedded, and then cover it horizontally with the initial pressure plate 106 and press it tightly.

[0129] After the above steps are completed, the internal processing of the vibration damping reinforced composite material laminate is finished. The next step is to form the experimental specimen. First, a weight is placed on the initial pressure plate 106 to press the experimental specimen firmly. Preferably, a 10kg weight is used for pressing for 30 minutes. Second, after pressing, the weight is removed, and the NiTi shape memory alloy wire between the outer surface of the vibration damping reinforced composite material laminate and the outer frame of the processing mold is cut off, and the experimental specimen is removed. Third, the experimental specimen with the embedded NiTi shape memory alloy wire is hot-pressed and cured to complete the final specimen forming. Preferably, a hot autoclave is used for high-temperature and high-pressure processing, with a pressure of 4 standard atmospheres, a temperature of 120℃, and a processing time of 5 hours. The alloy wire and the laminate are hot-pressed and cured together, and the physical properties of the laminate remain unchanged. The alloy wire and the composite material laminate are tightly fixed together.

[0130] This invention proposes a dynamic analysis method based on embedded wire design, constructs a vibration suppression model, verifies the vibration resistance performance under various layout schemes, and validates its performance through an experimental testing platform. This invention is applicable to vibration control needs in new energy aircraft and aerospace fields, providing new theoretical and technical support for the design and application of efficient vibration-resistant structures.

[0131] like Figure 5aAs shown, this embodiment provides a vibration suppression experimental platform and a specific process for verifying the vibration suppression capability of a composite laminate structure embedded with NiTi alloy wires. The vibration suppression verification platform includes a vibration suppression experimental verification device (experimental piece and fixture), a loading system, an environmental simulation device, and a data acquisition system. The vibration suppression experimental device includes an experimental device base plate 401, a support plate 402, a fixing angle rod 403, a support frame 404, a fixing block 405-1, and a vibration damping reinforced composite laminate 406. The installation process of the vibration suppression experimental verification device can be carried out according to the following steps:

[0132] Step 1: According to the preparation method of the composite laminate structure embedded with NiTi alloy wire, complete the processing of the vibration damping enhanced composite laminate, and process each component of the fixture part in the vibration suppression experimental verification device;

[0133] Step 2: The experimental device base plate 401 is fixed to the loading system by mounting bolts. Preferably, the present invention uses a vibration table system as the loading system, and the base plate 401 is installed on the vibration table platform.

[0134] Step 3: The support plate 402 is vertically installed on the base plate 401. The two components are fixed by the fixing angle 403. Furthermore, the fixing angle is connected to the support plate and the base plate by mounting bolts.

[0135] Step 4: One end of the support frame 404 is bolted to the support plate 402, and the other end is bolted to the experimental piece composed of the fixing block 405-1 and the composite material laminate 406.

[0136] Step 5: The fixing blocks are installed at the four corners of the composite material laminate 406, four blocks at the front and four at the back, and are bolted to the support frame 404. Furthermore, according to the installation requirements, the composite material laminate 406 has through holes at the corresponding positions at the four corners of the laminate to meet the installation requirements on the experimental device.

[0137] The above is the installation procedure for the vibration suppression experimental verification device. After completing the above work, the vibration suppression capability of the vibration-damping reinforced composite laminate can be verified. The specific procedure for verifying the vibration suppression capability can be carried out according to the following steps:

[0138] Step 1: Install the vibration suppression experimental device on the vibration table loading system and adjust its working frequency range and excitation range. Further, the working frequency range is 20-1000Hz, and the excitation range is 0.1-2.0g, where g refers to gravitational acceleration.

[0139] Step 2, the environmental simulation device includes an adjustable temperature chamber and a humidity control module, which are installed on the vibration suppression experimental device to realize simulation experiments under different temperatures and humidity levels. The chamber can isolate the influence of environmental noise and other factors on the vibration test results during the vibration test. Further, a temperature chamber is selected as the environmental simulation device described above.

[0140] Step 3: Install the high-precision sensor and determine its installation position on the experimental piece to obtain accurate measurement data. Furthermore, this invention selects a high-precision lightweight accelerometer for vibration suppression experiment testing.

[0141] Step 4: Following the installation procedure of the vibration suppression experimental verification device, after adjusting the installation status of the experimental piece, start the vibration table, record and analyze the vibration response of the system.

[0142] After the above steps are completed, vibration suppression experiments can be conducted to verify the vibration suppression capability of the reinforced structure designed in this invention. To comprehensively verify the vibration suppression capability, this invention conducted two sets of vibration test experiments to verify the vibration reduction capability of the vibration suppression scheme provided by this invention at different temperatures, as well as the vibration reduction capability of different NiTi shape memory alloy wire embedding schemes.

[0143] Vibration damping capacity at different temperatures:

[0144] This embodiment tested the vibration damping effect of the vibration-damping reinforced composite laminate at different temperatures using vibration tests. The results are shown in Figure 6. Figure 6a Midpoint frequency sweep experimental data representing unreinforced composite laminates. Figure 6b and Figure 6c The data presented represent midpoint frequency sweep experiments on vibration-damping reinforced composite laminates with longitudinal and transverse embedding schemes, respectively. Further, the frequency sweep range of the loading device is 200-1100Hz, the acceleration excitation provided by the vibration table is 0.3g, and the temperature range provided in the temperature chamber is -20℃ to 115℃. Experimental data are summarized at 15℃ intervals. The results show that the reinforced design with embedded NiTi shape memory alloy wires provided by this invention can achieve vibration suppression under different temperatures and embedding schemes. Preferably, transverse embedding provides better vibration reduction.

[0145] The vibration damping reinforced composite laminate test at different temperatures can be conducted according to the following steps:

[0146] Step 1: According to the specific process of vibration suppression capability verification, the vibration suppression experimental device shown is installed on the vibration table platform, and then the experimental piece is installed on the vibration suppression experimental device. Further, a high-precision lightweight accelerometer is installed at the midpoint of the experimental piece. Preferably, in this example, the accelerometer is installed by adhesive bonding.

[0147] Step 2: Install the environmental simulation device, preferably a temperature chamber in this example, on the vibration suppression experimental device to provide a constant temperature and humidity space for the experimental piece, and set the temperature to -20℃. Further, the experimental piece in this step is the unreinforced composite laminate.

[0148] Step 3: After the installation status of the vibration suppression experimental device and the environmental simulation device is adjusted, the vibration table is started to conduct vibration testing. The vibration test acceleration excitation range is 0.1-2.0g, preferably 0.3g in this example. The vibration test frequency range is 10-2000Hz, preferably 200-1100Hz in this example. Furthermore, after the vibration test is completed, the data acquisition system can obtain the amplitude-frequency response curve of the experimental piece. In this example, the data acquisition system is preferably an LMS system.

[0149] Step 4: After completing the experimental tests in Step 3, the experimental results of the unreinforced composite laminate at -20℃ can be obtained. Then, turn on the temperature chamber and set the temperature to -5℃. After the temperature stabilizes, repeat the operation of Step 3. Further, set the temperature sequentially to 10 / 25 / 40 / 55 / 70 / 85 / 100 / 115℃, with each step accompanied by the operation of Step 3. In this way, the frequency sweep results of the unreinforced composite laminate at different temperatures can be obtained.

[0150] Step 5: Open the temperature chamber, take out the test piece inside, namely the unreinforced composite laminate, and replace it with the longitudinally embedded vibration damping reinforced composite laminate. Repeat the operations of Step 2, Step 3 and Step 4 to obtain the frequency sweep results of the longitudinally embedded vibration damping reinforced composite laminate at different temperatures.

[0151] Step 6: Open the temperature chamber again, take out the test piece, replace it with a transversely embedded vibration damping reinforced composite material laminate, and repeat the operations of Step 2, Step 3 and Step 4 to obtain the frequency sweep results of the transversely embedded vibration damping reinforced composite material laminate at different temperatures.

[0152] Step 7: Organize the frequency sweep data of the unreinforced composite laminate and the longitudinally and laterally embedded vibration damping reinforced composite laminate obtained in Steps 4, 5 and 6 at different temperatures, and visualize them as images to obtain the vibration suppression law of the reinforced design with embedded NiTi shape memory alloy wire provided by the present invention.

[0153] After completing the above steps, the vibration testing method for the vibration damping reinforced composite laminate at different temperatures provided in this example has been completed. Based on this example, experimental evidence shows that the reinforced design with embedded NiTi shape memory alloy wires provided by this invention can achieve vibration suppression at different temperatures.

[0154] Vibration reduction effects of different embedding schemes:

[0155] Considering the vibration reduction adaptability of the reinforced design under various conditions, this embodiment conducts a study on the multi-resonance peaks and global vibration reduction of composite laminates under different boundary conditions, and discusses the vibration reduction effect of the cross-embedded method. By replacing the fixed block 405-1 in the vibration suppression experimental verification device with a fixed frame, the boundary condition can be changed to global fixation on all four sides, as shown below. Figure 5b As shown, furthermore, by changing the sensor installation position, vibration data at different positions can be measured. Preferably, in this example, the midpoint position (a / 2, b / 2) and the left point position (a / 4, b / 2) are selected. The vibration reduction effect of three embedding schemes is discussed, as shown in Figures 7 and 8. Figure 7 discusses the influence of different NiTi shape memory alloy wire diameters and different embedding schemes on the vibration reduction effect. Preferably, the diameter of the NiTi shape memory alloy wire is selected as 0.1 mm and 0.2 mm, the embedding scheme is selected as transverse embedding, longitudinal embedding, and transverse-longitudinal interleaved embedding, the installation position is the midpoint, and the acceleration excitation is selected as 0.2 g. The results show that different wire diameters and embedding schemes can effectively suppress vibration, and the 0.2 mm wire embedding scheme has less impact on the system's natural frequency. The transverse embedding and interleaved embedding effects are more obvious. Figure 8 discusses the vibration reduction of multiple resonance peaks. The embedding scheme is selected as transverse embedding, longitudinal embedding, and transverse-longitudinal interleaved embedding, the installation position is the left point, and the acceleration excitation is selected as 0.2 g, 0.3 g, and 0.5 g. The results show that the reinforced design with embedded NiTi shape memory alloy wires can achieve vibration reduction with multiple resonance peaks under different excitation conditions. Generally speaking, the multi-band vibration reduction effect of the cross-embedded wires is better.

[0156] The first boundary condition involved fixing the four corners of the laminate before vibration testing; the second boundary condition involved fixing both the four corners and four sides of the laminate before testing. Experimental results show that all three embedding schemes effectively improve the vibration resistance of the composite laminate. All three embedding schemes can reduce the vibration of the second-order resonance peaks of the composite laminate. The longitudinal and staggered embedding schemes achieve a reduction efficiency of over 60% for the first-order resonance, while the transverse and staggered embedding schemes achieve a reduction efficiency of over 50% for the second-order resonance. Overall, the staggered embedding reinforcement scheme is more effective at reducing vibration in composite laminates.

[0157] The study on multiple resonance peaks and global vibration reduction of composite laminates under different boundary conditions can be carried out according to the following steps:

[0158] Step a: According to the specific process of vibration suppression capability verification, the vibration suppression experimental device shown is installed on the vibration table platform, and the experimental piece is installed on the vibration suppression experimental device. Furthermore, a high-precision lightweight accelerometer is installed at the left point of the experimental piece by adhesive bonding.

[0159] Step b: Start the vibration table and perform vibration testing. The vibration test acceleration excitation range is 0.1-2.0g, and in this example, it is preferably 0.2g, 0.3g, and 0.5g. The vibration test frequency range is 10-2000Hz, and in this example, it is preferably 90-480Hz. The data acquisition system can obtain the amplitude-frequency response curve of the experimental piece. In this example, the data acquisition system is preferably an LMS system. The experimental piece in this step is the unreinforced composite laminate.

[0160] Step c: After the experimental test in step b is completed, the experimental piece is removed and replaced with the transversely embedded vibration damping reinforced composite material laminate, an acceleration sensor is installed, and the experimental procedure of step b is repeated.

[0161] Step d: After the experimental test in step b is completed, the experimental piece is removed and replaced with the longitudinally embedded vibration damping reinforced composite laminate, an acceleration sensor is installed, and the experimental procedure of step b is repeated.

[0162] Step e: After the experimental test in step b is completed, the experimental piece is removed and replaced with the vibration damping reinforced composite material laminate with cross-shaped embedding, an acceleration sensor is installed, and the experimental procedure of step b is repeated.

[0163] Step f: Organize the sweep frequency data of the unreinforced composite laminate and the longitudinally and laterally embedded vibration damping reinforced composite laminate obtained in steps c, d and e, and visualize them as images to obtain the multi-resonance peaks and global vibration reduction experimental results of the reinforced design with embedded NiTi shape memory alloy wires provided by the present invention under different boundary conditions.

[0164] Structural Examples

[0165] This embodiment discloses a composite material laminate structure embedded with NiTi alloy wires. The composite material laminate structure is prepared by the preparation method in the above embodiment. The composite material laminate structure includes: an alloy wire surface, and a first layer and a second layer symmetrically arranged along the alloy wire surface; the first layer and the second layer are connected to the alloy wire surface by hot pressing and curing.

[0166] The composite laminate structure can tightly fix the alloy wire between the two laminate sections and stabilize the alloy wire on its surface. Through a high-temperature and high-pressure method, the alloy wire surface is embedded in the two laminate sections, preventing significant displacement of the alloy wire. In the preparation method embodiment, vibration tests were conducted on the processed vibration-damping reinforced composite laminate to verify the feasibility of using the composite laminate structure as a vibration damping material.

[0167] Application Examples

[0168] This embodiment discloses an application of a composite material laminate structure embedded with NiTi alloy wires, specifically, the wall panel of a new energy aircraft is the composite material laminate structure embedded with NiTi alloy wires described in the above embodiment. The composite material laminate is used to simulate the front wall panel of a new energy aircraft cockpit with enhanced vibration resistance design. The composite material laminate simulating the front wall panel of a new energy aircraft cockpit includes both enhanced vibration-resistant and general types.

[0169] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for preparing a composite laminate structure embedded with NiTi alloy wires, characterized in that, Includes the following steps: Step 1: Fix the two ends of several NiTi alloy wires arranged along the first direction and / or the second direction onto the wire inserting mold to form an alloy wire surface; Step 2: Lay a first layer plate under the alloy wire surface and lay a second layer plate on the alloy wire surface. The first layer plate and the second layer plate are symmetrically arranged. A preliminary pressure bottom plate is set below the first layer plate and a preliminary pressure top plate is set above the second layer plate. Step 3: Apply a first pressure to the initial pressure top plate and the initial pressure bottom plate to form a prefabricated structure from the first layer plate, the alloy wire surface and the second layer plate. Step 4: Cut off the exposed NiTi alloy wire between the prefabricated structure and the embedded mold, and after high temperature and high pressure curing, it becomes a composite material laminate structure with embedded NiTi alloy wire. The pressure of the high temperature and high pressure curing is 4-5 standard atmospheres, and the temperature is 100-150℃. The first layer plate includes 2N layers of fiber composite material, and the second layer plate includes 2N layers of fiber composite material, where N = 1, 2, 3, 4, 5.

2. The method for preparing the composite laminate structure according to claim 1, characterized in that, In step 4, a thermostatic precipitator is used for the high-temperature and high-pressure curing and molding process.

3. The method for preparing the composite laminate structure according to claim 1, characterized in that, In step 4, the high-temperature and high-pressure curing process takes 4-6 hours.

4. The method for preparing the composite laminate structure according to claim 1, characterized in that, The first pressure is the weight of a 10-20 kg mass block, and the duration of applying the first pressure to the initial pressure top plate and the initial pressure bottom plate is ≥30 min.

5. The method for preparing the composite laminate structure according to claim 1, characterized in that, The first direction is horizontal, and the second direction is vertical; The spacing between adjacent NiTi alloy wires is 10~30 mm; The diameter of the NiTi alloy wire is 0.1~0.4 mm.

6. The method for preparing the composite laminate structure according to claim 1, characterized in that, The fiber composite material layer is made of carbon fiber prepreg or glass fiber composite material.

7. The method for preparing the composite laminate structure according to claim 1, characterized in that, The wire insert mold includes a square frame, a clamping and fixing block on the square frame, a semi-circular groove on the square frame, and a semi-circular protrusion on the clamping and fixing block. The shape and number of the semi-circular groove and the semi-circular protrusion are matched to fix the NiTi alloy wire. The shapes of the initial pressure top plate and the initial pressure bottom plate match the shape of the square frame and are slightly smaller than the space enclosed by the square frame.

Citation Information

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