Metamaterial device for noise control of transformer core and analysis method thereof

Abstract

The invention discloses a metamaterial device for noise control of a transformer core and an analysis method thereof, the metamaterial device for noise control of the transformer core is mounted on the front side and the rear side of the transformer core, and comprises a substrate and a metamaterial layer mounted on the substrate; the metamaterial layer comprises a plurality of cells; each cell is of a hollow tubular structure; the cross section, perpendicular to the extending direction, of the hollow tubular structure is of a cosine beam type structure. And the cells are positioned between the substrate and the transformer iron core. According to the metamaterial device for noise control of the transformer core, the cells are arranged to be of a cosine beam type structure, the low-frequency line spectrum noise vibration control effect of the metamaterial device for noise control of the transformer core can be improved, and the vibration isolation efficiency of the device within the range of 50-1000 HZ is 90% or above.

Description

Technical Field

[0001] The present invention relates to the field of vibration reduction and noise reduction, and in particular to a metamaterial device for transformer core noise control and an analysis method thereof. Background Art

[0002] In 500kV substations, transformers are the main noise source, and their low-frequency noise pollution has always attracted people's attention. Conventional noise reduction projects use a large number of auxiliary noise reduction measures such as sound barriers and soundproof covers to control the noise of 500kV transformers. However, due to limited protection range, high project cost, interference with fire protection and other issues, it has been difficult to solve the low-frequency noise problem. At present, a lot of research has been carried out on transformer core noise from the aspects of magnetic performance optimization, material improvement, and processing and assembly process optimization. However, transformer noise mainly comes from the vibration generated by the magnetostriction of the core. Reducing the core vibration can reduce the generation of equipment noise.

[0003] Specifically, the current transformer core is usually a laminated core, which is made of magnetic silicon steel sheets stacked together. After being magnetized, magnetostriction occurs, which causes the core to vibrate and leads to transformer core noise.

[0004] On the one hand, core noise can be controlled by optimizing the structure of the core itself. For example, the structure of the core is closely related to its modal dynamic characteristics. By optimizing the core structure, the natural frequency and the excitation frequency can be staggered to reduce vibration noise.

[0005] On the other hand, under the premise that no breakthrough has been made in silicon steel sheet manufacturing technology, improving the core manufacturing process is also an important means to control core noise. Specifically, core noise is closely related to its overlap form, seam size, binding force level and core surface magnetic density distribution. At present, in order to reduce the core noise level, acoustic metamaterials, such as disc spring superstructures, can be inserted between the laminations. Disc spring superstructures can effectively suppress the bending deformation of silicon steel sheets in the thickness direction, but disc spring superstructures are slotted boss structures, which are numerous and difficult to process. They require two butterfly quasi-zero stiffness springs to press and assemble, and the assembly process is difficult.

[0006] Therefore, there is a need to provide metamaterials for transformer core noise control with improved designs. Summary of the invention

[0007] In order to solve the deficiencies in the prior art, the present invention provides a metamaterial for transformer core noise control, so as to improve the vibration reduction and noise reduction effect of the transformer core, while reducing the difficulty of processing and assembly process.

[0008] The present invention adopts the following technical solution.

[0009] According to the first aspect of the present invention, a metamaterial device for transformer core noise control is provided. The device is installed on the front and rear sides of the transformer core, and includes a substrate and a metamaterial layer installed on the substrate; the metamaterial layer includes a plurality of cells; the plurality of cells are located between the substrate and the transformer core; each cell is a hollow tubular structure; the cross section of the hollow tubular structure perpendicular to the extension direction includes: an arched top, a convex beam, a horizontal bottom, and a first side and a second side perpendicular to the horizontal bottom; the upper edge and the lower edge of the arched top are both in the shape of a semi-cosine curve; the convex beam is arranged at the vertex of the upper edge of the arched top; the two ends of the arched top extend horizontally to both sides, respectively, and are connected to the top of the first side and the top of the second side, respectively; the two ends of the horizontal bottom are connected to the bottom of the first side and the bottom of the second side, respectively.

[0010] Furthermore, when the bottom of the cell is subjected to vertical pressure, the arched top can be deformed to become horizontal, reaching a quasi-zero stiffness state.

[0011] Furthermore, the thickness between the upper edge and the lower edge of the arched top is 1.5 mm, the width and length of the convex beam are 3 mm and 50 mm respectively, the width of the horizontal bottom is 40 mm, the distance between the inner side surface of the first side portion and the inner side surface of the second side portion is 32.5 mm, and the height of the first side portion and the second side portion are both 3 mm.

[0012] Furthermore, a bolt hole is provided at a central position of the bottom surface of the cell where the horizontal bottom of the cross section is located, for fastening the cell to the substrate.

[0013] Furthermore, the transformer core is a square ring core; the substrate is a square ring substrate whose shape matches the square ring core; the square ring substrate includes:

[0014] A first section and a second section respectively corresponding to the first group of parallel beams of the square ring core; the lengths of the first section and the second section are equal to the side length of the inner circle of the square ring-shaped substrate;

[0015] The third section and the fourth section respectively correspond to the second group of parallel beams of the square ring core; the length of the third section and the fourth section is equal to the side length of the outer ring of the square ring substrate;

[0016] Wherein, two rows of cells arranged closely together are installed on the first to fourth sections.

[0017] Furthermore, it also includes a clamping mechanism arranged at the upper end and the lower end of the transformer core, which is used to clamp the transformer core, the substrate and the metamaterial layer from the front and rear sides of the transformer core.

[0018] Furthermore, the transformer core is made of silicon steel sheets; the substrate is made of hard aluminum alloy; and the cell is made of nylon.

[0019] According to a second aspect of the present invention, there is provided a method for analyzing the metamaterial device for transformer core noise control according to the first aspect of the present invention. The method comprises the following steps:

[0020] (1) A single cell and a substrate and a transformer core in a section where a single cell cross section is located are used as a single vibration unit, a local coordinate system is established for the vibration unit, and a dynamic equation of the vibration unit is obtained based on the constructed local coordinates according to the Euler-Bernoulli theory;

[0021] (2) solving the dynamic equation of the vibration unit according to the harmonic balance method and boundary conditions to obtain the dispersion relation and energy band relation of the vibration of the vibration unit; the boundary conditions include the displacement continuity condition and force balance condition and Bloch boundary condition that need to be satisfied at both ends and the middle position of each vibration unit;

[0022] (3) According to the dispersion relation and the energy band relation, the length parameter of the cell and the thickness parameter of the silicon steel sheet are adjusted to obtain the band gap distribution and attenuation characteristics of the cell vibration under the corresponding parameter conditions to optimize the vibration reduction effect.

[0023] Furthermore, step (1) comprises:

[0024] A first local coordinate system x is established with the end point and the midpoint of the substrate in the vibration unit as the origin. 1 Oy 1 and the second local coordinate system x 2 Oy 2 , respectively establish a third local coordinate system x with the end point and the midpoint on the same side of the transformer core in the vibration unit as the origin 1 Oy 3 and the fourth local coordinate system x 2 Oy 4 The bending vibration displacement of each section of the transformer core in the vibration unit is represented by Y 1 (x 1 ,t),Y 2 (x 2 , t), the bending vibration displacement of each section of the substrate in the vibration unit is represented by Y 3 (x 1 ,t),Y 4 (x 2 ,t), according to the Euler-Bernoulli theory, the dynamic equation of the vibration unit can be derived as follows:

[0025]

[0026] Among them, x 1 and x 2 is the coordinate parallel to the substrate or transformer core surface, y 1 and 2 is the coordinate perpendicular to the transformer core surface, y 3 and 4 is the coordinate perpendicular to the substrate surface, E 1 , 1 , A 1 and I 1 are the elastic modulus, density, cross-sectional area and moment of inertia of the transformer core respectively; E 2 , 2 , A 2 and I 2 The elastic modulus, density, cross-sectional area and moment of inertia of the substrate are respectively.

[0027] Furthermore, step (2) includes:

[0028] (21) Based on the harmonic balance method, the harmonic solution of the dynamic equation of the vibration unit is assumed to be as follows:

[0029] Y 1 (x 1 ,t)=y 1 (x 1 ) iwt ,

[0030] Y 2 (x 2 ,t)=y 2 (x 2 ) iwt ,

[0031] Y 3 (x 1 ,t)=y 3 (x 1 ) iwt ,

[0032] Y 4 (x 2 ,t)=y 4 (x 2 )ejwt,

[0033] (22) Substituting the harmonic solution into the dynamic equation, we can obtain the generalized solution y 1 (x 1 ), y 2 (x 2 ), y 3 (x 1 ), y 4 (x 2 ) are respectively expressed as:

[0034]

[0035] (23) Substituting the generalized solution into the displacement continuity condition, force balance condition and Bloch boundary condition, the dispersion relation and band structure are obtained.

[0036] The dispersion relation is expressed as:

[0037] (e 4μ +e -4μ )+T 1 (e 3μ +e -3μ )+T 2 ( 2μ +e -2μ )+T 3 (e μ +e -μ )+T 4 =0,

[0038] μ=iqL,

[0039] The energy band relationship is expressed as:

[0040]

[0041] Where i is a unit imaginary number, q is a wave vector, L is the width of the horizontal bottom of a single cell, and T 1 ~T 4 They are the first coefficient matrix to the fourth coefficient matrix respectively.

[0042] Further, in step (23),

[0043] The displacement continuity condition and force balance condition are expressed as:

[0044]

[0045]

[0046] The Bloch boundary condition is expressed as:

[0047]

[0048] Among them, θ 1 (·) and θ 2 (·) respectively represent the angles of the corresponding positions on the transformer core; θ 3 (·) and θ 4 (·) respectively represent the angles of the corresponding positions on the substrate; Q 1 (·) and Q 2 (·) respectively represent the loads at corresponding positions on the transformer core; Q 3 (·) and Q4 (·) represents the load at the corresponding position on the substrate; M 1 (·) and M 2 (·) represent the bending moment at the corresponding position on the transformer core; M 3 (·) and M 4 (·) represent the bending moments at the corresponding positions on the substrate.

[0049] The beneficial effect of the present invention is that, compared with the prior art,

[0050] 1. The metamaterial device designed by the present invention is installed on the front and rear sides of the transformer core, including a substrate and a metamaterial layer installed on the substrate; the metamaterial layer includes a plurality of cells; each cell is a hollow tubular structure; the cross section of the hollow tubular structure perpendicular to the extension direction has a cosine beam configuration; the cell is located between the substrate and the transformer core. This structure including the cosine beam configuration is conducive to reducing the problem of low-frequency vibration noise of the silicon steel sheet of the transformer core, and improving the shock absorption and noise reduction effect of the transformer core. Specifically, the experimental results show that the vibration isolation efficiency of the metamaterial device of the present invention is above 90% in the range of 50-1000Hz, which is conducive to improving the low-frequency line spectrum noise vibration control effect of the metamaterial device. At the same time, the cellular structure adopts a hollow structure, which can be better bent when subjected to vertical pressure. The bottom of the cell is subjected to vertical pressure, and the edges of the two half-cosine curves are deformed, and finally change into horizontal edges, reaching a quasi-zero stiffness state. Furthermore, experimental results show that the restoring force curves of the cell with a cosine beam configuration of the present invention are perfectly consistent with those of the disc spring cell, and have the same quasi-zero stiffness characteristics near the equilibrium position of 3.5 mm, and the vibration reduction effects of the two are almost the same; however, the cell structure of the present invention is simpler, and the difficulty of processing and assembly is greatly reduced compared to the disc spring cell.

[0051] 2. The cells in the present invention are made of nylon material, and the manufacturing process is simple. While being able to achieve a good vibration reduction effect, the cost is low, and it is easy to promote and apply, and has a high practical value.

[0052] 3. The present invention establishes a local coordinate system for a vibration unit formed by a substrate and a transformer core including a single cell and a section where the cross section of the single cell is located, obtains the dynamic equation of the vibration unit according to the Euler-Bernoulli theory, and solves the dynamic equation of the vibration unit according to the harmonic balance method in combination with boundary conditions to obtain the dispersion relation and energy band relation of the vibration of the vibration unit, and according to the dispersion relation and energy band relation, adjusts the length parameter of the cell and the thickness parameter of the silicon steel sheet to obtain the band gap distribution and attenuation characteristics of the cell vibration under the corresponding parameter conditions, so as to optimize the vibration reduction effect, thereby being able to better provide theoretical guidance for transformer core noise control and metamaterial design. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a planar structure diagram of the cosine beam cell in an example of the present invention.

[0054] Figure 2 It is a three-dimensional structure diagram of the cosine beam cell in an example of the present invention.

[0055] Figure 3(a) and 3(b) They are respectively the overall structure diagram and the cross-sectional view of the cosine beam cell in the example of the present invention.

[0056] Figure 4 Schematic diagram of the overall structure of the cosine beam metamaterial in the example of the present invention.

[0057] Figure 5 FIG. 4 is a structural diagram of a substrate of a metamaterial in an example of the present invention.

[0058] Figure 6 FIG. 4 is a diagram of a square silicon steel sheet core containing metamaterials in an example of the present invention.

[0059] Figure 7(a) and 7(b) They are network model diagrams when no stress is applied and stress is applied to the top of the cosine beam metamaterial simulation analysis in an example of the present invention.

[0060] Figure 8 It is a comparison diagram of the disc-shaped / cosine beam quasi-zero stiffness spring structure in the example of the present invention.

[0061] Fig. 9 It is a dynamic model diagram of a single vibration unit formed by a single cell and a substrate in a section where the cross section of the single cell is located and a transformer core in an example of the present invention.

[0062] Fig.10 It is the energy band structure diagram of the vibration unit in the example of the present invention.

[0063] Figure 11(a) and 11(b) They are respectively the band gap distribution and band gap structure diagram of the vibration unit in the example of the present invention.

[0064] Figure 12(a) and 12(b) They are respectively the influence diagrams of stiffness on band gap distribution and attenuation constant in the examples of the present invention.

[0065] Figure 13(a) and 13(b) They are respectively the influence diagrams of the cell length L on the band gap distribution and the attenuation constant in the examples of the present invention.

[0066] Figure 14(a) and 14(b) They are respectively the influence diagrams of the geometric parameters of the vibration unit on the band gap distribution and the attenuation constant in the examples of the present invention.

[0067] Fig.15 FIG. 4 is a diagram of a finite element model of a metamaterial having 75 unit cells in an example of the present invention.

[0068] Fig.16 This is a comparative study diagram of the theoretical band gap and FRF of the vibration unit in the example of the present invention.

[0069] Fig.17 This is a test diagram of the vibration isolation efficiency of the cosine beam metamaterial in an example of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, other embodiments obtained by ordinary technicians in this field without creative work are all within the scope of protection of the present invention.

[0071] Example 1

[0072] Embodiment 1 of the present invention provides a metamaterial device for controlling transformer core noise.

[0073] like Figure 1-4 The metamaterial device for transformer core noise control is installed on the front and rear sides of the transformer core, and includes a substrate and a metamaterial layer installed on the substrate; the metamaterial layer includes a plurality of cells; each cell is a hollow tubular structure; the cross section of the hollow tubular structure perpendicular to the extension direction has a cosine beam configuration; the cell is located between the substrate and the square ring core. The cell with a cosine beam configuration is conducive to reducing the problem of low-frequency vibration noise of the transformer core made of silicon steel sheets, and improving the vibration reduction and noise reduction effect of the transformer core.

[0074] Figure 1 It is a planar structural diagram of a cell with a cosine beam configuration in an example of the present invention. Specifically, the cross section of the cell includes: an arched top, a convex beam 3, a horizontal bottom 6, and a first side portion 4 and a second side portion 5 perpendicular to the horizontal bottom 6. The upper edge 1 and the lower edge 2 of the arched top are both in the shape of a semi-cosine curve. The convex beam 3 is arranged at the vertex of the upper edge of the arched top. The two ends of the arched top extend horizontally to both sides, and are respectively connected to the top of the first side portion 4 and the top of the second side portion 5. The two ends of the horizontal bottom 6 are respectively connected to the bottom end of the first side portion 4 and the bottom end of the second side portion 5.

[0075] Through the above arrangement, during operation, when the bottom of the cell is subjected to vertical pressure, the arched top edge can be deformed and eventually changed into a horizontal edge, thus reaching a quasi-zero stiffness state.

[0076] Preferably, the central portion of the bottom edge 6 has a through bolt hole 7 (eg, a bolt hole of type M4) for fastening the cell to the substrate.

[0077] In this embodiment, as an example, Figure 2 , 3(a) and 3(b), the thickness between the upper edge 1 and the lower edge 2 of the arched top of the cell is 1.5 mm, the width and length of the convex beam 3 are 3 mm and 50 mm respectively, the width of the horizontal bottom is 40 mm, the distance between the inner side of the first side portion 4 and the inner side of the second side portion 5 is 32.5 mm, and the height of the first side portion 4 and the second side portion 5 are both 3 mm. The cell with the above parameter settings can have both sufficient material strength and good deformability.

[0078] like Figure 4 and 5 , the transformer core in this embodiment is a square ring core, and the substrate is a square ring substrate whose shape matches the square ring core. The square ring substrate includes a first section 8 and a second section 11 corresponding to the first group of parallel beams (e.g., left beam and right beam) of the square ring core, and also includes a third section 9 and a fourth section 10 corresponding to the second group of parallel beams (e.g., upper beam and lower beam) of the square ring core. The lengths of the first section 8 and the second section 11 are substantially equal to the side length of the inner circle of the square ring substrate. The lengths of the third section 9 and the fourth section 10 are substantially equal to the side length of the outer circle of the square ring substrate; wherein, two rows of cells arranged closely together are installed on the first section to the fourth section. In this embodiment, as an example, in the square ring-shaped substrate: the number of cells in each row on the first section 8 and the second section 11 is 15, that is, the first section 8 and the second section 11 are each installed with 2×15=30 cells; the number of cells in each row on the third section 9 and the fourth section 10 is 20, that is, the third section and the fourth section are each installed with 2×20=40 cells.

[0079] like Figure 5 , two rows of bolt holes are provided on the first to fourth sections of the square ring-shaped substrate, and the positions of the two rows of bolt holes correspond to the positions of the bolt holes in the two rows of cells arranged adjacently, so that the cells can be fixed on the substrate by bolts. In this embodiment, as an example, the bolts on the first to fourth sections of the square ring-shaped substrate are M4 bolt holes, and the diameter of the M4 bolt holes is 4.2 mm, and the spacing between the first section and the second section and the spacing between the third section and the fourth section are both 600 mm.

[0080] like Figure 6, a clamping mechanism for clamping the transformer core, the substrate and the metamaterial layer from the front and rear sides of the transformer core is shown, the clamping mechanism includes two groups of sub-clamping mechanisms, which are respectively arranged at the upper end and the lower end of the transformer core. Preferably, each group of sub-clamping mechanisms may include a pair of I-shaped clamps 12.

[0081] By installing the first metamaterial layer and the second metamaterial layer fixed on the substrate on the front and rear sides of the square ring-shaped transformer core, respectively, and clamping the square ring core with the I-shaped clamp 12, the low-frequency vibration of the square ring core can be efficiently suppressed. Considering that the operating temperature of the square ring core of the transformer is generally around 90°C, nylon PA12 is used to process the cells in each metamaterial layer. At the same time, in order to avoid magnetic conductivity, the substrate is processed with hard aluminum alloy, and the hard aluminum alloy is preferably hard aluminum alloy LY12.

[0082] Figure 7(a) and 7(b) This is a simulation analysis diagram of the cosine beam metamaterial in the example of the present invention. As with the disc spring metamaterial, the mechanical properties of the quasi-zero stiffness cell are analyzed based on the solid185 unit using the ANSYS finite element simulation analysis mode. Nylon HP3DHR-PA12 is used as the quasi-zero stiffness cell material, with an elastic modulus of 1.3 GPa, a density of 1150 kg / m3, and a Poisson's ratio of 0.4, to establish a quasi-zero stiffness cell solid model.

[0083] Figure 8 The results of butterfly / cosine beam quasi-zero stiffness springs in the present invention are compared. The parameters of the cosine beam cell are iteratively calculated and analyzed to obtain the optimal vibration reduction effect. Figure 8 It can be seen that the restoring force curves of the cosine beam cell and the disc spring cell are perfectly matched, and have the same quasi-zero stiffness characteristics near the equilibrium position of 3.5mm, and the vibration reduction effects of the two are almost the same. However, the structure of the latter is more complicated and the processing technology is difficult. It requires two disc-shaped quasi-zero stiffness springs to press and assemble, and the assembly process requirements are relatively high. Therefore, the cosine beam metamaterial can be selected as the preferred solution.

[0084] Example 2

[0085] Embodiment 2 provides an analysis method of the metamaterial device for transformer core noise control according to embodiment 1. The method specifically comprises the following steps:

[0086] Step 1: Take a single cell and the substrate and transformer core in the section where the single cell cross section is located as a single vibration unit, establish a local coordinate system for the vibration unit, and obtain the dynamic equation of the vibration unit based on the constructed local coordinates according to the Euler-Bernoulli theory.

[0087] Fig. 9The figure is a dynamic model diagram of the vibration unit in the example of the present invention. In order to further understand the low-frequency line spectrum noise vibration control effect of the acoustic metamaterial, the dynamic characteristics of the cosine beam metamaterial and its low-frequency vibration reduction band gap are analyzed. First, a theoretical analysis is performed to establish a local coordinate system x for the vibration unit. 1 Oy 1 、x 1 Oy 3 、x 2 Oy 2 and x 2 Oy 4 , where x 1 Oy 1 and x 2 Oy 2 are local coordinate systems established with one end point and the midpoint of the transformer core in the vibration unit as the origin, x 1 Oy 3 and x 2 Oy 4 are local coordinate systems established with the end point and the midpoint of the same side of the substrate in the vibration unit as the origin. Correspondingly, the bending vibration displacement of each section of the transformer core in the vibration unit is represented by Y 1 (x 1 ,t),Y 2 (x 2 , t), the bending vibration displacement of each section of the substrate in the vibration unit is represented by Y 3 (x 1 ,t),Y 4 (x 2 ,t), according to the Euler-Bernoulli theory, the dynamic equation of the vibration unit can be derived as follows:

[0088]

[0089] x 1 and x 2 is the coordinate parallel to the substrate and transformer core surface, y 1 and 2 is the coordinate perpendicular to the transformer core surface, y 3 and 4 is the coordinate perpendicular to the substrate surface, E 1 , 1 , A 1 and I 1 are the elastic modulus, density, cross-sectional area and moment of inertia of the transformer core respectively; E 2 , 2 , A 2 and I 2 The elastic modulus, density, cross-sectional area and moment of inertia of the substrate are respectively.

[0090] Step 2: Solve the dynamic equation of the vibration unit according to the harmonic balance method and boundary conditions to obtain the dispersion relation and energy band relation of the vibration unit; the boundary includes the displacement continuity condition and force balance condition and Bloch boundary condition that need to be satisfied at both ends and the middle position of each vibration unit.

[0091] This step specifically includes the following sub-steps:

[0092] Step 21: Based on the harmonic balance method, the harmonic solution of the dynamic equation of the vibration unit is assumed to be as follows:

[0093] Y 1 (x 1 ,t)=y 1 (x 1 ) iwt (5)

[0094] Y 2 (x 2 ,t)=y 2 (x 2 ) iwt (6)

[0095] Y 3 (x 1 ,t)=y 3 (x 1 ) iwt (7)

[0096] Y 4 (x 2 ,t)=y 4 (x 2 ) iwt (8)

[0097] Step 22: Substitute the harmonic solution into the dynamic equation to obtain the generalized solution y 1 (x 1 ), y 2 (x 2 ), y 3 (x 1 ), y 4 (x 2 ) are respectively expressed as:

[0098]

[0099] In the formula, a 11 ~a 44 are the corresponding coefficients respectively;

[0100] Step 23: Substitute the generalized solution into the displacement continuity condition, force balance condition and Bloch boundary condition to solve and obtain the dispersion relation and band structure.

[0101] Among them, the displacement continuity condition and force balance condition are expressed as:

[0102]

[0103] The Bloch boundary condition is expressed as:

[0104]

[0105]

[0106] Among them, θ 1 (·) and θ 2 (·) respectively represent the angles of the corresponding positions on the transformer core; θ 3 (·) and θ 4 (·) respectively represent the angles of the corresponding positions on the substrate; Q 1 (·) and Q 2 (·) respectively represent the loads at corresponding positions on the transformer core; Q 3 (·) and Q 4 (·) represents the load at the corresponding position on the substrate; M 1 (·) and M 2 (·) represent the bending moment at the corresponding position on the transformer core; M 3 (·) and M 4 (·) represent the bending moments at the corresponding positions on the substrate.

[0107] After substituting into the solution, the dispersion relation is expressed as:

[0108] (e 4μ +e -4μ )+T 1 (e 3μ +e -3μ )+T 2 (e 2μ +e -2μ )+T 3 (e μ +e -μ )+T 4 =0,

[0109] μ=iqL,

[0110] The energy band relationship is expressed as:

[0111]

[0112] where \(i\) is the unit imaginary number, \(q\) is the wave vector, \(L\) is the width of the horizontal bottom of a single unit cell, and \(T\) 1 ~\(T\) 4 are the first coefficient matrix to the fourth coefficient matrix respectively. The real part of \(qL\) determines the propagation direction of the longitudinal wave, which is called the phase constant; the imaginary part of \(qL\) characterizes the attenuation ability of the longitudinal wave in the local resonance rod, which is called the attenuation constant.

[0113] Step 3. According to the dispersion relation and the energy band relation, adjust the length parameter of the unit cell and the thickness parameter of the silicon steel sheet to obtain the band gap distribution and attenuation characteristics of the unit cell vibration under the corresponding parameter conditions, so as to optimize the vibration damping effect.

[0114] According to different mathematical forms of the wave vector \(q\), the flexural waves can be divided into three categories:

[0115] (1) Propagation (P): The wave vector \(q\) is a pure real number, i.e., \(q = \text{Re}(q)\). Under this working condition, when the elastic wave propagates on the unit cell, there is no attenuation, only a phase change occurs;

[0116] (2) Attenuation (A): The real part of the wave vector \(q\) is \(\text{Re}(q)=0\) or \(|\text{Re}(q)| = \pi\), and the imaginary part is non-zero, which corresponds to the attenuation of the elastic wave propagating along the unit cell.

[0117] (3) Complex (C): The wave vector \(q\) is a complex number, i.e., \(0\lt\text{Re}(q)\lt\) and \(|\text{Im}(q)|>0\). In this case, the elastic wave attenuates continuously when propagating along the unit cell.

[0118] By solving Equation (17), \(\pm q\) 1 、\(\pm q\) 2 、\(\pm q\) 3 and \(\pm q\) 4 are obtained, and their corresponding classifications are discriminated in turn. The metamaterial coupling the silicon steel sheet transformer core - hard aluminum alloy substrate will have three types of attenuation band gaps at a given frequency:

[0119] (1) Attenuation - Attenuation - Attenuation - Attenuation: All four wave numbers belong to the attenuation category. Under this working condition, adjacent unit cells vibrate either in phase or out of phase, causing the wave to attenuate when passing through the unit cell. This behavior is a typical Bragg scattering phenomenon. Therefore, this region is called the Bragg scattering region (BS region);

[0120] (2) Complex: \(q_1\), \(q_2\), \(q_3\) and \(q_4\) are conjugate complex numbers. Under this working condition, the four waves represent the same characteristic wave, which attenuates and undergoes a phase change when passing through the unit cell. This is usually a characteristic of the local resonance mechanism. Therefore, this region is denoted as the local resonance region (LR region);

[0121] (3) Attenuation - Complex mixture: One or more of the four wave number solutions belong to the attenuation category, and the rest belong to the complex category. At this time, all four elastic waves will be attenuated.

[0122] Fig.10 is the band structure of the vibration unit in the example of the present invention. In order to obtain a low-frequency band gap that can effectively suppress the low-frequency bending vibration of the silicon steel sheet of the transformer core, the cosine beam quasi-zero stiffness metamaterial is used to couple the silicon steel sheet transformer core and the hard aluminum alloy substrate, and the band gap is solved and analyzed. The quasi-zero stiffness spring stiffness can be approximated to a constant k1 near the equilibrium position. The geometric parameters of the silicon steel sheet and the hard aluminum alloy are shown in Table 1.

[0123] Table 1 Structural parameters of silicon steel sheet transformer core and hard aluminum alloy substrate in vibration unit

[0124] name Elastic modulus density Width thick Silicon steel sheet <![CDATA[2×10 11 Well]]> <![CDATA[7650kg / m 3 ]]> 0.1m <![CDATA[6×10 -4 m]]> Hard aluminum alloy <![CDATA[6.8×10 10 Well]]> <![CDATA[2700kg / m 3 ]]> 0.1m <![CDATA[3×10 -3 m]]>

[0125] According to the parameters provided in Table 1, the real and imaginary parts of the wave vector qL are calculated as follows: Fig.10 As shown on the left and right sides of . In the low-frequency band of 0Hz-1000Hz, there are a total of 4 low-frequency band gaps: the first band gap is distributed from 0Hz to 28.78Hz, and the corresponding wave numbers q1, q2, q3 and q4 are initially conjugate complex numbers, belonging to the LR attenuation type, which can achieve efficient attenuation of 4 elastic waves. When the excitation frequency increases to 28.78Hz, in the low-frequency band of 28.78Hz-37.57Hz, the wave numbers q1, q2, q3 and q4 contain two conjugate complex solutions and two solutions with non-zero imaginary parts, which belong to LR and BS mixed attenuation; the frequency distribution of the second, third and fourth band gaps is 96.1 2Hz-203.8Hz, 270.6Hz-378.9Hz, 470.8Hz-1000Hz, which can effectively attenuate the low-frequency vibration noise response of the transformer core at 100Hz, 200Hz, 300Hz, and 500Hz; in the second and fourth band gaps, the wave numbers q1, q2, q3, and q4 are two conjugate complex solutions and two wave number solutions with non-zero imaginary parts, that is, the mixed band gap produced by the mixing of LR and BS; in the third band gap, the wave numbers q1, q2, q3, and q4 all satisfy Re(q)=0 or Re(q)=π and the imaginary part is non-zero, which belongs to the BS attenuation class.

[0126] Figure 11(a) and 11(b) They are the band gap distribution and band gap structure diagram of the vibration unit in the example of the present invention. Figure 11(a) and 11(b) Further simplification yields Figure 12(a) and 12(b)As shown in Figure 12, the metamaterial of the coupled silicon steel sheet transformer core-duraluminum alloy substrate can achieve broadband vibration and noise reduction in the low frequency range of 0Hz-1000Hz, and as the frequency increases, the band gap range increases, and has a larger attenuation constant in the corresponding band gap, which is conducive to the efficient suppression of low-frequency bending waves of the transformer core silicon steel sheet.

[0127] Figure 13(a) and 13(b) They are respectively the influence of stiffness on the bandgap distribution and attenuation constant in the examples of the present invention. The metamaterial of coupling silicon steel sheet transformer core-hard aluminum alloy substrate is composed of periodic elastic coupling of cosine beam quasi-zero stiffness spring. The influence of the linear stiffness term k1 of the quasi-zero stiffness spring on the bandgap structure of the vibration unit is shown in Figure 13(a). Cosine beam metamaterials with different stiffnesses are used to couple the silicon steel sheet transformer core and the hard aluminum alloy substrate. It can be seen from Figure 13(a) that with the increase of k1, the bandgap also gradually increases, especially the low-frequency bandgap, and the starting frequency of each bandgap also increases with the increase of k1. In addition, with the increase of k1, the attenuation constant also increases in the low-frequency range, while the bandgap above 500Hz is insensitive to the stiffness k1, as shown in Figure 13(b).

[0128] Figure 14(a) and 14(b) They are respectively the influence of the geometric parameters of the vibration unit on the band gap distribution and the attenuation constant in the examples of the present invention. The influence of the cell length L on the band gap distribution frequency band is shown in Figure 14 (a). When the cell length L increases from 0.133m to 0.17m, the low-frequency band gap width decreases (as shown in the black scatter diagram), and as L increases, and the actual frequency of each band gap moves toward the low-frequency band, it is easier to form a band gap distribution in the low-frequency band for efficient suppression of low-frequency bending vibration of the transformer core. Similarly, increasing L makes the attenuation constant distribution move toward the low-frequency band, as shown in Figure 14 (b). Therefore, increasing the cell length L will help improve the performance of low-frequency vibration noise suppression.

[0129] Fig.15 The finite element model diagram of the metamaterial of the coupled silicon steel sheet transformer core-duraluminum alloy substrate with 75 unit cells in the present invention. The band gap of the metamaterial of the coupled silicon steel sheet transformer core-duraluminum alloy substrate also depends on the geometric parameters of the silicon steel sheet and the duraluminum alloy. The propagation characteristics of elastic waves in the transformer core and substrate depend on When the elastic modulus and density of the silicon steel sheet and the hard aluminum alloy are given, the dynamic characteristics of the system depend on the moment of inertia Ii and the cross-sectional area. Here, the geometric dimensions of the hard aluminum alloy substrate are given unchanged, and the thickness of the silicon steel sheet in Table 1 is adjusted from 6×10 -4 m increases to 12×10 -4 m, at this time the hard aluminum alloy substrate With β 1 The ratio of β = β 2 / β 1 When the value of the first band gap is reduced from 2.22 to 1.56, the corresponding band gap change is shown in Figure 14(a). When it is reduced from 2.22 to 1.56, the width of the first band gap in the low frequency band is greatly widened (as shown in the black scatter plot). Therefore, increasing the thickness of the silicon steel sheet helps to widen the low-frequency band gap width and significantly improve the low-frequency vibration noise suppression performance of the transformer core. In addition, with the increase of the thickness of the silicon steel sheet, the starting frequency and ending frequency of each band gap move toward high frequency; the corresponding attenuation constant is shown in Figure 14(b).

[0130] Fig.16 The figure is a comparative study of the theoretical band gap and FRF of the vibration unit in the example of the present invention. In order to study the vibration transfer characteristics of the metamaterial applied to the silicon steel sheet of the transformer core, the frequency response function (FRF) of the metamaterial is calculated. Fig.16 As shown in the figure, the beam4 and combin14 units are used in the ANSYS finite element software to establish the vibration unit model and the quasi-zero stiffness spring model respectively, and the two ends of the vibration unit are simply supported boundary conditions. The physical and geometric parameters of the transformer core and substrate and the length of the unit cell are shown in Table 1. Fig.16 The hard aluminum alloy substrate and transformer core in the vibration unit are meshed using 97,500 finite beam elements. In order to perform harmonic response analysis in ANSYS software, a harmonic excitation force with an amplitude of 500N is applied to the adjacent nodes of the left support of the hard aluminum alloy substrate of the vibration unit, and the lateral displacement of the adjacent nodes of the right support of each beam is measured. Note that the nodes where the harmonic force is applied cannot coincide with the connection points between the quasi-zero stiffness spring and the two beams. In addition, the damping coefficient of the system is assumed to be 0.01. Through finite element analysis, the results are as follows Fig.17 As shown in the figure, the black dispersion curve on the far left is the theoretical calculation result, while the red and blue frequency response function curves drawn in the middle and right are the vibration response results of silicon steel sheet and hard aluminum alloy respectively. It is obvious that the theoretical band gap result is in good agreement with the frequency response function calculated in ANSYS, proving the correctness of the theoretical model. Fig.17 The gray area in the figure is the band gap region, which leads to a strong attenuation of the core silicon steel sheet response, and the attenuation intensity of each region is Fig.16 The decay constants in are consistent.

[0131] Fig.17 This is a test diagram of the vibration isolation efficiency of the cosine beam metamaterial in the example of the present invention. In order to verify and analyze the actual vibration reduction and noise reduction effect of the cosine beam metamaterial, this project prepared a single cosine beam metamaterial cell structure through 3D printing technology, used a vibration test bench to test the vibration isolation efficiency of the metamaterial cell, and installed a pressure plate on the top of the cell to ensure that the cell is in a balanced position. Fig.17Under the condition of continuous sinusoidal wave vibration with an applied frequency of 50-1000Hz and an acceleration peak of 1g, the acceleration response amplitude of the cosine beam metamaterial is basically below 0.1g, indicating that more than 90% of the vibration energy is obviously absorbed in the main peak frequency band of the core vibration. Among them, vibration troughs are obviously seen at frequencies of 100Hz, 200Hz, 300Hz and 500Hz, indicating that the vibration suppression effect is best within this frequency range. The experimental results are basically consistent with the band gap frequency calculation results in the simulation analysis.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A metamaterial device for transformer core noise control, mounted on the front and rear sides of the transformer core, characterized in that: It includes a substrate and a metamaterial layer mounted on the substrate; the metamaterial layer includes a plurality of cells; The plurality of cells are located between the substrate and the transformer core; each cell is a hollow tubular structure; The cross section of the hollow tubular structure perpendicular to the extension direction includes: an arched top, a convex beam, a horizontal bottom, and a first side portion and a second side portion perpendicular to the horizontal bottom; The upper edge and the lower edge of the arched top are both in the shape of a half cosine curve; the convex beam is arranged at the vertex of the upper edge of the arched top; the two ends of the arched top extend horizontally to both sides and are respectively connected to the top end of the first side portion and the top end of the second side portion; the two ends of the horizontal bottom are respectively connected to the bottom end of the first side portion and the bottom end of the second side portion.

2. The metamaterial device for transformer core noise control according to claim 1, characterized in that: When the bottom of the cell is subjected to vertical pressure, the arched top can be deformed to become horizontal, reaching a quasi-zero stiffness state.

3. The metamaterial device for transformer core noise control according to claim 1, characterized in that: The thickness between the upper edge and the lower edge of the arched top is 1.5mm, the width and length of the convex beam are 3mm and 50mm respectively, the width of the horizontal bottom is 40mm, the distance between the inner side surface of the first side portion and the inner side surface of the second side portion is 32.5mm, and the height of the first side portion and the second side portion are both 3mm.

4. The metamaterial device for transformer core noise control according to claim 1, characterized in that: A bolt hole is provided at the central position of the bottom surface of the cell where the horizontal bottom of the cross section is located, for fastening the cell to the substrate.

5. The metamaterial device for transformer core noise control according to claim 1, characterized in that: The transformer core is a square ring core; the substrate is a square ring substrate whose shape matches the square ring core; the square ring substrate comprises: A first section and a second section respectively corresponding to the first group of parallel beams of the square ring core; the lengths of the first section and the second section are equal to the side length of the inner circle of the square ring-shaped substrate; The third section and the fourth section respectively correspond to the second group of parallel beams of the square ring core; the length of the third section and the fourth section is equal to the side length of the outer ring of the square ring substrate; Wherein, two rows of cells arranged closely together are installed on the first to fourth sections.

6. The metamaterial device for transformer core noise control according to claim 1, characterized in that: It also includes a clamping mechanism arranged at the upper end and the lower end of the transformer core, which is used to clamp the transformer core, the substrate and the metamaterial layer from the front side and the rear side of the transformer core.

7. The metamaterial device for transformer core noise control according to claim 1, characterized in that: The transformer core is made of silicon steel sheets; the base plate is made of hard aluminum alloy; and the cell is made of nylon.

8. An analysis method for a metamaterial device for transformer core noise control according to any one of claims 1 to 7, characterized in that: The steps include: (1) A single cell and a substrate and a transformer core in a section where a single cell cross section is located are used as a single vibration unit, a local coordinate system is established for the vibration unit, and a dynamic equation of the vibration unit is obtained based on the constructed local coordinates according to the Euler-Bernoulli theory; (2) solving the dynamic equation of the vibration unit according to the harmonic balance method and boundary conditions to obtain the dispersion relation and energy band relation of the vibration of the vibration unit; the boundary conditions include the displacement continuity condition and force balance condition and Bloch boundary condition that need to be satisfied at both ends and the middle position of each vibration unit; (3) According to the dispersion relation and the energy band relation, the length parameter of the cell and the thickness parameter of the silicon steel sheet are adjusted to obtain the band gap distribution and attenuation characteristics of the cell vibration under the corresponding parameter conditions to optimize the vibration reduction effect.

9. The analysis method according to claim 8, characterized in that Step (1) comprises: A first local coordinate system x1Oy1 and a second local coordinate system x2Oy2 are established with one end point and the midpoint of the transformer core in the vibration unit as the origin, and a third local coordinate system x1Oy3 and a fourth local coordinate system x2Oy4 are established with the same end point and the midpoint of the substrate in the vibration unit as the origin; the bending vibration displacement of each section of the transformer core in the vibration unit is expressed as Y1(x1, t) and Y2(x2, t), respectively, and the bending vibration displacement of each section of the substrate in the vibration unit is expressed as Y3(x1, t) and Y4(x2, t), respectively. According to the Euler-Bernoulli theory, the dynamic equation of the vibration unit can be derived as follows: Among them, x1 and x2 are coordinates in the direction parallel to the substrate or transformer core surface, y1 and y2 are coordinates in the direction perpendicular to the transformer core surface, y3 and y4 are coordinates in the direction perpendicular to the substrate surface, E1, ρ1, A1 and I1 are the elastic modulus, density, cross-sectional area and moment of inertia of the transformer core respectively; E2, ρ2, A2 and I2 are the elastic modulus, density, cross-sectional area and moment of inertia of the substrate respectively.

10. The analysis method according to claim 9, characterized in that Step (2) comprises: (21) Based on the harmonic balance method, the harmonic solution of the dynamic equation of the vibration unit is assumed to be as follows: Y1(x1,t)=y1(x1)e iwt , Y2(x2,t)=y2(x2)e iwt , Y3(x1,t)=y3(x1)e iwt , Y4(x2,t)=y4(x2)e iwt , (22) Substituting the harmonic solution into the dynamic equation, the generalized solutions y1(x1), y2(x2), y3(x1), and y4(x2) are expressed as: In the formula, a 11 ~a 44 are the corresponding coefficients respectively; (23) Substituting the generalized solution into the displacement continuity condition, force balance condition and Bloch boundary condition, the dispersion relation and band structure are obtained. The dispersion relation is expressed as: (e 4μ +e -4μ )+T1(e 3μ +e -3μ )+T2(e 2μ +e -2μ )+T3(e μ +e -μ )+T4=0, μ=iqL, The energy band relationship is expressed as: Among them, i is a unit imaginary number, q is a wave vector, L is the width of the horizontal bottom of a single cell, and T1 to T4 are the first coefficient matrix to the fourth coefficient matrix respectively.

11. The method according to claim 10, characterized in that In step (23), The displacement continuity condition and force balance condition are expressed as: The Bloch boundary condition is expressed as: Among them, θ1(·) and θ2(·) represent the angles of the corresponding positions on the transformer core, respectively; θ3(·) and θ4(·) represent the angles of the corresponding positions on the substrate, respectively; Q1(·) and Q2(·) represent the loads at the corresponding positions on the transformer core, respectively; Q1(·) and Q2(·) represent the loads at the corresponding positions on the substrate, respectively; M1(·) and M2(·) represent the bending moments at the corresponding positions on the transformer core, respectively; M3(·) and M4(·) represent the bending moments at the corresponding positions on the substrate, respectively.

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