Low profile ultra-wideband three-dimensional gradient twist electromagnetic wave-absorbing structure and construction method thereof

Abstract

This invention discloses a low-profile, ultra-wideband three-dimensional gradient torsional electromagnetic absorbing structure and its construction method, relating to the fields of electromagnetic absorbing and metamaterial structure design technology. The absorbing structure includes an upper absorbing unit, a middle uniform absorbing material plate, and a bottom metal reflector connected sequentially. The absorbing unit is an integrally formed structure doped with electromagnetic loss medium, and the edge contours of each horizontal section in the height direction are strictly defined by the Gielis super formula. The characteristic radius of the section decreases exponentially and nonlinearly with the normalized height, and the section undergoes continuous spatial torsion along the central axis, forming a gradient torsional outer surface. In addition, the shape factor of the section evolves piecewise with height, and a minimum physical cutoff radius and a smooth circularization protection mechanism are introduced at the top. This invention provides a smoother spatial wave impedance gradient and richer multiple scattering paths through nonlinear attenuation and continuous spatial torsion, effectively broadening the absorbing frequency band.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic absorbing materials and stealth technology, specifically to a low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic absorbing structure and its construction method. Background Technology

[0002] With the rapid development of electronic information technology, electromagnetic interference (EMI) and electromagnetic compatibility (EMC) problems are becoming increasingly prominent, leading to a growing demand for high-performance absorbing materials. Existing pyramidal absorbing structures commonly used in microwave anechoic chambers are typically made of foam, polyurethane, or resin-based materials impregnated or composited with conductive loss-dissipating agents. They achieve an impedance transition from free space to a high-loss medium through a gradually increasing geometric cross-section from tip to bottom. For example, the patent application (publication number CN110746671A) entitled "An absorbing material for a microwave anechoic chamber, an absorbing pyramid and its preparation method" utilizes a pyramidal shell and an internally filled absorbing material to synergistically dissipate electromagnetic wave energy. Although traditional pyramidal absorbing materials are widely used in microwave anechoic chambers, they still have the following limitations: First, their low-frequency performance is limited. To meet the requirements for low-frequency absorption, they often need to be quite tall, resulting in a large volume and increased weight, and the pointed area is prone to bending and deformation. Second, the geometry of traditional pyramids is relatively simple, with insufficient variation in cross-sectional morphology and spatial curvature. The transition of equivalent impedance from air to the back plate is not flexible enough, which limits their ultra-wideband absorption performance under low profile conditions.

[0003] Therefore, there is an urgent need to design an electromagnetic absorbing structure with optimized geometry that can achieve a smoother impedance gradient, thereby realizing an ultra-wideband, high-absorption structure in a smaller size. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to provide a low-profile ultra-wideband three-dimensional gradient torsional electromagnetic absorbing structure and its construction method. By introducing the Gielis super formula to control the cross-sectional shape and combining exponential radius decay with spatial torsion that increases linearly with height, an irregular three-dimensional absorber with continuous curvature variation is constructed to achieve better impedance matching and ultra-wideband absorption performance.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave-absorbing structure includes an upper layer of wave-absorbing units, a middle layer of uniform wave-absorbing material plates, and a bottom layer of metal reflective plates connected in sequence. The bottom of each wave-absorbing unit is in contact with the upper surface of the uniform wave-absorbing material plate, and the lower surface of the uniform wave-absorbing material plate is in contact with the metal reflective plate. Each wave-absorbing unit is a three-dimensional solid, and the three-dimensional solid is formed by stacking multiple parallel horizontal cross-sections in the height direction. The absorbing units and the uniform absorbing material plates are arranged periodically in the transverse and longitudinal directions. A polar coordinate system is established with the center of the bottom surface of the absorbing unit as the origin. The polar coordinates (r, φ) of the point set on the edge contour of the horizontal cross-section at any normalized height t satisfy the Gielis superformula: where t is the normalized height, t = z / H, z is the height of the current horizontal cross-section relative to the bottom of the absorbing unit, H is the total height of the absorbing unit, and 0 ≤ t ≤ 1; φ is the azimuth angle, and 0 ≤ φ ≤ 2π; r(φ) is the polar radius from the edge point of the cross-section at the azimuth angle φ to the central axis; m is the symmetry parameter of the Gielis superformula and is a positive integer; R(t) is the characteristic radius at the normalized height t; n(t) is the shape factor at the normalized height t.

[0006] The horizontal cross-section undergoes continuous torsion along the central axis of the three-dimensional entity, forming a gradually twisted outer surface with continuous curvature changes in space.

[0007] The symmetry parameter m is an integer between 3 and 8, and the horizontal cross-section presents a circular symmetry at the bottom; the characteristic radius R(t) decays non-linearly according to an exponential law with the normalized height t, and a minimum physical truncation radius is retained at the top, which satisfies the following relationship: where R base is the maximum envelope radius at the bottom of the absorbing unit, R top_min is the minimum physical radius of the top truncation and R top_min > 0, and p is the contour concavity index.

[0008] The shape factor n(t) shows a piecewise evolution with the normalized height t to achieve the tip shape transition and rounding protection. The specific piecewise evolution law is as follows: When 0 ≤ t ≤ 0.70, the shape factor satisfies: where n bottom is the bottom shape factor, n top is the target top shape factor, t1 is the first height threshold and t1 = 0.70; when t1 < t ≤ t2, the shape factor satisfies n(t) = n top , where t2 is the second height threshold and t2 = 0.92; when t2 < t ≤ 1, the shape factor satisfies a quadratic smooth transition: where the local interpolation ratio . n(t) is the shape factor of the top protection area, and n = 2 means that the topmost part converges to a rounded contour to reduce the tip grid singularity and improve the actual forming stability.

[0009] Rotation angle of continuous spatial torsion of horizontal cross section As the normalized height t increases linearly, it satisfies The total torsion angle The value ranges from 0 to 360°.

[0010] The three-dimensional entity is generated by sequentially lofting upwards at equal intervals from N discrete horizontal cross sections, where the number of layers N≥20; when lofting between two adjacent horizontal cross sections, the automatic minimization of the torsion path configuration is disabled to preserve the spatial torsion surface features defined by the rotation angle θ(t); all adjacent interlayer entity segments generated by lofting are seamlessly merged into a single structure through Boolean addition.

[0011] The absorbing unit is made of an electromagnetic loss composite material; the electromagnetic loss composite material includes a lightweight insulating matrix and an electromagnetic loss agent uniformly dispersed in the lightweight insulating matrix; the lightweight insulating matrix is ​​at least one of photosensitive resin, thermoplastic polymer, silicone rubber, polyurethane or aerogel material; the electromagnetic loss agent is at least one of carbonyl iron powder, graphene, carbon fiber, carbon nanotube or conductive carbon black; the metal reflector is made of aluminum plate, copper plate or carbon fiber reinforced composite material, and its thickness is much greater than the skin depth of the material in the operating frequency band.

[0012] The three-dimensional solid structure of the absorbing unit and the uniform absorbing material plate is formed by direct additive manufacturing or mold coating process. Specifically, it includes: converting the parametric geometric data of the three-dimensional solid into a surface subdivision mesh format file and slicing it, using composite polymer wire containing electromagnetic loss agent as consumable, and printing it layer by layer from the metal reflector upwards using fused deposition modeling (FDM) process.

[0013] A method for constructing a low-profile, ultra-wideband three-dimensional gradient torsional electromagnetic wave absorbing structure includes the following steps: 1) Geometric parameterization based on hyperformations and spatial torsion: 1.1) At height t, establish a planar polar coordinate system. Perform high-density 360-node equally spaced sampling within the range of [0, 2π]. The polar radius r(φ) of each node strictly follows the Gielis hyperformation: Where t is the normalized height, t=z / H, z is the height of the current horizontal section relative to the bottom of the absorbing unit, H is the total height of the absorbing unit, and 0≤t≤1; φ is the azimuth angle, and 0≤φ≤2π; r(φ) is the polar radius from the edge point of the section at azimuth angle φ to the central axis; m is the symmetry parameter of the Gielis hyperformation, and is a positive integer; R(t) is the characteristic radius at the normalized height t; n(t) is the shape factor at the normalized height t.

[0014] 1.2) The characteristic radius R(t) adopts an exponential non-linear contraction strategy; set the maximum bottom envelope radius R base , and the minimum physical radius R truncated at the top top_min , where p is the contour concave index; 1.3) In the low-frequency gradient region, i.e., when 0 ≤ t ≤ 0.70, , the cross-section gradually transitions from a full bottom shape to a star scattering shape; in the high-frequency characteristic region, i.e., when 0.70 < t ≤ 0.92, n(t) = ntop to maintain the star scattering characteristic; in the top protection region, i.e., when 0.92 < t ≤ 1, introduce the local interpolation ratio t_tip = (t - 0.92) / (1 - 0.92), and adopt the quadratic fusion algorithm to make the extremely narrow area at the very top converge rapidly to the standard circular contour (n = 2); 1.4) Define the total twist angle θ total , and the rotation angle of each layer cross-section is θ(t) = θ total ·t; after converting the polar coordinates to rectangular coordinates (x0, y0), substitute them into the rotation matrix to obtain the final two-dimensional spatial coordinates: where x0 and y0 are the rectangular coordinates of the cross-section contour points before rotation, x and y are the rectangular coordinates of the cross-section contour points after rotation, and θ(t) is the cross-section rotation angle at the normalized height t; this coordinate transformation makes each height cross-section continuously rotate around the central axis of the absorbing unit at a predetermined angle.

[0015] Append the starting coordinates at the end of the sequence, that is, forcefully satisfy x(end + 1) = x(1) and y(end + 1) = y(1); where x(1) and y(1) are the coordinates of the first contour point in the closed point set, x(end + 1) and y(end + 1) are the closed point coordinates appended at the end of the point set, and end represents the index of the last element of the current point set; this processing is used to make the polygon curve closed at both ends; 2) Automatic three-dimensional dynamic model construction: 2.1) Extract the set of rectangular coordinates (x base , y base ) of the cross-section at the bottom layer t = 0, and extract its global maximum widening through the algorithm: 2.2) Import the closed rectangular coordinate point set of N layers into the full-wave electromagnetic simulation software through automated code; for the i-th layer section at any normalized height t: firstly, calculate the two-dimensional rectangular coordinate closed point set that satisfies Gielis's hyperformation, nonlinear radius decay formula, and coordinate rotation matrix through numerical calculation software; secondly, activate the local coordinate system (WCS) of the electromagnetic simulation software through the communication interface, call the polygon curve drawing module in the simulation software, import and close the rectangular coordinate point set in sequence, and generate a two-dimensional closed curve representing the current section contour; then call the three-dimensional surface lofting construction module, select the closed curves of the i-th layer and the (i+1)-th layer in sequence for lofting, and generate a local three-dimensional entity between adjacent layers; 3) A genetic algorithm is used to design the structural parameters of a three-dimensional gradient torsional electromagnetic absorbing structure based on a hyperformula; 4) By using direct additive manufacturing technology, the complex mathematical topology model based on Gielis's hyperformation is transformed into a high-precision physical entity absorbing structure.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention presents a three-dimensional gradient torsional electromagnetic absorbing structure based on Gielis's superformula. By utilizing spatial torsion and continuous changes in cross-sectional morphology, it breaks the resonance laws of conventional geometries, significantly increasing the scattering and multiple reflection paths of electromagnetic waves within the structure and broadening the absorption bandwidth. The exponential nonlinear radius attenuation provides a smoother wave impedance gradient, significantly reducing the reflection coefficient over a wide bandwidth. The top employs a smooth truncation design with a minimum physical radius, avoiding mesh generation errors in electromagnetic simulations and improving the yield rate in actual manufacturing. The irregularly shaped three-dimensional absorber with continuously varying curvature constructed in this invention achieves superior impedance matching and ultra-wideband absorption performance compared to uniform commercial absorbing materials. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall periodic array of the absorbing structure in an embodiment of the present invention.

[0018] Figure 2 This is a three-dimensional geometric and parameter identification diagram of a single three-dimensional gradient torsional absorbing unit according to an embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of cross-sectional evolution and segmented control based on the hyperformula in an embodiment of the present invention.

[0020] Figure 4 The full-wave electromagnetic simulation reflectivity S in this embodiment of the invention 11 Line graph.

[0021] Figure 5 This is a schematic diagram of surface current distribution and electromagnetic energy loss in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the mathematical model calculations, automated modeling processes, and material manufacturing processes of the embodiments. The embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0023] Reference Figure 1 A low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave-absorbing structure includes an upper layer of wave-absorbing units, a middle layer of uniform wave-absorbing material plates, and a bottom layer of metal reflective plates connected in sequence. The bottom of the wave-absorbing unit is in contact with the upper surface of the uniform wave-absorbing material plate, and the lower surface of the uniform wave-absorbing material plate is in contact with the metal reflective plate. The wave-absorbing unit is a three-dimensional solid, which is formed by multiple parallel horizontal cross-sections stacked in the height direction. The aforementioned absorbing units and uniform absorbing material plates are periodically arranged in the horizontal and vertical directions. A polar coordinate system is established with the center of the bottom surface of the absorbing unit as the origin. The polar coordinates (r, φ) of the point set on the edge profile of the horizontal section at any normalized height t satisfy the Gielis hyperformation: Where t is the normalized height, t=z / H, z is the height of the current horizontal section relative to the bottom of the absorbing unit, H is the total height of the absorbing unit, and 0≤t≤1; φ is the azimuth angle, and 0≤φ≤2π; r(φ) is the polar radius from the edge point of the section at azimuth angle φ to the central axis; m is the symmetry parameter of the Gielis hyperformation, and is a positive integer; R(t) is the characteristic radius at the normalized height t; n(t) is the shape factor at the normalized height t.

[0024] The horizontal cross section is continuously twisted along the central axis of the three-dimensional solid, forming a gradually twisted outer surface with a continuous curvature change in space.

[0025] The symmetry parameter m is an integer between 3 and 8, and the horizontal cross-section exhibits a circular symmetry at the bottom; the characteristic radius R(t) decreases exponentially and non-linearly with the normalized height t, and retains the minimum physical cutoff radius at the top, satisfying the following relationship: Among them, R base R is the maximum envelope radius at the bottom of the absorbing unit. top_min Minimum physical radius for top truncation and R top_min >0, where p is the contour concavity index, used to characterize the degree of nonlinear decay of the feature radius along the height direction.

[0026] The total height of the wave-absorbing unit is 15 to 30 mm; the maximum envelope radius R at the bottom base is 10 to 20 mm, and the minimum physical radius R at the truncated top top_min is 0.5 mm, and the contour concave index p is 0.5 to 4.

[0027] The shape factor n(t) evolves in a piecewise manner with the normalized height t to achieve tip morphology transition and rounding protection. The specific piecewise evolution rule is as follows: When 0 ≤ t ≤ 0.70, the shape factor satisfies: where n bottom is the bottom shape factor, n top is the target top shape factor, t1 is the first height threshold t1 = 0.70; when t1 < t ≤ t2, the shape factor satisfies n(t) = n top , where t2 is the second height threshold and t2 = 0.92; when t2 < t ≤ 1, the shape factor satisfies a quadratic smooth transition: where t tip is the local normalized interpolation ratio within the top protection area and ; n(t) is the shape factor of the top protection area, n = 2 indicates that the topmost converges to a rounded contour to reduce tip mesh singularities and improve actual forming stability.

[0028] The rotation angle of the spatially continuous twist of the horizontal section increases linearly with the normalized height t and satisfies , where the total twist angle takes values in 0 to 360°.

[0029] The side length dimension of the metal reflector is adaptively defined by the maximum widening of the bottom contour of the wave-absorbing unit; let the set of rectangular coordinates at t = 0, i.e., the bottom surface of the wave-absorbing unit, be (x base , y base ), and the unilateral limit reference value Substrate of the metal reflector in the X-axis and Y-axis directions satisfies: The length a of the metal reflector is 2 * Substrate + 1, in mm.

[0030] The three-dimensional solid is generated by lofting N discrete horizontal sections upward at equal intervals in sequence, where the number of layers N ≥ 20; when lofting between adjacent two horizontal sections, the automatic minimization of the twist path configuration is disabled to retain the rotation angle Defined spatial torsional surface features; all adjacent interlayer solid segments generated by lofting are seamlessly merged into a single formed structure through Boolean addition.

[0031] The absorbing unit is made of an electromagnetic loss composite material; the electromagnetic loss composite material includes a lightweight insulating matrix and an electromagnetic loss agent uniformly dispersed in the lightweight insulating matrix; the lightweight insulating matrix is ​​at least one of photosensitive resin, thermoplastic polymer, silicone rubber, polyurethane or aerogel material; the electromagnetic loss agent is at least one of carbonyl iron powder, graphene, carbon fiber, carbon nanotube or conductive carbon black; the metal reflector is made of aluminum plate, copper plate or carbon fiber reinforced composite material, and its thickness is much greater than the skin depth of the material in the operating frequency band.

[0032] The three-dimensional solid structure of the absorbing unit and the uniform absorbing material plate is formed by direct additive manufacturing or mold coating process. Specifically, it includes: converting the parametric geometric data of the three-dimensional solid into a surface subdivision mesh format file and slicing it, using composite polymer wire containing electromagnetic loss agent as consumable, and printing it layer by layer from the metal reflector upwards using fused deposition modeling (FDM) process.

[0033] Reference Figure 2 A method for constructing a three-dimensional gradient torsional electromagnetic absorbing structure based on a hyperformation includes the following steps: 1) Geometric parameterization based on hyperformation and spatial torsion: This embodiment details the core mathematical model and morphological evolution mechanism of the three-dimensional absorbing unit. In this embodiment, the main body height of the three-dimensional gradient torsional electromagnetic absorbing structure is set to h. To achieve high-precision surface reconstruction, the main body is discretized into N=20 horizontal sections at equal intervals along the height direction, and the normalized height of the i-th layer section is defined as... , where i = 1, 2, ..., N, where This describes the relative position of the current layer within the total height. 1.1) Calculation of two-dimensional polar coordinates of the cross section: At height t, a planar polar coordinate system is established, and the azimuth angle φ is sampled at equal intervals with a high density of 360 nodes within the range of [0, 2π]. The polar radius r(φ) of each node strictly follows the Gielis hyperformation: Where t is the normalized height, t=z / H, z is the height of the current horizontal section relative to the bottom of the absorbing unit, H is the total height of the absorbing unit, and 0≤t≤1; φ is the azimuth angle, and 0≤φ≤2π; r(φ) is the polar radius from the edge point of the section at azimuth angle φ to the central axis; m is the symmetry parameter of the Gielis hyperformation, and is a positive integer; R(t) is the characteristic radius at the normalized height t; n(t) is the shape factor at the normalized height t.

[0034] In this embodiment, the symmetry parameter m makes the cross-section exhibit symmetric topological characteristics; 1.2) Adaptive exponential radius decay: To ensure the smooth transition of impedance when electromagnetic waves are incident from air, the characteristic radius R(t) adopts an exponential non-linear contraction strategy; set the maximum bottom envelope radius R base = 15 mm, the minimum physical radius R at the top truncation top_min = 0.5 mm. The minimum physical radius at the top truncation can effectively eliminate the electromagnetic simulation singularity and physical tip stress concentration caused by the absolute tip. p is the profile concave index, and the decay relationship satisfies: ; 1.3) Piecewise cross-section morphology evolution and tip rounding protection: To balance low-frequency broadband absorption and top mechanical stability, the shape factor n(t) adopts piecewise control: In the low-frequency gradual change region (0 ≤ t ≤ 0.70): , the cross-section gradually transitions from a plump pentagon to a sharp star; in the high-frequency characteristic region (0.70 < t ≤ 0.92): n(t) = n top , maintaining a strong star scattering characteristic and enhancing the absorption of high-frequency electromagnetic waves; in the top protection region (0.92 < t ≤ 1): Introduce the local interpolation ratio , and adopt the quadratic fusion algorithm , so that the extremely narrow area at the top quickly converges to the standard circular contour (n = 2), realizing a smooth transition at the top; 1.4) Continuous rotation coordinate transformation: In this embodiment, the total twist angle θ total is defined, and the rotation angle of each layer cross-section is θ(t) = θ total ·t; After converting the polar coordinates to rectangular coordinates (x0, y0), substitute them into the rotation matrix to obtain the final two-dimensional spatial coordinates: Among them, x0 and y0 are the rectangular coordinates of the cross-section contour points before rotation, x and y are the rectangular coordinates of the cross-section contour points after rotation, and θ(t) is the cross-section rotation angle at the normalized height t; This coordinate transformation makes the cross-sections at each height continuously rotate around the central axis of the absorbing unit at a predetermined angle.

[0035] To ensure the subsequent three-dimensional lofting to generate a closed solid, the starting coordinates are appended at the end of the sequence, that is, forced to satisfy x(end + 1) = x(1) and y(end + 1) = y(1); Among them, x(1) and y(1) are the coordinates of the first contour point in the closed point set, x(end + 1) and y(end + 1) are the closed point coordinates appended at the end of the point set, and end represents the index of the last element of the current point set; This processing is used to make the polygon curve close at both ends.

[0036] 2) Automated 3D Dynamic Model Construction: This example illustrates how to convert a mathematical point set into a physical entity model and define the underlying metal reflector.

[0037] 2.1) Modeling of Adaptive Uniform Absorbing Material Plate and Metal Reflector: Extracting the Cartesian Coordinate Set (x, y, t) of the Bottom Section (t=0) base , y base The algorithm extracts its global maximum width: In this embodiment, the X-axis and Y-axis coordinate generation domain of the metal reflector is precisely defined as [-Substrate -0.5, Substrate +0.5] mm. Within this region, a carbon black uniform absorbing material plate with a thickness of 1 mm and an ideal electrical conductor (PEC) model are constructed from top to bottom respectively. 2.2) Solid modeling of the upper-layer absorbing unit: The closed rectangular coordinate point set of N=20 layers is imported into the full-wave electromagnetic simulation software through automated code; for the i-th layer section at any normalized height t: firstly, the Gielis standard is calculated using numerical calculation software. The system first uses a set of two-dimensional rectangular coordinate closed points, including the hyperformation formula, the nonlinear radius decay formula, and the coordinate rotation matrix. Then, it activates the local coordinate system (WCS) of the electromagnetic simulation software via a communication interface, calls the polygon curve drawing module in the simulation software, and imports and closes the aforementioned rectangular coordinate point set sequentially to generate a two-dimensional closed curve representing the current cross-sectional profile. Next, it calls the three-dimensional surface lofting construction module, sequentially selecting the closed curves of the i-th and i+1-th layers for lofting, generating local three-dimensional entities between adjacent layers. When executing the lofting command, the system's "automatic minimization of torsion" function is disabled to ensure that the irregular torsion mathematical model can be accurately restored to a physical geometric entity. After generating N-1 segments of local three-dimensional entities, using the bottom-most local entity as the main body, it uses a loop to call Boolean addition commands to seamlessly merge all local entities into a homogeneous absorbing unit entity model without internal interfaces. Finally, it imports the relevant electromagnetic dispersion properties of the carbon black-PLA material used in this embodiment into the model for full-wave electromagnetic simulation. 3) Structural parameter optimization design and full-wave electromagnetic simulation verification based on genetic algorithm: 3.1) Structural parameter optimization design: The genetic algorithm is used to design the structural parameters of the three-dimensional gradient torsional electromagnetic absorbing structure based on the super formula. The design goal is to enable the electromagnetic absorbing structure to achieve efficient electromagnetic wave absorption in the ultra-wideband of 4~18GHz within a limited thickness and period size, i.e., reflection loss S11<-10dB, while taking into account the low profile characteristics, geometric continuity and practical additive manufacturing feasibility of the structure.

[0038] Referring to FIG. 2, the three-dimensional gradient torsion absorbing unit in this embodiment gradually shrinks from the bottom to the top. Its main geometric parameters include the total height H of the absorbing unit, the maximum bottom envelope radius R base , the minimum physical radius R top_min truncated at the top, the contour concave index p, the total continuous torsion angle θtotal in space, and the number of cross-sectional layers N. Among them, the total height H is used to define the low-profile degree of the absorbing unit; the maximum bottom envelope radius R base is used to determine the contact area between the bottom of the absorbing unit and the homogeneous absorbing material plate and the low-frequency coupling ability; the minimum physical radius R top_min truncated at the top is used to avoid forming an absolute tip, thereby reducing the electromagnetic simulation grid singularity and the risk of tip collapse during the actual printing process; the contour concave index p is used to control the contraction rate of the absorbing unit along the height direction; the total continuous torsion angle θtotal in space is used to control the cumulative rotation degree from the bottom cross-section to the top cross-section. By adjusting the contour concave index p, the concave degree of the side wall of the absorbing unit in FIG. 2 and the impedance gradient path can be changed. When p is small, the radius decays rapidly in the area near the bottom, and the contraction trend in the upper part of the structure is relatively gentle; when p is large, the radius maintains a relatively large lateral scale at the bottom and middle, and rapidly shrinks in the area near the top. This non-linear contraction method enables the incident electromagnetic wave to experience a smoother equivalent impedance transition when entering the absorbing structure from free space, thereby reducing the front surface reflection.

[0039] Referring to FIG. 3, in this embodiment, the cross-sectional shape factor n(t) is further used as an important optimization object to control the continuous evolution of the cross-sectional contour from a full shape to a star scattering shape and a rounded shape at the top at different heights. Specifically, in the low-frequency gradient region 0 ≤ t ≤ 0.70, the shape factor gradually transitions from the bottom shape factor nbottom to the target top shape factor ntop. This region corresponds to the cross-sectional evolution process from the bottom to the middle and upper parts in FIG. 3, and its function is to make the absorbing unit form a transition from a large-scale full contour to a sharp scattering contour in the direction close to the incident surface, so as to balance the low-frequency impedance matching and the mid-frequency scattering loss. In the high-frequency characteristic region 0.70 < t ≤ 0.92, the shape factor remains n(t) = n top , so as to maintain a strong star or sharp corner scattering characteristic in this height interval to increase the diffraction, reflection and multi-path propagation of high-frequency electromagnetic waves on the surface of the absorbing unit. In the top protection region 0.92 < t ≤ 1, a local interpolation ratio t tip = (t - 0.92) / (1 - 0.92) is introduced, and the shape factor transitions to a rounded contour according to the following quadratic fusion rule: n(t) = n top ·(1 t tip ^2)+2.0·t tip ^2 Through the above-mentioned top protection design, the top region of the absorbing unit can gradually transition from a sharp star shape to a smooth cross-section that is close to a circle. This not only preserves the strong scattering characteristics of the middle and upper regions, but also avoids problems such as sharp point singularities, difficult mesh division, or insufficient processing strength at the extremely small top cross-section.

[0040] Meanwhile, referring to the spatial torsion parameters shown in Figure 2, this embodiment uses the rotation angle θ(t) of each height section as a function of the optimization variable θtotal, satisfying: θ(t) = θtotal·t Here, θtotal represents the total torsion angle of the absorbing unit from bottom to top. By adjusting θtotal, the relative rotation between adjacent sections can be changed, allowing the three-dimensional absorbing unit to form a continuous torsional outer surface. This torsional outer surface can break the single resonant path in conventional axisymmetric absorbers, causing the incident electromagnetic waves to produce more complex oblique propagation, polarization deflection, and multiple scattering within the structure, thereby broadening the effective absorption bandwidth.

[0041] Therefore, the optimization variables of the genetic algorithm in this embodiment include: the symmetry parameter m, and the maximum envelope radius R at the bottom of the symmetry parameter. base Concave index p, bottom shape factor n bottom Target top shape factor n top And the total continuous spatial torsion angle θtotal.

[0042] Where m is the symmetry parameter in the Gielis hyperformation, used to determine the symmetric topological characteristics of the cross-sectional profile; Rbase is used to adjust the maximum bottom broadening and low-frequency coupling capability; p is used to adjust the radius nonlinear attenuation curve; nbottom and ntop are used to adjust the evolution amplitude of the cross-sectional profile in Figure 3 from a full bottom shape to a star-shaped scattering shape in the upper middle part; θtotal is used to adjust the overall spatial torsion of the three-dimensional absorbing unit in Figure 2. The above parameters are coupled: Rbase and H jointly affect the equivalent electrical size in the low-frequency band, p and Rtop_min jointly affect the impedance gradient smoothness, nbottom and ntop jointly affect the sharpness of the cross-section and scattering capability, and θtotal affects the degree of spatial misalignment and multiple reflection paths between cross-sections of different heights.

[0043] In the optimization process, an initial population is first randomly generated based on a given parameter range. Then, each set of parameters is substituted into the Gielis super formula, the radius attenuation formula, the shape factor piecewise evolution formula, and the spatial rotation formula to generate the corresponding three-dimensional gradient torsional absorbing unit model. After that, full-wave electromagnetic simulation is performed on the model, and the reflection loss S11 curve in the range of 4–18 GHz is extracted. Finally, a fitness function is constructed based on whether the reflection loss is lower than -10 dB, the average reflection level across the entire frequency band, and the degree of curve fluctuation. The population is then subjected to selection, crossover, and mutation iterations until a combination of structural parameters that meets the broadband absorbing target is obtained.

[0044] In this embodiment, based on the optimization results of the genetic algorithm, the following optimal parameter set was determined: After determining the total structural height H to be 25mm, the symmetry parameter m was optimized to be 5, and the maximum envelope radius R was determined to be... base The diameter is 15mm, the concavity index p is 1.6, and the bottom shape factor n is 1.6. bottom The target top shape factor ntop is 1, and the total torsion angle θtotal is 120°. Therefore, the three-dimensional absorbing unit shown in Figure 2 exhibits an overall low-profile irregular structure that gradually contracts and continuously twists from bottom to top. The horizontal section shown in Figure 3 undergoes an evolution along the height direction, successively transforming into a full bottom section, a star-shaped scattering section in the upper middle part, and a rounded protective section at the top. This parameter combination can simultaneously enhance low-frequency impedance matching, mid-to-high frequency multiple scattering, and top processing stability within a limited height, providing an optimized geometric model for subsequent full-wave electromagnetic simulation verification.

[0045] 3.2) Full-wave electromagnetic simulation verification: The main material was set as homogeneous carbon black electromagnetic loss medium, and the metal reflector was set as an ideal electrical conductor (PEC). Full-wave simulation was performed in the CST microwave studio with periodic boundary conditions and plane wave excitation. The results are as follows: Figure 4 As shown, Figure 4 The reflection loss S11 curves of the absorbing structure in this embodiment are given in the range of 2~20GHz. The curves are generally lower than those in the range of 4~20GHz. A 10dB threshold indicates that the structure can achieve effective electromagnetic absorption over a wide frequency range, validating the optimization objective of the genetic algorithm. Combined with... Figure 5As shown in the electric field and loss density distribution diagrams, the absorbing unit constructed in this embodiment exhibits a synergistic broadband dissipation mechanism at different frequency bands. In the mid-to-low frequency band of 4.8 GHz, thanks to the exponential impedance gradient, electromagnetic energy is smoothly coupled into the structure, with losses mainly concentrated in the upper and middle gradient contour region. In the high frequency band of 19.6 GHz, the continuously twisted spatial surface significantly enhances the parasitic coupling and multiple scattering effects between adjacent array units, causing strong multimodal resonance and polarization deflection of high-frequency electromagnetic waves throughout the entire three-dimensional contour and bottom gap, thereby achieving efficient global dissipation within the dielectric volume. This physical field characteristic demonstrates that the irregular topology structure of this embodiment can balance impedance gradient and multiple scattering loss under low profile conditions, thereby improving ultra-wideband absorption performance.

[0046] 4) Manufacturing method of three-dimensional gradient torsional absorbing structure based on fused deposition modeling (FDM) process: This embodiment details how to transform the complex mathematical topological model based on Gielis's super formula into a high-precision physical absorbing structure through direct additive manufacturing technology (3D printing), and gives the key process parameters and their mechanism of action on the final electromagnetic performance.

[0047] 4.1) Preparation of electromagnetic loss composite wire: In order to meet the requirements of FDM printing and broadband electromagnetic absorption characteristics, a homogeneous composite printing consumable is first prepared. Thermoplastic polyurethane (TPU) or polylactic acid (PLA), polymers with excellent interlayer adhesion, are selected as lightweight, microwave-transparent matrices. Conductive carbon black is added as an electromagnetic loss agent at a mass percentage of 20-50%. The mixture is melt-blended in a twin-screw extruder at 180°C-220°C and then extruded and drawn into fibers to obtain electromagnetic loss composite wires with a diameter of 1.75±0.05mm. The technical purpose and beneficial effect of this step is that the loss agent is pre-dispersed under high shear in the twin-screw extruder, which not only prevents nozzle clogging during FDM printing but also ensures that the carbon-based nanomaterials construct a continuous and uniform three-dimensional conductive network in the polymer matrix, thereby providing a stable macroscopic equivalent complex permittivity for the subsequent solid structure. 4.2) Data Discretization and Slicing of the 3D Model: The parametric 3D solid model generated by mathematical topological formulas is exported as a surface subdivision mesh format file (STL) and imported into slicing software for path planning; the single-layer printing thickness is set to 0.2mm~0.4mm. Since the wave-absorbing unit of this invention has a 120° spatial continuous twist along the height direction and an exponential radius contraction characteristic of p=1.6, if the layer thickness is set too large, it will lead to a serious step effect; strictly controlling the layer thickness to below 0.4mm can reconstruct the continuous gradual gradient of the equivalent wave impedance with extremely high physical fidelity and avoid the unexpected high-frequency electromagnetic wave scattering caused by macroscopic steps; the internal fill rate is set to 100%, and concentric circles or straight lines are used to alternately fill the path; 4.3) FDM Deposition Printing and Dynamic Temperature Control Strategy: After surface polishing, the metal reflector is fixed on the heating platform of the FDM 3D printer. The aforementioned composite filament is used to directly print the microwave absorbing unit from bottom to top. The key parameter constraints during the printing process are as follows: 4.3.1) Printhead and heated bed temperature: Set the printhead temperature to 270°C~290°C, select a printhead with a diameter of 0.4mm, and the heated bed temperature to 50°C~70°C; 4.3.2) Zoned frequency conversion printing speed: In the uniform absorbing material plate and the middle and lower part of the structure (area with a height of less than 20mm), the printing speed is set to 30mm~50mm / s; when printing to the top extremely narrow area (the tip area with a height of 20~25mm), since the cross-sectional feature radius has been reduced to close to 0.5mm, the single-layer printing speed is forcibly reduced to 10mm~15mm / s, and the minimum interlayer cooling time is extended to more than 5s.

[0048] The technical mechanism and beneficial effects of this embodiment are as follows: In the extremely small cross-sectional area at the top, if the normal speed is maintained, the continuously extruded high-temperature molten material will accumulate heat due to insufficient heat dissipation, causing the rounded part of the tip to collapse or deform. By introducing a low-speed cooling and forced heat dissipation cooling strategy, the smooth truncated characteristics of the microwave absorbing structure can be perfectly solidified, and the electromagnetic simulation model that eliminates singularities can be accurately reproduced while ensuring mechanical strength.

Claims

1. A low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure, characterized in that, It includes an upper layer of absorbing units, a middle layer of uniform absorbing material plate, and a bottom layer of metal reflector plate connected in sequence; the absorbing unit is a three-dimensional entity, which is formed by multiple parallel horizontal cross-sections stacked in the height direction; The aforementioned absorbing units and uniform absorbing material plates are periodically arranged in the horizontal and vertical directions. A polar coordinate system is established with the center of the bottom surface of the absorbing unit as the origin. The polar coordinates (r, φ) of the point set on the edge profile of the horizontal section at any normalized height t satisfy the Gielis hyperformation: Where t is the normalized height, t=z / H, z is the height of the current horizontal section relative to the bottom of the absorbing unit, H is the total height of the absorbing unit, and 0≤t≤1; φ is the azimuth angle, and 0≤φ≤2π; r(φ) is the polar radius from the edge point of the section at azimuth angle φ to the central axis; m is the symmetry parameter of the Gielis hyperformation, and is a positive integer; R(t) is the characteristic radius at the normalized height t; n(t) is the shape factor at the normalized height t; The horizontal cross section is continuously twisted along the central axis of the three-dimensional solid, forming a gradually twisted outer surface with a continuous curvature change in space.

2. The low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 1, characterized in that, The symmetry parameter m is an integer between 3 and 8, and the horizontal cross-section exhibits a circular symmetry at the bottom; the characteristic radius R(t) decreases exponentially and non-linearly with the normalized height t, and retains the minimum physical cutoff radius at the top, satisfying the following relationship: Among them, R base R is the maximum envelope radius at the bottom of the absorbing unit. top_min Minimum physical radius for top truncation and R top_min >0, where p is the contour concavity index, used to characterize the degree of nonlinear decay of the feature radius along the height direction.

3. The low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 2, characterized in that, The total height of the absorbing unit is 15~30mm; the maximum bottom envelope radius R base The minimum physical radius R of the top cutoff is 10~20mm. top_min The diameter is 0.5 mm, and the concavity index p is 0.5~4.

4. The low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 1, characterized in that, The shape factor n(t) evolves in a segmented manner with the normalized height t to achieve tip shape transition and rounding protection. The specific segmented evolution law is as follows: When 0≤t≤0.70, the shape factor satisfies: where n bottom is the bottom shape factor, and n top is the target top shape factor, t1 is the first height threshold and t1 = 0.70; when t1 < t ≤ t2, the shape factor satisfies n(t) = n top , where t2 is the second height threshold and t2 = 0.92; when t2 < t ≤ 1, the shape factor satisfies a quadratic smooth transition: Where t tip The local normalized interpolation ratio within the top protected area and n(t) is the shape factor of the apex protection zone. n=2 indicates that the apex converges to a rounded profile to reduce the singularity of the tip mesh and improve the actual forming stability.

5. The low-profile ultra-wideband three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 1, characterized in that, Rotation angle of continuous spatial torsion of horizontal cross section As the normalized height t increases linearly, it satisfies The total torsion angle The value ranges from 0 to 360°.

6. The low-profile ultra-wideband three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 5, characterized in that, The side length of the metal reflector is adaptively defined by the maximum widening of the bottom surface profile of the absorbing unit; let the rectangular coordinate set of the bottom surface of the absorbing unit, i.e., at t=0, be (x base , y base The single-sided constraint reference values ​​Substrate of the metal reflector in the X and Y axes satisfy: Where, x base and y base These are the coordinate sets of the bottom contour points of the absorbing unit in the X-axis and Y-axis directions, respectively. Substrate is the single-sided constraint reference value of the metal reflector in the X-axis and Y-axis directions. The length a of the metal reflector is 2*Substrate+1, in mm.

7. The low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 1, characterized in that, The three-dimensional entity is generated by sequentially lofting upwards at equal intervals from N discrete horizontal cross-sections, where the number of layers N ≥ 20; when lofting between adjacent horizontal cross-sections, automatic minimization of the torsion path configuration is disabled to preserve the rotation angle. Defined spatial torsional surface features; All adjacent interlayer solid segments generated by the lofting are seamlessly merged into a single formed structure through Boolean addition.

8. A low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure as described in any one of claims 1-7, characterized in that, The absorbing unit is made of an electromagnetic loss composite material; the electromagnetic loss composite material includes a lightweight insulating matrix and an electromagnetic loss agent uniformly dispersed in the lightweight insulating matrix; the lightweight insulating matrix is ​​at least one of photosensitive resin, thermoplastic polymer, silicone rubber, polyurethane or aerogel material; the electromagnetic loss agent is at least one of carbonyl iron powder, graphene, carbon fiber, carbon nanotube or conductive carbon black; the metal reflector is made of aluminum plate, copper plate or carbon fiber reinforced composite material, and its thickness is much greater than the skin depth of the material in the operating frequency band.

9. The low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic wave absorbing structure as described in claim 1, characterized in that, The three-dimensional solid structure of the absorbing unit and the uniform absorbing material plate is formed by direct additive manufacturing or mold coating process. Specifically, it includes: converting the parametric geometric data of the three-dimensional solid into a surface subdivision mesh format file and slicing it, using composite polymer wire containing electromagnetic loss agent as consumable, and printing it layer by layer from the metal reflector upwards using fused deposition modeling (FDM) process.

10. A method for constructing a low-profile, ultra-wideband, three-dimensional gradient torsional electromagnetic absorbing structure according to any one of claims 1-9, comprising the following steps: 1) Geometric parameterization based on hyperformation and spatial torsion: 1.1) At height t, establish a planar polar coordinate system. Perform high-density 360-node equally spaced sampling within the range of [0, 2π]. The polar radius r(φ) of each node strictly follows the Gielis hyperformation: Where t is the normalized height, t=z / H, z is the height of the current horizontal section relative to the bottom of the absorbing unit, H is the total height of the absorbing unit, and 0≤t≤1; φ is the azimuth angle, and 0≤φ≤2π; r(φ) is the polar radius from the edge point of the section at azimuth angle φ to the central axis, and is a positive integer; R(t) is the characteristic radius at normalized height t; n(t) is the shape factor at normalized height t; 1.2) The characteristic radius R(t) adopts an exponential nonlinear contraction strategy; the maximum bottom envelope radius R is set. base Minimum physical radius R of top truncation top_min p is the concavity index of the profile; 1.3) In the low-frequency gradual change region, i.e., when 0 ≤ t ≤ 0.70, , the cross-section gradually transitions from a full-bottom shape to a star-shaped scattering shape; in the high-frequency characteristic region, i.e., when 0.70 < t ≤ 0.92, n(t) = ntop to maintain the star-shaped scattering characteristic; in the top protection region, i.e., when 0.92 < t ≤ 1, a local interpolation ratio t_tip = (t - 0.92) / (1 - 0.92) is introduced, and a quadratic fusion algorithm is adopted to make the extremely narrow region at the very top converge rapidly to the standard circular contour (n = 2); 1.4) Define the total twist angle θ total The rotation angle of each cross-section is θ(t) = θ total ·t; After converting the polar coordinates to rectangular coordinates (x0, y0), substituting them into the rotation matrix yields the final two-dimensional spatial coordinates: Where x0 and y0 are the rectangular coordinates of the profile point of the cross section before rotation, x and y are the rectangular coordinates of the profile point of the cross section after rotation, and θ(t) is the rotation angle of the cross section at the normalized height t; this coordinate transformation causes each height cross section to rotate continuously around the central axis of the absorbing unit at a predetermined angle; The starting coordinates are appended to the end of the sequence, that is, the conditions x(end+1) = x(1) and y(end+1) = y(1) are forced to be met; where x(1) and y(1) are the coordinates of the first contour point in the closed point set, x(end+1) and y(end+1) are the coordinates of the closed point appended to the end of the point set, and end represents the index of the last element of the current point set; this process is used to make the beginning and end of the polygon curve closed. 2) Automated 3D dynamic model construction: 2.1) Extract the rectangular coordinate set (x) of the bottom section at t=0. base , y base The algorithm extracts its global maximum width: 2.2) Import the closed rectangular coordinate point set of N layers into the full-wave electromagnetic simulation software through automated code; for the i-th layer section at any normalized height t: firstly, calculate the two-dimensional rectangular coordinate closed point set that satisfies Gielis's hyperformation, nonlinear radius decay formula, and coordinate rotation matrix through numerical calculation software; secondly, activate the local coordinate system (WCS) of the electromagnetic simulation software through the communication interface, call the polygon curve drawing module in the simulation software, import and close the rectangular coordinate point set in sequence, and generate a two-dimensional closed curve representing the current section contour; then call the three-dimensional surface lofting construction module, select the closed curves of the i-th layer and the (i+1)-th layer in sequence for lofting, and generate a local three-dimensional entity between adjacent layers; 3) A genetic algorithm is used to design the structural parameters of a three-dimensional gradient torsional electromagnetic absorbing structure based on a hyperformation. 4) By using direct additive manufacturing technology, the complex mathematical topology model based on Gielis's hyperformation is transformed into a high-precision physical entity absorbing structure.

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