Discrete fractal structure of quadratic surface structure and multi-level approximation suspended 3D printing method

Abstract

A discrete fractal structure of a quadratic surface structure and a multi-level approximation suspended 3D printing method are divided into a Cartesian coordinate discrete structure and a polar coordinate discrete structure according to the discretization method. The Cartesian coordinate discrete structure and the polar coordinate discrete structure both include an edge bracket, the edge bracket is internally connected to a suspended approximation curve structure, the suspended approximation curve structure is connected to a discrete polyhedron, and the discrete polyhedron is connected to a quadratic surface. The suspended approximation curve structure in the form of a Cartesian coordinate discrete structure consists of a multi-level approximation curve structure and an intersecting approximation curve structure, and the suspended approximation curve structure in the form of a polar coordinate discrete structure consists of a multi-level approximation curve structure, a fractal unit structure, and a surrounding polygon structure. The multi-level approximation curve structure, the intersecting approximation curve structure, the fractal unit structure, and the surrounding polygon structure are manufactured using a multi-level approximation suspended 3D printing method to achieve efficient suspended forming of the quadratic surface structure.

Description

Technical Field

[0001] The present invention belongs to the field of additive manufacturing technology, and specifically relates to a discrete fractal structure of a quadratic surface structure and a multi-level approximation suspended 3D printing method. Background Art

[0002] A quadratic surface is a mathematical concept that describes any type of surface that can be represented by a quadratic equation. These include spheres, paraboloids, cylinders, cones, and hyperboloids. A straight line other than the generatrix of a surface intersects a quadratic surface at two points and is tangent to it at one point. In engineering, quadratic surfaces are widely used in the design of structural components in fields such as acoustics, electromagnetics, and fluid mechanics. For example, quadratic surfaces are used to model the propagation and reflection of sound to optimize audio system design; they are used to adjust the distribution of electric and magnetic fields to analyze and optimize the directivity of antennas; and they are used to adjust the flow and pressure distribution of fluids to optimize the design of external structures such as wings and vehicles.

[0003] Traditional manufacturing methods for quadratic surface structures require mold development, resulting in complex processes, long production cycles, and high manufacturing costs. Furthermore, mold size limitations make it difficult to form large, integrated curved structures. 3D printing technology has greatly facilitated the development of quadratic surface structures, with material extrusion 3D printing being the most widely used 3D printing technology.

[0004] However, existing material extrusion 3D printing methods often require additional supports for curved structures with large inclination angles to overcome external forces such as gravity, preventing material collapse and ensuring the component's shape accuracy. This type of support extends from the platform to the component surface, consuming a large amount of material and manufacturing time, while also increasing the component's weight. To reduce the support structure required for 3D printing, a patent application entitled "An Efficient 3D Printing Apparatus and Method for Composite Material Sparse Structures" (Publication No.: CN115320093B) proposes a suspended 3D printing method that utilizes continuous fiber tension to achieve support-free printing of composite material sparse structures. Although this method principle has a good forming effect on linear structures, it is difficult to achieve the manufacture of quadratic curved surface structures with high surface accuracy requirements. Summary of the Invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a discrete fractal structure of a quadratic surface structure and a multi-level approximation suspended 3D printing method to achieve efficient suspended forming of the quadratic surface structure.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The discrete fractal structure of the quadratic surface structure is divided into a Cartesian coordinate discrete structure and a polar coordinate discrete structure according to the discretization method. The Cartesian coordinate discrete structure and the polar coordinate discrete structure both include an edge bracket 1, the upper surface of the edge bracket 1 is connected to a suspended approximation curve structure, the upper surface of the suspended approximation curve structure is connected to a discrete polyhedron 3, and the upper surface of the discrete polyhedron 3 is connected to a quadratic surface 4; the suspended approximation curve structure in the form of the Cartesian coordinate discrete structure is composed of a multi-level approximation curve structure 2-1 and an intersecting approximation curve structure 2-2, and the suspended approximation curve structure in the form of the polar coordinate discrete structure is composed of a multi-level approximation curve structure 2-1, a fractal unit structure 2-3 and a surrounding polygon structure 2-4; the suspended approximation curve structure is manufactured using a multi-level approximation suspended 3D printing method.

[0008] The multi-level approximation suspended 3D printing method of the multi-level approximation curve structure 2-1 comprises the following steps:

[0009] 1) First-order approximation line 3D printing: A continuous fiber composite material tow forms a node at point A on a hollow edge support 1. Internal tension is applied to the tow, and the tow is suspended and pulled from point A to point B. When the 3D printing head moves to point B to form the node, a long-span suspended straight line segment AB is formed. This straight line segment AB is defined as the first-order approximation line. The straight line segment AB is tangent to the target curve CF, and the tangent point is O.

[0010] 2) 3D printing of the secondary approximation line: A node is formed at the intersection C of the target curve CF and the edge bracket 1. The tow is pulled from point C to point D, forming node D on the straight line segment AB. Similarly, the tow is pulled from point D to point E and then to point F, forming a series of strong nodes. The continuous broken line segment CDEF is defined as the secondary approximation line. It is necessary to ensure that the straight line segment CD is tangent to the target curve CF at point C, the straight line segment EF is tangent to the target curve CF at point F, and the straight line segment DE coincides with the primary approximation line. Due to symmetry, the inflection points D and E of the secondary approximation line are equidistant axially from the target curve.

[0011] 3) 3D printing of three-level approximation lines: After forming a node at point C, the tow is pulled from point C to point G, forming node G on the straight line segment CD. Similarly, the tow is pulled through points G, H, I, J, and F in sequence to form strong nodes. The continuous broken line segments CGHIJF are defined as the three-level approximation lines. It is necessary to ensure that the straight lines GH and IJ are tangent to the curve CF respectively, and the straight lines CG, HI, and JF coincide with the two-level approximation lines respectively. At the same time, it is necessary to ensure that the axial distances between the inflection points G, H, I, and J of the three-level approximation lines and the target curve are equal.

[0012] 4) Multi-level approximation line 3D printing: The configuration of the broken line segment with more than three levels of approximation lines adopts the method of steps 1) to 3) by analogy. New tangents are introduced to cut the inflection points on the previous level of broken line segments. The distance between the new inflection points of the broken line segments composed of the new tangents and the curve is reduced to achieve further approximation to the target curve CF.

[0013] The curve approximated by the intersection approximation curve structure 2-2 is the intersection line of the quadratic surface and the intersection plane; the intersection plane intersects the reference plane in an orthogonal manner; the intersection plane intersects with the highest-level approximation lines of multiple side-by-side multi-level approximation curve structures 2-1 and the upper frame of the edge bracket 1 to obtain discrete connection points. When the print head pulls the wire bundle along one direction through the discrete connection points in sequence and deposits and fixes it, the intersection approximation curve structure 2-2 is formed; all the intersection approximation curve structures 2-2 and the highest-level approximation lines of the multi-level approximation curve structure 2-1 together constitute the framework of the discrete polyhedron 3.

[0014] The quadratic surface of the polar coordinate discrete structure is a surface of revolution, and its suspended approximation curve structure does not cross the axis of revolution. Assume that the distance from the plane to the axis of revolution, i.e., the offset distance, is equal to a. In the multi-level approximation curve structure 2-1 of the rotation array, if the latitudinal spacing is greater than the parallel line spacing 2a at a position far from the axis center in the sector area formed by the two intersecting lines, the fractal unit structure 2-3 is also a rotation array around the central axis and is evenly distributed in each sector area. The fractal unit structure 2-3 is composed of multi-level approximation lines. For each level of the structure, the configuration is determined by the axial projection of two parallel line segments and the connecting line segment at that level. The multi-level approximation suspended 3D printing method of the fractal unit structure 2-3 comprises the following steps:

[0015] 1) 3D printing of the primary structure of the fractal unit: Pull the tow from point P on the edge support 1 until it intersects with the primary approximation line of the multi-level approximation curve structure 2-1, forming a solid node M; then turn the tow at a 90° angle to intersect with another primary approximation line in the fan-shaped area, forming a node N; then turn the tow at a 90° angle back to the edge support 1 to form a node Q; define the continuous broken line structure PMNQ as the primary structure of the fractal unit, and ensure that the parallel line spacing is 2a, which is equal to the parallel line spacing of the multi-level approximation curve structure 2-1 of the array;

[0016] 2) 3D printing of multi-level structure of fractal unit: Similar to the forming principle of multi-level approximation line, the difference is that after the broken line segment of each level intersects with the approximation line of the same level of multi-level approximation curve structure 2-1, the printing path turns, which is the same as the previous step.

[0017] The fractal unit structure introduced for the first time is defined as a first-order fractal unit structure. After adding the first-order fractal unit structure, it is determined whether the latitudinal spacing of the new sector-shaped area formed by the segmentation is greater than the parallel line spacing 2a at the distance from the axis. If so, it is necessary to further introduce a second-order fractal unit structure to continue segmenting the new sector-shaped area. The construction principle of the second-order fractal unit structure is the same as above. After the second-order fractal unit structure is formed, it is determined whether the next stage of fractal unit structure needs to be introduced, and so on, until the latitudinal spacing of the final sector-shaped area away from the axis is no greater than the parallel line spacing 2a.

[0018] The forming steps of the multi-level approximation curve structure 2-1 and the fractal unit structure 2-3 are only for a single array element, while for the overall forming of the radial support structure, each array element needs to be manufactured from bottom to top according to the level; for multiple multi-level approximation curve structures 2-1 of the rotating array, and each order fractal unit structure 2-3, first surround and form the first-level approximation lines and first-level structures of all array elements, and then superimpose and form the approximation lines and fractal structures of all array elements at different levels in sequence.

[0019] The multi-level approximation suspended 3D printing method of the surrounding polygonal structure 2-4 is understood as the points formed by the intersection of the plane perpendicular to the axis of the revolution quadratic surface and the multi-level approximation curve structure 2-1 of the array and the fractal unit structures 2-3 of each order at the inflection point of the broken line segment, and the intersection points are connected in sequence to form the surrounding polygonal structure 2-4; the surrounding polygonal structure 2-4 and the highest-level approximation line of the multi-level approximation curve structure 2-1 and the fractal unit structure 2-3 together constitute the framework of the discrete polyhedron 3.

[0020] The 3D printing of the discrete polyhedron 3 is based on its frame and relies on the method of 3D printing filling surface. The wire bundles form nodes on the frame in sequence, and the print head pulls the tensioned wire bundles to fill all the surface pieces, finally obtaining a polyhedron structure.

[0021] The quadratic surface 4 and the discrete polyhedron 3 are respectively composed of multiple curved surface patches 4-1 and planar surface patches 3-1 seamlessly connected, and a single planar surface patch 3-1 corresponds to the curved surface patch 4-1 in the spatial projection direction; there is a minimum and maximum spacing between the planar surface patch 3-1 and the curved surface patch 4-1. When the spacing range is within the adjustable layer thickness range of the 3D printing filament, the transition printing from plane to curved surface is realized; 3D printing with variable layer thickness is based on the discrete polyhedron structure and relies on the flow control of the printing material to obtain the adjustability of the printing layer thickness, thereby realizing precise manufacturing from polyhedron to curved surface.

[0022] The degree of discrete refinement directly determines the size of a single facet of the discrete polyhedron 3 corresponding to the same curved surface structure. Under the premise that the surface curvature remains unchanged, it further determines the spacing range between the plane facet 3-1 and the curved facet 4-1. Before planning the 3D printing path for the quadratic surface structure, the degree of discrete refinement must be determined based on the process parameter constraints to ensure that the spacing range between all plane faces 3-1 and curved facets 4-1 is achievable.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The multi-level approximation 3D printing method adopted by the present invention solves the problem of suspended manufacturing from straight lines to curves. The curve is approximated layer by layer by stacking broken line segments with increasing approximation, replacing the traditional layer-by-layer stacked support structure, greatly reducing the use of support materials.

[0025] The discrete fractal structure adopted in the present invention solves the manufacturing problem from polyhedron to curved surface, and utilizes the layer thickness adjustable feature of the material extrusion 3D printing process to achieve high-precision manufacturing of curved surface structure based on the polyhedron structure.

[0026] The discrete fractal structure and the multi-level approximation suspended 3D printing method of the present invention are connected through the frame of the polyhedron, thereby realizing the process from suspended straight line printing to curved surface printing, which has the advantages of large span, less support and high precision.

[0027] In summary, compared to traditional additive manufacturing methods, this invention employs a structure-oriented, integrated process design, combining the characteristics of configuration and continuous path, fully leveraging the material's performance advantages within a limited, suspended structure, achieving efficient manufacturing of lightweight, high-performance monolithic structures. This invention closely aligns large-scale functional devices with the development of curved surface design, and has significant implications for reducing costs, improving performance, and overcoming limitations in the engineering field. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of a discrete fractal structure according to an embodiment of the present invention.

[0029] Figure 2 Schematic diagram of multi-level approximation suspended 3D printing of a multi-level approximation curve structure according to an embodiment of the present invention.

[0030] Figure 3 Schematic diagram of multi-level approximate suspended 3D printing of a fractal unit structure according to an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram of the axial projection of the radial support structure after multi-order fractal processing according to an embodiment of the present invention.

[0032] Figure 5 Schematic diagram of the transition relationship between the curved surface and the discrete polyhedron according to an embodiment of the present invention.

[0033] Figure 6 Other curved surface structures manufactured by the method of the embodiment of the present invention. DETAILED DESCRIPTION

[0034] The present invention is further described below with reference to the embodiments and accompanying drawings.

[0035] Reference Figure 1 The discrete fractal structure of the quadratic surface structure is divided into two categories according to the discretization method: Cartesian coordinate discrete structure and polar coordinate discrete structure. Both the Cartesian coordinate discrete structure and the polar coordinate discrete structure include an edge bracket 1, the edge bracket 1 is internally connected to a suspended approximation curve structure, the suspended approximation curve structure is connected to a discrete polyhedron 3, and the discrete polyhedron 3 is connected to a quadratic surface 4; wherein the suspended approximation curve structure in the form of the Cartesian coordinate discrete structure is composed of a multi-level approximation curve structure 2-1 and an intersecting approximation curve structure 2-2, and the suspended approximation curve structure in the form of the polar coordinate discrete structure is composed of a multi-level approximation curve structure 2-1, a fractal unit structure 2-3 and a surrounding polygon structure 2-4; the suspended approximation curve structure is manufactured by a multi-level approximation suspended 3D printing method.

[0036] The edge bracket 1 is a basic supporting structure and can be manufactured using conventional additive manufacturing methods.

[0037] The curve in the suspended approximation curve structure is the intersection line of the reference plane and the quadratic surface; the reference plane is a plane with a certain direction in space that is artificially selected when the surface is discretized into polyhedral facets.

[0038] The multi-level approximation curve structure 2-1 of the suspended approximation curve structure of the Cartesian coordinate discrete structure and the polar coordinate discrete structure is manufactured by suspended 3D printing. In order to realize suspended 3D printing, a tensionable printing filament is used to overcome the unsupported collapse in the gravity field, a continuous fiber composite material printing filament is selected, and tensioning force is applied.

[0039] Reference Figure 2 The multi-level approximation suspended 3D printing method of the multi-level approximation curve structure 2-1 comprises the following steps:

[0040] 1) First-order approximation line 3D printing: A continuous fiber composite material tow forms a node at point A on a hollow edge support 1. Internal tension is applied to the tow, and the tow is suspended and pulled from point A to point B. When the 3D printing head moves to point B to form the node, a long-span suspended straight line segment AB is formed. This straight line segment AB is defined as the first-order approximation line. The straight line segment AB is tangent to the target curve CF, and the tangent point is O.

[0041] 2) 3D printing of the secondary approximation line: A node is formed at the intersection C of the target curve CF and the edge bracket 1. The tow is pulled from point C to point D, forming node D on the straight line segment AB. Similarly, the tow is pulled from point D to point E and then to point F to form strong nodes in sequence. The continuous broken line segment CDEF is defined as the secondary approximation line. It is necessary to ensure that the straight line segment CD is tangent to the target curve CF at point C, the straight line segment EF is tangent to the target curve CF at point F, and the straight line segment DE coincides with the primary approximation line. Obviously, due to symmetry, the inflection points D and E of the secondary approximation line are equidistant from the target curve in the axial direction.

[0042] 3) 3D printing of three-level approximation lines: After forming a node at point C, the tow is pulled from point C to point G, forming node G on the straight line segment CD. Similarly, the tow is pulled through points G, H, I, J, and F in sequence to form strong nodes. The continuous broken line segments CGHIJF are defined as the three-level approximation lines. It is necessary to ensure that the straight lines GH and IJ are tangent to the curve CF respectively, and the straight lines CG, HI, and JF coincide with the two-level approximation lines respectively. At the same time, it is necessary to ensure that the axial distances between the inflection points G, H, I, and J of the three-level approximation lines and the target curve are equal.

[0043] 4) Multi-level approximation line 3D printing: The configuration of the broken line segments exceeding the third level of approximation lines is analogous to the method described in steps 1) to 3). New tangents are introduced to cut the inflection points on the previous level of broken line segments. The distance between the new inflection points of the broken line segments composed of the new tangents and the curve is reduced to achieve further approximation to the target curve CF.

[0044] Due to symmetry, the forming direction of the approximation line of any series is free and can be from any end to the other end.

[0045] For the intersection approximation curve structure 2-2 of the Cartesian coordinate discrete structure, the approximated curve is the intersection line of the quadratic surface and the intersection plane; the intersection plane intersects with the reference plane. Generally, an orthogonal method can be used to obtain a better discrete effect and improve manufacturing efficiency; the intersection plane intersects with the highest-level approximation lines of multiple side-by-side multi-level approximation curve structures 2-1 and the upper frame of the edge bracket 1 to obtain discrete connection points. When the print head pulls the wire bundle along one direction through the discrete connection points in sequence and is deposited and fixed, the intersection approximation curve structure 2-2 is formed; all the intersection approximation curve structures 2-2 and the highest-level approximation lines of the multi-level approximation curve structure 2-1 together constitute the framework of the discrete polyhedron 3.

[0046] The quadratic surface of the polar coordinate discrete structure is usually a surface of revolution, and its suspended approximation curve structure does not exceed the axis of revolution to avoid the intersection and stacking of multiple lines. The distance from the plane to the axis of revolution, that is, the offset distance, is equal to a. The fractal unit structure 2-3 is a supplement to the multi-level approximation curve structure 2-1 of the polar coordinate discrete structure. In the multi-level approximation curve structure 2-1 of the rotation array, if the latitudinal spacing is greater than the parallel line spacing 2a at the distance from the axis of the fan-shaped area formed by the two intersecting lines, the approximate approximation accuracy is reduced, and the fractal unit structure 2-3 needs to be introduced. Figure 1 , the fractal unit structure 2-3 is also rotated around the central axis and evenly distributed in each fan-shaped area.

[0047] Reference Figure 3 The fractal unit structure 2-3 is consistent with the multi-level approximation curve structure 2-1 and is composed of multi-level approximation lines. For each level of structure, the configuration is determined by the axial projection of two parallel line segments and the connecting line segment at that level. The multi-level approximation suspended 3D printing method of the independent fractal unit structure 2-3 includes the following steps:

[0048] 1) 3D printing of the primary structure of the fractal unit: Pull the tow from point P on the edge support 1 until it intersects with the primary approximation line of the multi-level approximation curve structure 2-1, forming a solid node M; then turn the tow at a 90° angle to intersect with another primary approximation line in the fan-shaped area, forming a node N; then turn the tow at a 90° angle back to the edge support 1 to form a node Q; define the continuous broken line structure PMNQ as the primary structure of the fractal unit, and ensure that the parallel line spacing is 2a, which is equal to the parallel line spacing of the multi-level approximation curve structure 2-1 of the array;

[0049] 2) 3D printing of multi-level structure of fractal unit: Similar to the forming principle of multi-level approximation line, the difference is that after the broken line segment of each level intersects with the approximation line of the same level of multi-level approximation curve structure 2-1, the printing path turns, which is the same as the previous step.

[0050] According to the above principle, the fractal unit structure 2-3 and the multi-level approximation curve structure 2-1 have the same number of levels.

[0051] The fractal unit structure introduced for the first time is defined as a first-order fractal unit structure. After adding the first-order fractal unit structure, it is determined whether the latitudinal spacing of the new sector-shaped area formed by the segmentation is greater than the parallel line spacing 2a at the distance from the axis. If so, it is necessary to further introduce a second-order fractal unit structure to continue segmenting the new sector-shaped area. The construction principle of the second-order fractal unit structure is the same as above. After the second-order fractal unit structure is formed, it is determined whether the next stage of fractal unit structure needs to be introduced, and so on, until the latitudinal spacing of the final sector-shaped area away from the axis is no greater than the parallel line spacing 2a.

[0052] Reference Figure 4 , Figure 4 Based on the rotating array multi-level approximation curve structure 2-1, the radial support structure composed of the first-order, second-order and third-order fractal unit structures is introduced to form the axial projection view.

[0053] The steps for forming the multi-level approximation curve structure 2-1 and fractal unit structure 2-3 only apply to a single array element. To form the entire radial support structure, each array element must be fabricated from bottom to top in order of level. For the multiple multi-level approximation curve structures 2-1 and the various fractal unit structures 2-3 of the rotating array, to avoid manufacturing interference and collision, the primary approximation lines and primary structures of all array elements are first formed in a circular manner, and then the various levels of approximation lines and fractal structures of all array elements are sequentially stacked to form the structures.

[0054] The multi-level approximation suspended 3D printing method of the surrounding polygonal structure 2-4 is understood as the points formed by the intersection of the plane perpendicular to the axis of the revolution quadratic surface and the multi-level approximation curve structure 2-1 of the array and the fractal unit structures 2-3 of each order at the inflection point of the broken line segment, and the intersection points are connected in sequence to form the surrounding polygonal structure 2-4; the surrounding polygonal structure 2-4 and the highest-level approximation line of the multi-level approximation curve structure 2-1 and the fractal unit structure 2-3 together constitute the framework of the discrete polyhedron 3.

[0055] The 3D printing of the discrete polyhedron 3 is based on its frame and relies on the method of 3D printing filling surface. The wire bundles form nodes on the frame in sequence, and the print head pulls the tensioned wire bundles to fill all the surface pieces, finally obtaining a polyhedron structure.

[0056] Reference Figure 5 Taking the Cartesian coordinate discrete structure as an example, the quadratic surface 4 and the discrete polyhedron 3 are respectively composed of multiple curved surface patches 4-1 and plane surface patches 3-1 seamlessly connected, and a single plane surface patch 3-1 corresponds to the curved surface patch 4-1 in the spatial projection direction; there is a minimum and maximum spacing between the plane surface patch 3-1 and the curved surface patch 4-1. When the spacing range is within the adjustable layer thickness range of the 3D printing filament, the transition printing from plane to curved surface is achieved; therefore, 3D printing with variable layer thickness is adopted, based on the discrete polyhedron structure, relying on the flow control of the printing material, and then obtaining the adjustability of the printing layer thickness, thereby realizing the precise manufacturing from polyhedron to curved surface.

[0057] The degree of discrete refinement directly determines the size of a single facet of the discrete polyhedron 3 corresponding to the same curved surface structure. Under the premise that the surface curvature remains unchanged, it further determines the spacing range between the plane facet 3-1 and the curved facet 4-1. This is limited by the variable layer thickness range in the 3D printing process parameters used. Therefore, before planning the 3D printing path for the quadratic surface structure, it is necessary to first determine the appropriate degree of discrete refinement based on the process parameter constraints to ensure that the spacing range from all plane faces 3-1 to curved facets 4-1 is process-achievable.

[0058] The degree of discretization refinement will affect the parallel spacing of the multi-level approximation curve structure 2-1, the parallel spacing of the intersecting approximation curve structure 2-2, and the number of approximation series in the Cartesian coordinate discretization structure, and affect the values ​​of related parameters such as the offset distance a, the number of rotation arrays, the number of approximation series, and the fractal order in the polar coordinate discretization structure.

[0059] Reference Figure 6 The outer contour of the edge bracket 1 is not limited to a quadrilateral or a circle, and can be any symmetrical or asymmetrical shape. The lowest point of the curved surface is not limited to the middle of the edge bracket 1.

[0060] It should be understood that the above description of the preferred embodiment is relatively detailed and cannot be regarded as limiting the scope of protection of the patent of the present invention. Under the guidance of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which all fall within the scope of protection of the present invention. The scope of protection requested by the present invention shall be based on the attached claims.

Claims

1. A discrete fractal structure of a quadratic surface structure, characterized by: According to the discretization method, it is divided into a Cartesian coordinate discrete structure and a polar coordinate discrete structure. Both the Cartesian coordinate discrete structure and the polar coordinate discrete structure include an edge bracket (1), the edge bracket (1) is internally connected to a suspended approximation curve structure, the suspended approximation curve structure is connected to a discrete polyhedron (3), and the discrete polyhedron (3) is connected to a quadratic surface (4); wherein the suspended approximation curve structure in the form of a Cartesian coordinate discrete structure is composed of a multi-level approximation curve structure (2-1) and an intersecting approximation curve structure (2-2), and the suspended approximation curve structure in the form of a polar coordinate discrete structure is composed of a multi-level approximation curve structure (2-1), a fractal unit structure (2-3) and a surrounding polygon structure (2-4); the suspended approximation curve structure is manufactured by a multi-level approximation suspended 3D printing method; The multi-level approximation suspended 3D printing method of the multi-level approximation curve structure (2-1) in the discrete fractal structure comprises the following steps: 1) First-order approximation line 3D printing: The continuous fiber composite material tow forms a node at point A on the hollow edge bracket (1), and an internal tension force is applied to the tow. The tow is suspended and pulled from point A to point B. When the 3D printing head moves to point B to form the node, the formation of a long-span suspended straight line segment AB is completed. The straight line segment AB is defined as the first-order approximation line; the straight line segment AB is tangent to the target curve CF, and the tangent point is O; 2) 3D printing of the secondary approximation line: A node is formed at the intersection C of the target curve CF and the edge bracket (1), and the filament bundle is pulled from point C to point D to form node D on the straight line segment AB; similarly, the filament bundle is pulled from point D to point E and then to point F to form a firm node in sequence, and the continuous broken line segment CDEF is defined as the secondary approximation line; it is necessary to ensure that the straight line segment CD is tangent to the target curve CF at point C, the straight line segment EF is tangent to the target curve CF at point F, and the straight line segment DE coincides with the primary approximation line; due to symmetry, the axial distances of the inflection points D and E of the secondary approximation line to the target curve are equal; 3) 3D printing of three-level approximation lines: After forming a node at point C, the tow is pulled from point C to point G, forming node G on the straight line segment CD. Similarly, the tow is pulled through points G, H, I, J, and F in sequence to form strong nodes. The continuous broken line segments CGHIJF are defined as the three-level approximation lines. It is necessary to ensure that the lines GH and IJ are tangent to the curve CF respectively, and the lines CG, HI, and JF coincide with the two-level approximation lines respectively. At the same time, it is necessary to ensure that the axial distances between the inflection points G, H, I, and J of the three-level approximation lines and the target curve are equal. 4) Multi-level approximation line 3D printing: The configuration of the polyline segment exceeding the third level of approximation line adopts the method of steps 1) to 3) by analogy. New tangents are introduced to cut the inflection point of the previous polyline segment. The distance between the new inflection point of the polyline segment formed by the new tangents and the curve is reduced to achieve further approximation to the target curve CF. For the intersection approximation curve structure (2-2) of the Cartesian coordinate discrete structure, the approximated curve is the intersection line of the quadratic surface and the intersection plane; the intersection plane and the reference plane intersect orthogonally; the intersection plane intersects with the highest level approximation lines of multiple parallel multi-level approximation curve structures (2-1) and the upper frame of the edge bracket (1) to obtain discrete connection points. When the print head pulls the wire bundle along one direction through the discrete connection points in sequence and deposits and fixes it, the intersection approximation curve structure (2-2) is formed; all the intersection approximation curve structures (2-2) and the highest level approximation lines of the multi-level approximation curve structure (2-1) together form the framework of the discrete polyhedron (3).

2. The discrete fractal structure of the quadratic surface structure according to claim 1, characterized in that: The quadratic surface of the polar coordinate discrete structure is a surface of revolution, and its suspended approximation curve structure does not pass through the axis of revolution. Assume that the distance from the plane to the axis of revolution, i.e., the offset distance, is equal to a. In the multi-level approximation curve structure (2-1) of the rotation array, if the latitudinal spacing is greater than the parallel line spacing 2a at a position far from the axis center in the fan-shaped area formed by the two intersecting lines, the fractal unit structure (2-3) is also an array rotated around the central axis and is evenly distributed in each fan-shaped area. The fractal unit structure (2-3) is composed of multi-level approximation lines. For each level of the structure, the configuration is determined by the axial projection of two parallel line segments and the connecting line segment at that level. The multi-level approximation suspended 3D printing method of the fractal unit structure (2-3) comprises the following steps: 1) 3D printing of the primary structure of the fractal unit: pull the wire bundle from point P of the edge bracket (1) until it intersects with the primary approximation line of the multi-level approximation curve structure (2-1) and forms a solid node M; then turn the wire bundle at a 90° angle to intersect with another primary approximation line in the fan-shaped area and form a node N; then turn the wire bundle at a 90° angle to return to the edge bracket (1) to form a node Q; define the continuous broken line structure PMNQ as the primary structure of the fractal unit, and ensure that the parallel line spacing is 2a, which is equal to the parallel line spacing of the multi-level approximation curve structure (2-1) of the array; 2) 3D printing of multi-level structures of fractal units: Similar to the forming principle of multi-level approximation lines, the difference is that after the broken line segment of each level intersects with the approximation line of the same level of the multi-level approximation curve structure (2-1), the printing path turns, which is the same as the previous step.

3. The discrete fractal structure of the quadratic surface structure according to claim 2, characterized in that: The fractal unit structure introduced for the first time is defined as a first-order fractal unit structure. After adding the first-order fractal unit structure, it is determined whether the latitudinal spacing of the new sector-shaped area formed by the segmentation is greater than the parallel line spacing 2a at the distance from the axis. If so, it is necessary to further introduce a second-order fractal unit structure to continue segmenting the new sector-shaped area. The construction principle of the second-order fractal unit structure is the same as above. After the second-order fractal unit structure is formed, it is determined whether the next stage of fractal unit structure needs to be introduced, and so on, until the latitudinal spacing of the final sector-shaped area away from the axis is no greater than the parallel line spacing 2a.

4. The discrete fractal structure of the quadratic surface structure according to claim 2, characterized in that: The forming steps of the multi-level approximation curve structure (2-1) and the fractal unit structure (2-3) are only for a single array element, while for the overall forming of the radial support structure, each array element needs to be manufactured from bottom to top according to the level; for multiple multi-level approximation curve structures (2-1) of the rotating array, and each order of fractal unit structure (2-3), first, the first-level approximation lines and the first-level structure of all array elements are formed in a circular manner, and then the approximation lines and fractal structures of all array elements are stacked in sequence to form each level.

5. The discrete fractal structure of the quadratic surface structure according to claim 1, characterized in that: The multi-level approximation suspended 3D printing method of the surrounding polygonal structure (2-4) is understood as the points formed by the intersection of the plane perpendicular to the axis of the revolution quadratic surface and the multi-level approximation curve structure (2-1) of the array and the fractal unit structures (2-3) of each order at the inflection point of the broken line segment, and the intersection points are connected in sequence to form the surrounding polygonal structure (2-4); the surrounding polygonal structure (2-4) and the highest level approximation line of the multi-level approximation curve structure (2-1) and the fractal unit structure (2-3) together constitute the framework of the discrete polyhedron (3).

6. The discrete fractal structure of the quadratic surface structure according to claim 1, characterized in that: The 3D printing of the discrete polyhedron (3) is based on its frame and relies on the method of 3D printing filling surface. The wire bundles form nodes on the frame in sequence, and the printing head pulls the tensioned wire bundles to fill all the surface pieces, and finally obtains the polyhedron structure.

7. The discrete fractal structure of the quadratic surface structure according to claim 1, characterized in that: The quadratic surface (4) and the discrete polyhedron (3) are respectively composed of a plurality of curved surface patches (4-1) and planar surface patches (3-1) that are seamlessly connected, and a single planar surface patch (3-1) corresponds to the curved surface patch (4-1) in the spatial projection direction; there is a minimum and a maximum spacing between the planar surface patch (3-1) and the curved surface patch (4-1), and when the spacing range is within the adjustable layer thickness range of the 3D printing filament, the transition printing from the plane to the curved surface is achieved; 3D printing with variable layer thickness, based on discrete polyhedron structure, relies on the flow control of printing material to obtain the adjustability of printing layer thickness, and realizes the precise manufacturing from polyhedron to curved surface.

8. The discrete fractal structure of the quadratic surface structure according to claim 7, characterized in that: The degree of discrete refinement directly determines the size of a single facet of the discrete polyhedron (3) corresponding to the same curved surface structure. Under the premise that the curvature of the surface remains unchanged, it further determines the spacing range between the plane facet (3-1) and the curved surface facet (4-1). Before planning the 3D printing path for the quadratic curved surface structure, the degree of discrete refinement must be determined based on the process parameter constraints to ensure that the spacing range from all plane facets (3-1) to the curved surface facet (4-1) is achievable.

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