Parameterized segmentation-based method for determining back frame structure of parabolic reflection antenna

Abstract

The invention belongs to the technical field of satellite antennas, and relates to a parameterized segmentation-based method for determining a back frame structure of a parabolic reflection antenna, which comprises the following steps of: performing grid division on a cross section plane of a curved surface of the parabolic reflection antenna by using a regular hexagon, and projecting the divided grid onto the curved surface of the parabolic reflection antenna; segmenting the parabolic reflection antenna according to the curve projected on the curved surface of the parabolic reflection antenna, wherein each antenna module unit obtained after segmentation corresponds to one back frame; and finally, all the back frames are connected in sequence to form an integral back frame which can be attached to the curved surface of the parabolic reflection antenna. After the back frame unit is assembled, the integral back frame attached to the curved surface of the parabolic reflection antenna is formed, and the effective reflection area ratio of the reflection surface unit can be increased; the positions and the sizes of the back frames are obtained through a parameterization method, the supporting direction of each back frame is the normal direction of the point where the paraboloid unit is located, and the connection stability can be improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite antennas, and relates to a method for determining a parabolic reflector antenna back frame structure based on parameterized segmentation. BACKGROUND

[0002] The existing space system is difficult to perform high-sensitivity detection, effective jamming and countermeasures on related high-value signals, and there is an urgent need for a large-aperture parabolic antenna as shown in the figure. However, due to the size limitation of the fairing of the launch vehicle, it is difficult to launch the overall large-aperture parabolic antenna, so it is necessary to modularize the parabolic antenna, transport the segmented antenna modules to space by the launch vehicle, and perform on-orbit assembly. Figure 1

[0003] It is pointed out in the document (Development Review of Space Extremely Large Aperture On-orbit Assembly Antenna Technology[J]. Space Electronic Technology. DOI:10.3969 / j.issn.1674-7135.2025.S1.004) that so far, humans have not deeply studied the key technologies of space extremely large aperture antennas, and how to realize space extremely large aperture antennas has attracted high attention from the scientific and technological circles; the on-orbit construction technology of space extremely large aperture antennas has become the focus of strategic planning of space powers around the world, but the related theoretical method foundation is weak, and a series of key technologies need to be broken through, so it is necessary to carry out research on the on-orbit assembly technology of space extremely large aperture antennas.

[0004] It is stated in patent CN107436978A that modular design can become a research hotspot for deployable antennas due to the advantages of short processing period, easy-to-ensure profile precision, strong expansion capability, and suitability for large-aperture antennas.

[0005] It is pointed out in patent CN118701316A that the reflector size of the current deployable space antenna is mostly within 20m, which belongs to the category of large antennas, but for larger 50m size and above even kilometer-level super-large antennas, due to the limitations of materials and mechanical structures, the size requirements cannot be met at present. At the same time, due to the limitations of the volume and capacity of launch vehicles, only spacecraft or parts with a diameter of five meters or less can be launched at present, and the launch cannot be completed as a whole. In this case, on-orbit assembly can help humans to carry out more extensive, more in-depth and more innovative space exploration activities, so on-orbit assembly is a key link in the process of space exploration. At present, on-orbit assembly technology needs to be further developed, spacecraft components are launched into orbit in batches, and advanced measurement navigation, rendezvous and docking, and dexterous manipulator control technologies are used to assemble spacecraft systems with larger scale, more flexible structure and stronger function in orbit.

[0006] ​Space deployable antenna is an important device for information acquisition and transmission of on-orbit satellite. With the rapid development of 5G, Internet of Things and space Internet, satellite communication can provide high-frequency large-capacity data transmission to meet the application requirements of high-definition video, real-time remote sensing and other applications. Satellite signals are less affected by ground disasters (such as earthquakes and floods), and stable communication in extreme environments can be ensured through high-precision parabolic antenna design.

[0007] As shown in Figure 3 In the modular design of the antenna and the on-orbit assembly, the structure of the back frame affects the fitting effect of the antenna. If the design of the back frame is not accurate enough, the single antenna module cannot be installed at the target installation position after installation, resulting in that the reflector module cannot be utilized. Therefore, the structure size of the back frame is very important and closely affects the accuracy of the on-orbit installation of the antenna.

[0008] Therefore, it is of great significance to study a method for determining the structure of the back frame of the parabolic reflector antenna based on parameterized segmentation to solve the problems in the prior art. SUMMARY

[0009] The purpose of the present application is to solve the problems in the prior art and provide a method for determining the structure of the back frame of the parabolic reflector antenna based on parameterized segmentation.

[0010] To achieve the above-mentioned purpose, the technical solutions adopted by the present application are as follows:

[0011] A method for determining the structure of the back frame of the parabolic reflector antenna based on parameterized segmentation, first, the cross-sectional plane of the parabolic reflector antenna surface is grid divided with a regular hexagon, and then the divided grid is projected onto the parabolic reflector antenna surface; then the parabolic reflector antenna is segmented according to the curve on the parabolic reflector antenna surface after projection, and each antenna module unit obtained after segmentation corresponds to a back frame; finally, all the back frames are connected in sequence to form an overall back frame that can be fitted with the parabolic reflector antenna surface.

[0012] As a preferred technical solution:

[0013] The method for determining the structure of the back frame of the parabolic reflector antenna based on parameterized segmentation as described above specifically comprises the following steps:

[0014] Step 1: determining the parabolic reflector antenna surface;

[0015] Determine a cylinder, the center line of which is a straight line passing through a point P(0, h, 0) on the y-axis and parallel to the x-axis, and the radius of the cylinder is R, and the closed part of the cylinder surface intersecting the parabolic surface is the parabolic reflector antenna surface;

[0016] Step 2: determining the segmentation method of the parabolic reflector antenna;

[0017] The cross-sectional plane of the parabolic reflector antenna surface is divided into multiple grids using a regular hexagon. The divided grids are then projected onto the parabolic reflector antenna surface to segment the parabolic reflector antenna.

[0018] Step 3: Number and store the grid cells;

[0019] For a certain regular hexagonal grid, when it is projected onto a parabolic surface, the distances between the edges of the resulting hexagon are also different due to the different curvatures at each point on the parabolic surface. In order to distinguish the individual dividing surfaces and the corresponding relationship of the back frame, the grid needs to be numbered separately.

[0020] The divided grid data is stored after being numbered. The grid data is divided into two parts: the first part is the grid cell data, where each row records a hexagonal grid cell, the first column of each row is the number of the hexagonal grid cell, and the other six columns are the numbers of the six vertices; the second part is the vertex coordinate data, where each row records a vertex, the first column of each row is the vertex number, and the other three columns are the X, Y, and Z coordinates of the vertex in space, respectively.

[0021] Step 4: Determine the projection point;

[0022] Let the coordinates of a feature point on a hexagon be... The projection direction is The projected points are ;according to and projection direction Able to determine a The straight line containing the point The equation of the parabola is compared with that of the straight line. Solve the equations simultaneously to determine the projection point. The coordinates of the projection points are determined using the same method;

[0023] Step 5: Determine the position of the backpack frame;

[0024] The normal to the parabolic reflector surface at a point has two directions: the direction towards the convexity of the parabolic reflector surface is defined as outward, and the opposite direction is defined as inward; the position of the back frame is such that the parabolic reflector surface is offset outward. and On the two curved surfaces, the two curved surfaces are respectively denoted as the back frame offset surface at the near end and the back frame offset surface at the far end;

[0025] The feature point corresponding to the back frame on the proximal offset surface is determined by the following formula:

[0026] ;

[0027] The feature point corresponding to the back frame on the offset surface at the far end is determined by the following formula:

[0028] ;

[0029] Step 6: Determine the length of each rod;

[0030] Let a point on the surface of the parabolic reflector antenna be... ,Pass The points are along the normal direction of the parabolic reflector antenna surface, and the vertices of the back frame on the near-end offset surface and the far-end offset surface are denoted as follows: and , and The distance between them is , and The distance between them is The length of the rod along the normal direction of the parabolic reflector surface is ,and This is to allow for a margin in the subsequent design of the connection method between the reflector and the back frame;

[0031] Except for the rods along the normal direction of the parabolic reflector antenna surface, the lengths of all other rods are calculated using the distance formula between two points.

[0032] Step 7: Determine the connection method between the back frames;

[0033] Each back frame is conical, containing three sides on either the near-end or far-end offset curved surface. All back frames are connected sequentially to form the outer envelope of a parabolic reflector antenna. This structure allows for a tight connection between adjacent back frames. The back frames are connected using two types of connectors. Connector I fixes the connection angle between the back frames, ensuring the resulting curved surface approximates the surface of a parabolic antenna. Connector II interlocks the sub-interface with the female interface, making the connection more robust and increasing its rigidity. The connector II used in this invention employs existing technology, such as the radially inserted self-locking quick connector disclosed in patent number CN110512745 A.

[0034] As described above, the method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation includes the following steps: Select a regular hexagon A to enclose the outer contour of the cross-sectional plane of the parabolic reflector antenna surface. The center of the regular hexagon coincides with the center of the cross-sectional plane. Then, use small regular hexagons B with side length r to fill the cross-sectional plane. After that, project all the small regular hexagons B onto the parabolic reflector antenna surface in a direction perpendicular to the cross-sectional plane. The sketch projected onto the parabolic reflector antenna surface is the segmentation line.

[0035] The method for determining the structure of a parabolic reflector antenna back frame based on parameterized segmentation as described above, the cross section plane of the parabolic reflector antenna curve refers to the plane uniquely determined by the geometric intersection of the cylindrical surface and the parabolic surface.

[0036] The method for determining the structure of a parabolic reflector antenna back frame based on parameterized segmentation as described above, the relationship between the length L of the short diagonal of the regular hexagon A (i.e. the distance from the first vertex to the third vertex) and the length r of the side of the small regular hexagon B is L = (3n-1) r, where n is an integer, so that the large regular hexagon can be completely divided into multiple small regular hexagons.

[0037] The method for determining the structure of a parabolic reflector antenna back frame based on parameterized segmentation as described above, the equation of the straight line in step 4 is , and the equation of the parabolic surface is .

[0038] The back frame includes closed and open types. The back frame is divided into two sheet planes, and the most obvious difference between the closed and open types is whether the outer ring rods in the upper and lower planes can be connected end to end. The six edges of the outer ring in the upper and lower planes of the "closed" hexagonal back frame are connected end to end, while only three rods are present in the outer ring of the upper and lower planes of the "open" hexagonal back frame as shown in Figure 5 .

[0039] As shown in Figure 4 , the "closed" back frame is commonly used in the prior art, the seven red hexagons in the division sketch are shown in red, the blue points are the vertices corresponding to the actual hexagonal back frame, and the three red hexagon sketch vertices selected in the yellow circle are a point, but the actual back frame needs to calculate three points around it, and the calculation is relatively complex.

[0040] The "open" back frame as shown in Figure 5 of the present application coincides with the vertices of the sketch segmentation, and the calculation is convenient, which is the reason why the present application selects this back frame structure. The single back frame does not present a hexagonal shape, and the back frames are combined through shared edges to form a hexagonal shape.

[0041] Advantages:

[0042] (1) The method for determining the structure of a parabolic reflector antenna back frame based on parameterized segmentation divides, projects and segments the large aperture antenna, the single back frame after segmentation and the back frames can be closely connected, and after all the back frames are connected, a complete back frame that fits the parabolic reflector antenna curve can be formed, so that each reflector surface unit can be fully used.

[0043] (2) The method for determining the back frame structure of the parabolic reflector antenna based on parameterized segmentation, the position and size of the back frame are obtained through the parameterized method, and the support direction of each back frame is the normal direction of the point of the parabolic unit, so that the stability of the connection can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 It is a large aperture parabolic reflector antenna schematic diagram;

[0045] Figure 2 It is a large aperture parabolic reflector antenna after modular division;

[0046] Figure 3 It is an antenna module target installation position diagram (left) and an actual possible installation position diagram (right);

[0047] Figure 4 It is a closed back frame modular division schematic diagram;

[0048] Figure 5 It is an open back frame modular division schematic diagram;

[0049] Figure 6 It is a parabolic antenna curve, two offset planes of the parabolic antenna and a projection plane schematic diagram;

[0050] Figure 7 It is a projection plane segmentation grid schematic diagram;

[0051] Figure 8 It is the relationship between the length of the short diagonal of the regular hexagon A and the length of the side of the small regular hexagon B;

[0052] Figure 9 It is Figure 7 It is a part of the grid numbering schematic diagram in the figure, wherein 9-36 represent grid point numbers;

[0053] Figure 10 It is a back frame structure schematic diagram;

[0054] Figure 11 It is a joint mechanism schematic diagram;

[0055] Figure 12 It is Figure 9 It is a three back frame connection schematic diagram corresponding to the grid in the figure;

[0056] Figure 13 It is an overall installation process demonstration diagram;

[0057] In the figure, 1-parabolic reflector surface, 2-near-end offset surface, 3-far-end offset surface, 4-projection plane, 6-grid I, 7-grid II, 8-grid III, 37-sub-interface, 38-female interface, 39-pole I, 40-pole II, 41-pole III, 42-connector I, 43-tee tube, 44-sleeve. Detailed Implementation

[0058] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0059] A method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation includes the following steps:

[0060] Step 1: Determine the surface of the parabolic reflector antenna;

[0061] Define a cylinder, the center line of which is a straight line passing through a point P(0,h,0) on the y-axis and parallel to the x-axis, the radius of the cylinder is R, and the closed part where the surface of the cylinder intersects the parabola is the surface of the parabolic reflector antenna.

[0062] Step 2: Determine the segmentation method for the parabolic reflector antenna;

[0063] Select a regular hexagon A and enclose the outer contour of the cross-sectional plane of the parabolic reflector surface. The center of the regular hexagon coincides with the center of the cross-sectional plane. Then, use small regular hexagons B with side length r to fill the cross-sectional plane. Next, project all the small regular hexagons B onto the parabolic reflector surface in a direction perpendicular to the cross-sectional plane. The sketch projected onto the parabolic reflector surface is the dividing line, which realizes the division of the cross-sectional plane of the parabolic reflector surface. The cross-sectional plane of the parabolic reflector surface is the plane uniquely determined by the geometric intersection of the cylindrical surface and the parabola.

[0064] like Figure 8 As shown, the relationship between the length L of the shorter diagonal of regular hexagon A and the side length r of smaller regular hexagon B is: L = (3n-1)r, where n is an integer;

[0065] Step 3: Number and store the grid cells;

[0066] The divided grid data is stored after being numbered. The grid data is divided into two parts: the first part is the grid cell data, where each row records a hexagonal grid cell, the first column of each row is the number of the hexagonal grid cell, and the other six columns are the numbers of the six vertices; the second part is the vertex coordinate data, where each row records a vertex, the first column of each row is the vertex number, and the other three columns are the X, Y, and Z coordinates of the vertex in space, respectively.

[0067] Step 4: Determine the projection point;

[0068] Let the coordinates of the feature point of a certain hexagon be... The projection direction is The projected points are ;according to and projection direction Able to determine a The straight line containing the point The equation of the parabola is compared with that of the straight line. Solve the equations simultaneously to determine the projection point. The coordinates of the projection points are determined using the same method;

[0069] straight line The equation is The equation of the parabola is ;

[0070] Step 5: Determine the position of the backpack frame;

[0071] The normal to the parabolic reflector surface at a point has two directions: the direction towards the convexity of the parabolic reflector surface is defined as outward, and the opposite direction is defined as inward; the position of the back frame is such that the parabolic reflector surface is offset outward. and On the two curved surfaces, the two curved surfaces are respectively denoted as the back frame offset surface at the near end and the back frame offset surface at the far end;

[0072] The feature point corresponding to the back frame on the proximal offset surface is determined by the following formula:

[0073] ;

[0074] The feature point corresponding to the back frame on the offset surface at the far end is determined by the following formula:

[0075] ;

[0076] Step 6: Determine the length of each rod;

[0077] Let a point on the surface of the parabolic reflector antenna be... ,Pass At a point and along the normal direction of the paraboloid reflector antenna surface, the vertices of the back frame on the proximal offset surface and the distal offset surface are respectively denoted as and , the distance between P1 and is , The distance between and is The length of the rod along the normal direction of the paraboloid reflector antenna surface is and is a margin reserved for the subsequent design of the connection method between the reflector and the back frame;

[0078] Except for the rod along the normal direction of the paraboloid reflector antenna surface, the lengths of all other rods are calculated by the distance formula between two points; <Gaps in the original text seem to be represented by these tags but no clear text for translation. Just preserving the tags as they are for now.>

[0079] <Gaps in the original text seem to be represented by these tags but no clear text for translation. Just preserving the tags as they are for now.>

[0079] Step 7: Determine the connection method between the back frames;

[0080] A single back frame is conical. A single back frame has three sides on the proximal offset surface or the distal offset surface. After all the back frames are connected in sequence, an outer envelope surface of the paraboloid reflector antenna is formed.

[0081] The following uses specific embodiments to illustrate a method for determining the back frame structure of a paraboloid reflector antenna based on parametric segmentation. Unless otherwise specified, the unit of the length data involved is m, and the details are as follows:

[0082] Step 1: Determine the paraboloid reflector antenna surface; <Gaps in the original text seem to be represented by these tags but no clear text for translation. Just preserving the tags as they are for now.> First, a sketch is divided on the paraboloid reflector antenna surface. The paraboloid reflector antenna surface is the plane where the closed part of the intersection of the paraboloid and the cylinder is located. By联立 the paraboloid equation and the cylinder equation , we can obtain: , that is , this equation is in the standard form of the plane equation, so we can obtain the closed part of the paraboloid and the cylinder, that is, the paraboloid reflector antenna surface. This plane is the plane where the divided sketch is located, such as the projection plane 4 in Figure 6 ; where p = 80, R = 25, h = 30, is the height position where the center line of the cylinder surface is located, R is the radius of the cross-sectional circle of the cylinder surface, and R < h is to make the intercepted antenna part on the same side of the paraboloid symmetry axis;

[0084] Step 2: Determine the segmentation method of the paraboloid reflector antenna;

[0085] A regular hexagon A is selected to enclose the cross-sectional plane profile of the parabolic reflector antenna surface, the center of the regular hexagon is coincident with the center of the cross-sectional plane, then a small regular hexagon B with a side length of r (r = 2) is used to cover the cross-sectional plane, and then all the small regular hexagons B are projected onto the parabolic reflector antenna surface in the direction perpendicular to the cross-sectional plane, the sketch on the parabolic reflector antenna surface is the division line, thereby the cross-sectional plane of the parabolic reflector antenna surface is divided; wherein the cross-sectional plane of the parabolic reflector antenna surface refers to the plane uniquely determined by the geometric intersection of the cylindrical surface and the parabolic surface;

[0086] The division result is shown in Figure 2 It can be seen that the instance grid number of each small regular hexagon B and the corresponding feature point coordinates on each grid can be obtained after division.

[0087] The total number of hexagons N obtained after division m The relationship between the number n of hexagons occupied by the large hexagon single side and the large hexagon is The relationship between the length (antenna aperture) L of the short diagonal of the large hexagon and the side length r of the small hexagon used for division is L = (3n-1) r.

[0088] Step 3: Numbering and storing the grid;

[0089] Taking three small regular hexagon grids in Figure 9 as an example, 6-8 represent the numbering of the three grids, and 9-36 represent the numbering of the vertices and midpoints of the edges of the hexagon grid. In the saved grid division file, the numbering of a single grid is stored in the form of clockwise arrangement in the file. The numbers in the figure are only used for example, and the actual numbering may not be arranged according to the number size.

[0090] Taking grid 6 and grid 7 as an example, their saved formats in the file are respectively:

[0091] Grid 6: 9, 11, 13, 15, 17, 19;

[0092] Grid 7: 17, 15, 22, 24, 26, 28;

[0093] Grid 8: 35, 19, 17, 28, 31, 33.

[0094] Taking grid 6: 9, 11, 13, 15, 17, 19 as an example, the coordinate data corresponding to the numbering of grid 6 is:

[0095] Number 9: (4.5813, 29.0171, 1.7321);

[0096] Number 11: (4.9499, 30.9829, 1.7321);

[0097] Number 13: (5.1342, 31.9657, 0);

[0098] Number 15: (4.9499, 30.9829, -1.7321);

[0099] Number 17: (4.5813, 29.0171, -1.7321);

[0100] Number 19: (4.3970, 28.0343, 0);

[0101] Step 4: Determine the projection point;

[0102] by Figure 9 Taking target mesh cell number 6 as an example, the projection direction is denoted as... , Perpendicular to the divided sketch plane, based on the plane determined in step 1 The projection vector can be obtained. ). Given the coordinates of the feature points of the hexagonal grid, then after... Point and direction is The equation of the straight line is , make the straight line With the equation of a parabola By combining the two equations, we can obtain the projected points. Based on the above method, the projected points of the corresponding points on grid I 6 can be determined, and the segmented region of the antenna surface corresponding to this grid can be determined, that is, the single reflector element corresponding to number 6 can be obtained.

[0103] The calculated coordinates of the projection point are:

[0104] (2.7048, 29.3690, 1.7321);

[0105] (2.8883, 30.3520, 1.7321);

[0106] (3.0775, 31.3339, 1.7321);

[0107] (3.1676, 31.8258, 0.8660);

[0108] (3.2636, 32.3165, 0);

[0109] (3.1676, 31.8258, -0.8660);

[0110] (3.0775, 31.3339, -1.7321);

[0111] (2.8883, 30.3520, -1.7321);

[0112] (2.7048, 29.3690, -1.7321);

[0113] (2.6085, 28.8783, -0.8660);

[0114] (2.5181, 28.3866, 0);

[0115] (2.6085, 28.8783, 0.8660);

[0116] (2.8792, 30.3537, 0);

[0117] Step 5: determining the position of the back frame;

[0118] After obtaining the single reflecting surface unit, the back frame corresponding to the unit is then determined.

[0119] The normal of the parabolic reflector surface at a point has two directions, the direction pointing to the convex of the parabolic reflector surface is defined as outward, and the opposite direction is defined as inward; the position of the back frame is the two surfaces respectively outwardly offset from the parabolic reflector surface and (F2, F3) , which are respectively denoted as the back frame offset near-end surface and the back frame offset far-end surface;

[0120] The vertex corresponding to the back frame offset near-end surface 2 is , and the vertex corresponding to the back frame offset far-end surface 3 is According to actual requirements, if a connecting interface is designed between the back frame and the reflecting surface, or a Stewart platform is installed between the reflecting surface unit and the back frame for fine adjustment, there should be a certain gap between the back frame and the reflecting surface unit. Taking the gap as 0.5m (i.e. =0.5) and the normal length of the back frame as 1m (i.e. =1) as an example. The normal of the parabolic surface where the projection point is located is the support direction of the back frame.

[0121] Step 6: determining the length of each rod;

[0122] like Figure 6 As shown, let point 1 on the parabolic reflector antenna surface 1 be... ,Pass The point is located along the normal direction of the parabolic reflector surface, and the corresponding vertex of the back frame on the near-end offset surface 2 is... The vertex corresponding to the back frame on the far-end offset surface 3 is ; and The distance between them is , and The distance between them is The length of the rod along the normal direction of the parabolic reflector surface is ;

[0123] Except for the rods along the normal direction of the parabolic reflector antenna surface, the lengths of all other rods are calculated using the distance formula between two points.

[0124] The equation of a parabolic antenna is given as ( The normal vector pointing outwards from the parabola is found to be... Its unit normal vector is The points can be obtained separately. With point They are respectively:

[0125] ;

[0126] ;

[0127] The point determined in step 5 These are the six vertices on the corresponding members of the hexagonal back frame on the near-end offset curved surface; These points are the midpoints of the corresponding edges in the sketch. This is the center point of the projection. There are a total of 13 points (feature points); using... Figure 9 To illustrate, let's use grid I 6, where the above... - exist Figure 9 A point can be represented as a center. The above points ~ exist Figure 9 The middle can be represented as This represents the midpoint of the hexagon in the sketch, where the midpoint of the hexagon lies at... Figure 9 The Chinese character is represented as .

[0128] The coordinates on the proximal offset surface are obtained through calculation:

[0129] (2.2130, 29.4592, 1.7374);

[0130] (2.3971, 30.4452, 1.7374);

[0131] (2.5869, 31.4300, 1.7374);

[0132] (2.6772, 31.9233, 0.8687);

[0133] (2.7735, 32.4155, 0);

[0134] (2.6772, 31.9233, -0.8687);

[0135] (2.5869, 31.4300, -1.7374);

[0136] (2.3971, 30.4452, -1.7374);

[0137] (2.2130, 29.4592, -1.7374);

[0138] (2.1164, 28.9671, -0.8687);

[0139] (2.0258, 28.4739, 0);

[0140] (2.1164, 28.9671, 0.8687);

[0141] (2.3880, 30.4469, 0);

[0142] Coordinates on the distal offset curve:

[0143] (1.2295, 29.6398, 1.7480);

[0144] (1.4146, 30.6316, 1.7480);

[0145] (1.6056, 31.6222, 1.748);

[0146] (1.6964, 32.1184, 0.8740);

[0147] (1.7933, 32.6135, 0);

[0148] (1.6964, 32.1184, -0.8740);

[0149] (1.6056, 31.6222, -1.7480);

[0150] (1.4146, 30.6316, -1.7480);

[0151] (1.2295, 29.6398, -1.7480);

[0152] (1.1323, 29.1448, -0.8740);

[0153] (1.0412, 28.6486, 0);

[0154] (1.1323, 29.1448, 0.8740);

[0155] (1.4055, 30.6333, 0);

[0156] The length of the bar between two points is calculated by the following formula:

[0157] ;

[0158] Proximal offset curve:

[0159] The length of the bar between number 9~10 is: 1.00296874;

[0160] The length of the bar between number 10~11 is: 1.00297135;

[0161] The length of the bar between number 11~12 is: 1.00304318;

[0162] The length of the bar between number 12~13 is: 1.00304357;

[0163] The length of the bar between number 13~14 is: 1.00304357;

[0164] The length of the rods numbered 14-15 is 1.00304318.

[0165] The length of the rods numbered 15-16 is 1.00297135.

[0166] The length of the rods numbered 16-17 is 1.00296874.

[0167] The length of the rods numbered 17-18 is 1.00305498.

[0168] The length of the rods numbered 18-19 is 1.00305267.

[0169] The length of the rods numbered 19-20 is 1.00305267.

[0170] The length of the rods numbered 20 to 9 is 1.00305498.

[0171] The length of the rods numbered 6 to 10 is 1.73739289.

[0172] The length of the rods numbered 6-12 is 1.73725952.

[0173] The length of the rods numbered 6 to 14 is 1.73725952.

[0174] The length of the rods numbered 6 to 16 is 1.73739289.

[0175] The length of the rods numbered 6 to 18 is 1.73725261.

[0176] The length of the rods numbered 6 to 0 is 1.73725261.

[0177] Distal offset surface:

[0178] The length of the rods numbered 9 to 10 is 1.00890551.

[0179] The length of the rods numbered 10-11 is 1.00888821.

[0180] The length of the rods numbered 11 to 12 is 1.00912497.

[0181] The length of the rods numbered 12-13 is 1.00911518.

[0182] The length of the rods numbered 13-14 is 1.00911518.

[0183] The length of the rods numbered 14-15 is 1.00912497.

[0184] The rod length between No. 15 and No. 16 is 1.00888821;

[0185] The rod length between No. 16 and No. 17 is 1.00890551;

[0186] The rod length between No. 17 and No. 18 is 1.00914672;

[0187] The rod length between No. 18 and No. 19 is 1.00915469;

[0188] The rod length between No. 19 and No. 20 is 1.00915469;

[0189] The rod length between No. 20 and No. 9 is 1.00914672;

[0190] The rod length between No. 6 and No. 10 is 1.74802808;

[0191] The rod length between No. 6 and No. 12 is 1.74759162;

[0192] The rod length between No. 6 and No. 14 is 1.74759162;

[0193] The rod length between No. 6 and No. 16 is 1.74802808;

[0194] The rod length between No. 6 and No. 18 is 1.74763692;

[0195] The rod length between No. 6 and No. 20 is 1.74763692;

[0196] The normal rod length is 1.

[0197] Step 7: Determine the connection mode between the back frames;

[0198] The single back frame contains three edges on the proximal offset curved surface or the distal offset curved surface, and the overall back frame formed by sequentially connecting all the back frames is conical.

[0199] The close connection between the back frames can improve the utilization rate of the reflecting surface and improve the accuracy, and the basic topological shape of the back frame is as shown in Figure 11 A single back frame cannot form a complete hexagon, but when the back frame is connected with the surrounding back frames, a hexagon can be formed. For the back frame corresponding to the grid I 6 (i.e., the back frame 6, the back frame corresponding to the grid II 7 is the back frame 7, and the back frame corresponding to the grid III 8 is the back frame 8), the point , of the back frame away from the proximal end of the antenna can be obtained. The rod length of the rod I 39 in the back frame 6 corresponding to Figure 10 can be obtained through the point and the point It is confirmed that the length of rod II 40 can be determined by point. With point It is confirmed that the length of rod III 41 can be determined by point 41. With point Confirmed. The dimension of the back frame away from the antenna end mast can be calculated in the same way.

[0200] After all reflective surfaces and back frame modules are identified, they need to be assembled. This embodiment only assembles all back frame modules and does not involve the connection methods between the reflective surfaces and the back frames. The back frames are connected using two types of connectors. The basic structure of connector I 42 is as follows... Figure 11 As shown. This connector mainly consists of two parts: a 43-inch T-pipe, which has different sizes for different back frames. Figure 9 Taking the connector I 42 at the midpoint 17 as an example, the angular relationship between the three pipes of the tee pipe 43 here can be determined by... , , These three vectors are determined as follows:

[0201] ;

[0202] in, The above Point Components on the x-axis .

[0203] After obtaining the angular relationship between the branch pipes of the tee pipe 43, the size of the tee pipe 43 can be uniquely determined. The tee pipe 43 of this connector can be mass-produced by 3D printing. The other part of the connector I 42 is the sleeve 44, which is connected to the tee pipe 43. Its main structural principle is similar to that of a press-button pen. Pressing the sleeve can control the extension and retraction of the sleeve. Figure 9 For the connection between the back frames corresponding to grids 6-8, connector I 42 can first be connected to the rods numbered 15_21 and 17_22 in back frame 7. Then, the rods numbered 15_16 and 16_17 in back frame 6 are moved to their corresponding positions in back frame 7. Finally, the sleeve 44 of connector I 42 extends and connects to the corresponding rods in back frame 6. In addition to the connectors at numbers 15 and 17, another connector is used at number 16 to further increase the stability of the connection between the back frames. Figure 12 As shown, the connection between back frame 8 and back frames 6 and 7 follows the same method as above, first connected by a three-bar connector, and then connected by another connector. After the three-bar connector is connected, back frame 8 also needs to be connected simultaneously at midpoint 18 and midpoint 22 with connectors. This location is Y-shaped. If the connector is inserted in an axial manner, it will be difficult to connect. Therefore, a radial connection is used.

[0204] The installation of the whole back frame can adopt a row-by-row installation mode, and the first row of back frames can be installed first, and the connection mode between the first row of back frames is the connection method between the back frame 6 and the back frame 7. When installing the second layer and the subsequent layers, in addition to the connection with one back frame, the single back frame will also appear the connection with two back frames, and the single case is the same as the connection method between the back frame 6 and the back frame 7. When the single back frame is connected with two back frames, the connection between the back frame 8 and the back frame 6 and the back frame 7 can be referred to, and the row-by-row installation can complete the installation of the back frame of the whole antenna, and the whole installation path is S-shaped, as shown in Figure 13 The installation mode of three rows of back frames is shown, and the back frame assembled by the application mostly adopts the structure of Figure 4 Only the back frame of the outer ring part is slightly different, and the back frame of the outer ring part is supplemented with the surrounding rods on the basis of the back frame.

[0205] The joint II adopts the radial insertion self-locking quick joint disclosed in the patent CN110512745A, and the joint II is composed of a female interface 37 and a male interface 38, which adopts a radial insertion connection mode and is suitable for connecting the back frame in the application.

[0206] For the “closed” back frame, 6 vertexes, 6 center points of edges, and a center point of each hexagon need to be calculated, and a total of 13 points are calculated. Then the calculation amount Nc is: For the “open” back frame, the calculation is derived as follows: .

[0207] As shown in Figure 7 The antenna with a caliber of 50m is used for demonstration. The caliber (2r) of the small hexagon is 4m, and the number n of hexagons occupied by a single side of the large hexagon is 8. When n=8 is brought into the calculation Nc, the calculation amounts of the “closed” back frame and the “open” back frame are 2197 and 1105 respectively, and the calculation efficiency is improved by 49.70%. When n=17, that is, the caliber of the antenna reaches the level of hundreds of meters, the calculation amounts are 10621 and 5101 respectively, and the calculation efficiency is improved by 51.97%. It can be seen that when the caliber of a single reflector unit is fixed, the calculation amount will become larger and larger as the caliber of the required antenna increases, but the calculation efficiency of the application is much higher than that of the “closed” back frame, so this structure can well adapt to the parameterization method of the application.

Claims

1. A method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation, characterized in that: First, the cross-sectional plane of the parabolic reflector antenna surface is divided into a grid using regular hexagons, and then the grid is projected onto the parabolic reflector antenna surface. Next, the parabolic reflector antenna is divided according to the curve on the parabolic reflector antenna surface after projection, and each antenna module unit obtained after division corresponds to a back frame. Finally, all the back frames are connected in sequence to form an overall back frame that can fit with the parabolic reflector antenna surface.

2. The method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation according to claim 1, characterized in that, Specifically, the steps include the following: Step 1: Determine the surface of the parabolic reflector antenna; Define a cylinder, the center line of which is a straight line passing through a point P(0,h,0) on the y-axis and parallel to the x-axis, the radius of the cylinder is R, and the closed part where the surface of the cylinder intersects the parabola is the surface of the parabolic reflector antenna. Step 2: Determine the segmentation method for the parabolic reflector antenna; The cross-sectional plane of the parabolic reflector antenna surface is divided into multiple grids using a regular hexagon. The divided grids are then projected onto the parabolic reflector antenna surface to segment the parabolic reflector antenna. Step 3: Number and store the grid cells; The divided grid data is stored after being numbered. The grid data is divided into two parts: the first part is the grid cell data, where each row records a hexagonal grid cell, the first column of each row is the number of the hexagonal grid cell, and the other six columns are the numbers of the six vertices; the second part is the vertex coordinate data, where each row records a vertex, the first column of each row is the vertex number, and the other three columns are the X, Y, and Z coordinates of the vertex in space, respectively. Step 4: Determine the projection point; Let the coordinates of the feature point of a certain hexagon be... The projection direction is The projected points are ;according to and projection direction Able to determine a The straight line containing the point The equation of the parabola is compared with that of the straight line. Solve the equations simultaneously to determine the projection point. The coordinates of the projection points are determined using the same method; Step 5: Determine the position of the backpack frame; The normal to the parabolic reflector surface at a point has two directions: the direction towards the convexity of the parabolic reflector surface is defined as outward, and the opposite direction is defined as inward; the position of the back frame is such that the parabolic reflector surface is offset outward. and On the two curved surfaces, the two curved surfaces are respectively denoted as the back frame offset surface at the near end and the back frame offset surface at the far end; The feature point corresponding to the back frame on the proximal offset surface is determined by the following formula: ； The feature point corresponding to the back frame on the offset surface at the far end is determined by the following formula: ； Step 6: Determine the length of each rod; Let a point on the surface of the parabolic reflector antenna be... ,Pass The points are along the normal direction of the parabolic reflector antenna surface, and the vertices of the back frame on the near-end offset surface and the far-end offset surface are denoted as follows: and , and The distance between them is , and The distance between them is The length of the rod along the normal direction of the parabolic reflector surface is ; Except for the rods along the normal direction of the parabolic reflector antenna surface, the lengths of all other rods are calculated using the distance formula between two points. Step 7: Determine the connection method between the back frames; Each back frame is conical and has three sides on either the near-end or far-end offset surface. All back frames are connected in sequence to form the outer envelope of the parabolic reflector antenna.

3. The method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation according to claim 2, characterized in that, Step 2 is as follows: Select a regular hexagon A and enclose the outer contour of the cross-section plane of the parabolic reflector antenna surface. The center of the regular hexagon coincides with the center of the cross-section plane. Then, use small regular hexagons B with side length r to fill the cross-section plane. After that, project all the small regular hexagons B onto the parabolic reflector antenna surface in a direction perpendicular to the cross-section plane. The sketch projected onto the parabolic reflector antenna surface is the dividing line.

4. The method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation according to claim 3, characterized in that, The cross-sectional plane of a parabolic reflector antenna is the plane uniquely determined by the geometric intersection of the cylindrical surface and the parabola.

5. The method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation according to claim 4, characterized in that, The relationship between the length L of the shorter diagonal of regular hexagon A and the side length r of smaller regular hexagon B is: L = (3n-1)r, where n is an integer.

6. The method for determining the back frame structure of a parabolic reflector antenna based on parametric segmentation according to claim 5, characterized in that, In step 4, the straight line The equation is The equation of the parabola is .

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