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CN112531319B - Construction method of multisection expansion arm of satellite-borne mesh antenna - Google Patents

Construction method of multisection expansion arm of satellite-borne mesh antenna Download PDF

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CN112531319B
CN112531319B CN202011369186.XA CN202011369186A CN112531319B CN 112531319 B CN112531319 B CN 112531319B CN 202011369186 A CN202011369186 A CN 202011369186A CN 112531319 B CN112531319 B CN 112531319B
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coordinate system
arm
mesh
reflecting surface
antenna
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CN112531319A (en
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宗亚雳
张铎
王杰
吕昂
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Northwestern Polytechnical University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/12—Supports; Mounting means
    • H01Q1/1235—Collapsible supports; Means for erecting a rigid antenna
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/08—Means for collapsing antennas or parts thereof
    • H01Q1/10—Telescopic elements
    • H01Q1/103—Latching means; ensuring extension or retraction thereof
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/27—Adaptation for use in or on movable bodies
    • H01Q1/28—Adaptation for use in or on aircraft, missiles, satellites, or balloons
    • H01Q1/288—Satellite antennas
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/50—Structural association of antennas with earthing switches, lead-in devices or lightning protectors
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/14—Reflecting surfaces; Equivalent structures
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q19/00—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic
    • H01Q19/10—Combinations of primary active antenna elements and units with secondary devices, e.g. with quasi-optical devices, for giving the antenna a desired directional characteristic using reflecting surfaces

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Abstract

本发明属于卫星天线技术领域，具体是一种星载网状天线的多节展开臂构建方法，该方法根据网状天线的馈源位置和偏置反射面的根部节点C坐标，以展开臂总长度最小为目标，结合网状天线反射面与展开臂的位置约束，构建多节展开臂的数量N、臂长Li及在全局坐标系下的优化模型，根据该模型，锁死展开臂关节，完成展开臂的构建；本发明保证了多节展开臂合拢时能满足运载整流罩包络要求；同时，保证了多节展开臂展开到位并锁定后，天线馈源和网状天线的反射面焦点位置的完美匹配。

Figure 202011369186

The invention belongs to the technical field of satellite antennas, in particular to a method for constructing a multi-section deployment arm of a space-borne mesh antenna. The minimum length is the goal, combined with the position constraints of the mesh antenna reflector and the deployment arm, the number N of the multi-section deployment arms, the arm length Li and the optimization model in the global coordinate system are constructed. According to this model, the joints of the deployment arm are locked. , to complete the construction of the deployment arm; the invention ensures that the envelope requirements of the carrying fairing can be met when the multi-section deployment arms are folded; Perfect match for focus position.

Figure 202011369186

Description

Construction method of multisection expansion arm of satellite-borne mesh antenna
Technical Field
The invention belongs to the technical field of satellite antennas, and particularly relates to a construction method of a mesh-shaped deployable antenna unfolding arm.
Background
The mesh deployable antenna is more and more widely applied due to the advantages of wide aperture application range, large accommodation rate, light weight and the like, but has higher requirements on the performances of on-orbit gain, pointing accuracy and the like of the satellite-borne mesh deployable antenna in order to accurately capture target signals in spacecrafts such as mobile communication satellites, relay satellites and microwave remote sensing satellites, improve communication efficiency and reduce the size of ground terminals. The unfolding arm is used as a key device for connecting the mesh antenna and the satellite body, is a main component for supporting and fixing the large satellite-borne mesh reflector antenna, and whether the design is reasonable or not plays a crucial role in rocket transportation and space unfolding success of the antenna.
And limited by the space effectively carried by the spacecraft, the large satellite-borne netted expandable antenna is fixed in the fairing and is in a folded state, when the satellite enters a preset orbit, the netted antenna and the expansion arm are expanded under the control of an instruction, and the expanded arm is locked by the locking mechanism after being expanded in place. With the development of technologies such as modularization and on-track assembly, the aperture of the mesh deployable antenna can even be as high as hundreds of meters. Therefore, the unfolding arm needs to be designed into a multi-joint series structure so as to shorten the height of the folded unfolding arm and facilitate loading into the spacecraft fairing.
For the satellite-borne netted expandable antenna, under the condition of a certain fixed focal length ratio, the positive ratio of the focal length to the aperture is formed, and in order to match the reflecting surface with the feed source position, the larger the aperture of the antenna is, the more the number of joints of the expansion arm is required. However, the more spreading arms, the more interstitial spreading joints are introduced, which is more likely to cause mismatching of the reflecting surface and the focus. Considering the size limitation of rocket carrying space, excessive gap-containing unfolding arm joints cannot be introduced, so that various parameters of the unfolding arm joints need to be reasonably designed according to actual conditions, and the unfolding arms can be loaded into fairings of the spacecraft.
Disclosure of Invention
The invention aims to avoid the defects of the prior art and provides a method for constructing a multi-section unfolding arm of a satellite-borne mesh antenna, which can meet the size limitation of a rocket carrying space and reasonably construct the unfolding arm according to actual conditions.
In order to achieve the purpose, the invention adopts the technical scheme that: a method for constructing a multi-section unfolding arm of a spaceborne mesh antenna comprises the following steps
Establishing a standard reflecting surface under a global coordinate system (X, Y, Z) with a given focal length f and a given caliber D of a reflecting surface of the mesh antenna and an origin of coordinates O, and generating an offset reflecting surface according to an offset distance D' of the reflecting surface of the mesh antenna;
secondly, determining the coordinates of key nodes A and B of the net-shaped antenna upper net surface under a global coordinate system according to the standard reflecting surface and the bias reflecting surface, and calculating the height H of the net-shaped antenna upper net surfaceup；
Step three, the height H of the lower net surface of the net-shaped antenna is givendownAnd the distance H' between the upper mesh surface and the lower mesh surface, calculating the overall height H of the mesh antenna;
step four, according to the overall height H of the mesh antenna obtained through calculation, under a global coordinate system, calculating the coordinates of a root node C of the offset reflecting surface, namely the tail end node of the unfolding arm;
step five, according to the feed source position of the mesh antenna and the root node C coordinate of the offset reflector obtained in the step four, the minimum total length of the unfolding arm is taken as a target, and the position constraints of the mesh antenna reflector and the unfolding arm are combined to construct the number N and the arm length L of the multi-section unfolding armiAnd under the global coordinate system, the included angle between the jth node of the unfolding arm and the X axis
Figure BDA0002806085470000021
And obtaining the included angle theta between the two expansion armsk；
Step six, constructing the multi-section unfolding arm according to the step five, wherein when two connecting rods connected by a hinge are in a theta shapekWhen the unfolding arm joint is locked.
Further, the step one of generating the offset reflecting surface specifically includes:
establishing a standard reflecting surface under a global coordinate system (X, Y, Z) with a coordinate origin as a point O, and taking a cylindrical axial direction D with an offset distance of D' as an X axial direction of an (XOZ) surface of the global coordinate system (X, Y, Z)aAt said DaAnd D/2 is taken as the radius to generate a cylinder, and the intersecting line of the cylinder and the standard reflecting surface is the offset reflecting surface of the mesh antenna.
Further, the second step is specifically as follows:
the standard reflecting surface can be expressed as an equation under a global coordinate system:
Figure BDA0002806085470000031
the focal length f of the antenna reflecting surface is the focal length of the reflecting surface;
on the (XOZ) plane of the global coordinate system (X, Y, Z), two intersection points of the bias reflecting plane and the standard reflecting plane are key nodes of the net surface on the net antennaA and B, establishing coordinates of a network key node A on the mesh antenna as (X) under a global coordinate systemA,YA,ZA) And B has the coordinates of (X)B,YB,ZB)：
Figure BDA0002806085470000032
Y is Y since the world Wide Key Point coordinates are on the (XOZ) plane of the Global coordinate System (X, Y, Z)AAnd YBIs 0 and XAAnd XBCan be expressed as:
Figure BDA0002806085470000033
on said (XOZ) plane, the equation of the straight line AB is thus established, which can be expressed as:
ZAB＝KAB(XAB-XA)+ZA，
wherein KABThe slope of line AB can be expressed as:
Figure BDA0002806085470000041
in the global coordinate system, the distance between the node on the offset reflecting surface and the line segment AB is recorded as HNFrom the point-to-line distance formula, one can obtain:
Figure BDA0002806085470000042
for the obtained HNThe function is derived and extremed, when X is d', HNObtaining a maximum value, and calculating to obtain:
Figure BDA0002806085470000043
is obtained byHeight H of the upper net surfaceup。
Further, the second step further includes calculating the height H of the mesh surface of the mesh antennaupThe integrity verification step of (1): according to key nodes A and B of the upper net surface of the mesh antenna, taking the cylindrical axis D with the offset distance as DaAnd (3) establishing a local coordinate system (x, y, z) of the offset reflecting surface at an intersection point o of the line segment AB and taking the tangential direction and the normal direction of the point as the axial directions of the local coordinate systems x and z, and completely coinciding the projections of the upper mesh surface and the lower mesh surface in the (xoy) plane in the local coordinate system to ensure the integrity of the mesh antenna.
Further, the third step is specifically:
the overall height H of the mesh antenna may be expressed as:
H＝Hup+Hdown+H′。
the mesh antenna comprises an upper mesh surface, a lower mesh surface and a vertical cable net, wherein the upper mesh surface of the mesh antenna determines the electrical property of the antenna, and the lower mesh surface of the mesh antenna is given only for meeting the structural requirement.
Further, the fourth step is specifically:
coordinate (X) of the deployment arm root node CC,YC,ZC) Since the C point coordinates are on the (XOZ) plane of the global coordinate system (X, Y, Z), Y isCIs 0, according to the geometric relationship, XCAnd ZCCan be expressed as:
Figure BDA0002806085470000051
i.e. the coordinates of point C on the (XOZ) plane of the global coordinate system (X, Y, Z).
Further, the fifth step is specifically:
according to the coordinates of the feed source point F (0, 0, F) and the coordinates of the expansion arm tail end node C, the rod length connected with the point C must be larger than the whole height H of the mesh antenna, P is the distance from the key node A to the rod length, and for convenient installation, the distance must be between the valuesPAnd
Figure BDA0002806085470000052
in the number of the unfolded arms N and the length of the unfolded arms Li(i 1.... N) and the j-th node of the unfolding arm form an angle with the X-axis
Figure BDA0002806085470000053
For design variables, with the goal of minimizing the sum of all rod lengths, the following optimization model is established:
find
Figure BDA0002806085470000054
min
Figure BDA0002806085470000055
s.t
Figure BDA0002806085470000056
Figure BDA0002806085470000061
Figure BDA0002806085470000062
Figure BDA0002806085470000063
Figure BDA0002806085470000064
wherein d is a design variable, L is the sum of the lengths of the unfolding arms, and X1And Z1Respectively an X coordinate and a Z coordinate of the F point under the global coordinate system, XN+1And ZN+1Respectively are the X coordinate and the Z coordinate of the C point under the global coordinate system,
Figure BDA0002806085470000065
is the largest loadable dimension of the fairing,kand
Figure BDA0002806085470000066
the upper limit and the lower limit of the slope of the connection line between the nth node and the (N + 1) th node are respectively expressed as follows:
Figure BDA0002806085470000067
the angle between the two arms is denoted as θk(k 1...., N-1), which can be expressed as:
Figure BDA0002806085470000068
furthermore, multisection exhibition arm through locking mechanism lock and expand the arm joint, expansion arm joint refer to the hinge that is equipped with between two liang of single-section arms of expansion arm, locking mechanism include be equipped with the draw-in groove on the hinge, still include the connecting rod, the one end of connecting rod is connected on expansion arm, the other end of connecting rod is equipped with the horizontal pole perpendicular with the connecting rod expansion arm hinge free rotation time, the connecting rod does not constitute the constraint relation with the hinge, two expansion arms when hinged joint are thetakAnd when the hinge is closed, the cross rod falls into the clamping groove to lock the hinge.
The invention has the beneficial effects that: the invention aims at minimizing the total length of the unfolding arm, applies corresponding constraint, simultaneously completes the design of the rod number and the length of the joints of the unfolding arm and the included angle between the joints based on an optimized design method, and ensures that the envelope requirement of the carrying fairing can be met when the multiple sections of unfolding arms are folded; at the same timeAfter the included angle of the unfolding arm is obtained based on the optimization design method, when the two connecting rods connected by the hinge are in a theta shapekWhen the telescopic antenna is used, the hinge is locked, and the perfect matching of the focal positions of the reflecting surfaces of the antenna feed source and the mesh antenna is ensured after the multi-section unfolding arm is unfolded in place and locked.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a schematic representation of an offset reflector antenna reflector generation of the present invention;
FIG. 3 is a schematic view of multiple deployed knuckle configurations of the mesh antenna of the present invention;
FIG. 4 is a schematic view of the locking mechanism of the deployment arm joint of the present invention;
FIG. 5 is a top view of the deployment arm joint of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, the examples of which are set forth to illustrate, but are not to be construed to limit the scope of the invention.
The construction method of the multisection unfolding arm of the satellite-borne mesh antenna provided by the invention can establish the construction parameters of the unfolding arm of the mesh antenna in a limited space through calculation as long as the focal length f, the caliber D and the offset distance D' of the reflecting surface of the given mesh antenna are input, and the constructed unfolding arm parameters enable the perfect matching of the focal positions of the reflecting surfaces of the antenna feed source and the mesh antenna when the mesh antenna is actually unfolded and used. In order to achieve the above object, the present invention provides the following embodiments:
example 1: as shown in fig. 1, 2, 3 and 4, a method for constructing a multi-section unfolding arm of a space-borne mesh antenna includes
Step one, a focal length f and a caliber D of a reflecting surface of a mesh antenna are given, a standard reflecting surface is established under a global coordinate system (X, Y, Z) with a coordinate origin as a point O, and a cylindrical shaft with an offset distance D' is taken in the X axial direction of an (XOZ) surface of the global coordinate system (X, Y, Z)To DaAt said DaAnd D/2 is taken as a radius to generate a cylinder, and the intersecting line of the cylinder and the standard reflecting surface is used for generating the offset reflecting surface of the mesh antenna.
Secondly, determining the coordinates of key nodes A and B of the net-shaped antenna upper net surface under a global coordinate system according to the standard reflecting surface and the bias reflecting surface, and calculating the height H of the net-shaped antenna upper net surfaceupThe specific calculation steps are as follows:
the standard reflecting surface can be expressed as an equation under a global coordinate system:
Figure BDA0002806085470000081
the focal length f of the antenna reflecting surface is the focal length of the reflecting surface;
on the (XOZ) surface of the global coordinate system (X, Y, Z), two intersection points of the bias reflecting surface and the standard reflecting surface are key nodes A and B of the upper net surface of the mesh antenna, and under the global coordinate system, the coordinate of the key node A of the upper net surface of the mesh antenna is established as (X, Y, Z)A,YA,ZA) And B has the coordinates of (X)B,YB,ZB)：
Figure BDA0002806085470000082
Y is Y since the world Wide Key Point coordinates are on the (XOZ) plane of the Global coordinate System (X, Y, Z)AAnd YBIs 0 and XAAnd XBCan be expressed as:
Figure BDA0002806085470000083
on said (XOZ) plane, the equation of the straight line AB is thus established, which can be expressed as:
ZAB＝KAB(XAB-XA)+ZA，
wherein KABThe slope of line AB can be expressed as:
Figure BDA0002806085470000084
in the global coordinate system, the distance between the node on the offset reflecting surface and the line segment AB is recorded as HNFrom the point-to-line distance formula, one can obtain:
Figure BDA0002806085470000091
for the obtained HNThe function is derived and extremed, when X is d', HNObtaining a maximum value, and calculating to obtain:
Figure BDA0002806085470000092
namely, the height H of the upper net surface is obtainedup。
Step three, the height H of the lower net surface of the net-shaped antenna is givendownAnd the distance H' between the upper mesh surface and the lower mesh surface, calculating the overall height H of the mesh antenna, and expressing the overall height H as the following formula:
H＝Hup+Hdown+H′。
step four, according to the overall height H of the mesh antenna obtained by calculation, under a global coordinate system, calculating the coordinates of a root node C of the offset reflecting surface, namely the end node of the deployment arm, and the specific steps are as follows:
coordinates (X) of the deployment arm end node CC,YC,ZC) Since the C point coordinates are on the (XOZ) plane of the global coordinate system (X, Y, Z), Y isCIs 0, according to the geometric relationship, XCAnd ZCCan be expressed as:
Figure BDA0002806085470000093
i.e. the coordinates of point C on the (XOZ) plane of the global coordinate system (X, Y, Z).
Step five, constructing the number N and the arm length L of the multi-section unfolding arms according to the coordinates F (0, 0, F) of the feed source position points of the mesh antenna and the coordinates C of the root nodes of the offset reflecting surfaces obtained in the step fouriAnd under the global coordinate system, the j-th node of the unfolding arm forms an included angle with the X axis
Figure BDA0002806085470000094
And obtaining the included angle between the two expansion arms as thetakThe method comprises the following specific steps:
aiming at the minimum total length of the unfolding arm, combining the position constraint of the reflecting surface of the mesh antenna and the unfolding arm, ensuring that the rod length connected with the point C is larger than the overall height H of the mesh antenna, P is the distance from the key node A to the rod length, and the distance is required to be between the numerical value for convenient installationPAnd
Figure BDA0002806085470000101
in the number of the unfolded arms N and the length of the unfolded arms Li(i 1.... N) and the j-th node of the unfolding arm form an angle with the X-axis
Figure BDA0002806085470000102
Figure BDA0002806085470000103
For design variables, the following optimization model is established with the goal of minimizing the sum of all rod lengths:
find
Figure BDA0002806085470000104
min
Figure BDA0002806085470000105
s.t
Figure BDA0002806085470000106
Figure BDA0002806085470000107
Figure BDA0002806085470000108
Figure BDA0002806085470000109
Figure BDA00028060854700001010
wherein d is a design variable, L is the sum of the lengths of the unfolding arms, and X1And Z1Respectively an X coordinate and a Z coordinate of the F point under the global coordinate system, XN+1And ZN+1Respectively are the X coordinate and the Z coordinate of the C point under the global coordinate system,
Figure BDA00028060854700001011
is the largest loadable dimension of the fairing,kand
Figure BDA00028060854700001012
the upper limit and the lower limit of the slope of the connection line between the nth node and the (N + 1) th node are respectively expressed as follows:
Figure BDA0002806085470000111
the angle between the two arms is denoted as θk(k 1...., N-1), which can be expressed as:
Figure BDA0002806085470000112
step six, constructing the multi-section unfolding arm according to the step five, wherein when two connecting rods connected by a hinge are in a theta shapekWhen the unfolding arm joint is locked.
The specific operation example is as follows:
1. simulation parameters
A typical structure of a mesh antenna with some offset feed is shown in fig. 2. The caliber D is 10m, the focal diameter ratio is 0.6m, and the offset distance D' is 5 m.
2. Simulation content and results
Given HdownAnd H' is respectively 1.04m and 0.2m, the height of the antenna is calculated to be 2.2m, the coordinate of the root node C is calculated according to the height of the antenna, and an optimization model is established and solved according to the position of the feed source and the coordinate C of the key node on the obtained mesh antenna. To simplify the operation, the simulation case specifies that all the rod lengths and the included angles between the joints are equal.
The solved key parameters are shown in table 1, and the unfolding joint morphology schematic diagram is shown in fig. 3.
Number of rods/piece 3
Length of pole/m 2.83
Included angle theta/DEG 155.65
The invention provides a design method of a multi-section unfolding arm of a large satellite-borne netted expandable antenna, which ensures that the requirement of carrying a fairing for enveloping can be met when the multi-section unfolding arm is folded, and meanwhile, the design method can become key equipment for supporting the netted antenna and a satellite body after being unfolded. Meanwhile, the invention only carries out structural and mechanism scheme design and does not consider mechanical property.
Example 2: the same as the embodiment 1, except that the method further comprises the step of calculating the mesh antenna upper net surface obtained in the step twoHeight H ofupThe integrity verification step of (1): according to key nodes A and B of the upper net surface of the mesh antenna, taking the cylindrical axis D with the offset distance as DaAnd (3) establishing a local coordinate system (x, y, z) of the offset reflecting surface at an intersection point o of the line segment AB and taking the tangential direction and the normal direction of the point as the axial directions of the local coordinate systems x and z, and completely coinciding the projections of the upper mesh surface and the lower mesh surface in the (xoy) plane in the local coordinate system to ensure the integrity of the mesh antenna.
Example 3: as shown in fig. 5, the same as embodiment 1, except that the multi-section unfolding arm of the present invention locks the unfolding arm joint through a locking mechanism, the unfolding arm joint is a hinge 6 arranged between every two single-section arms 8 of the unfolding arm, the locking mechanism comprises a slot 61 arranged on the hinge 6, and further comprises a connecting rod 7, one end of the connecting rod 7 is connected to the unfolding arm, the other end of the connecting rod 7 is provided with a cross rod 71 perpendicular to the connecting rod 7, when the unfolding arm hinge 6 rotates freely, the connecting rod 7 and the hinge 6 do not form a constraint relation, and when the two unfolding arms connected by the hinge 6 are in a θ shapekWhen the hinge is closed, the cross rod 71 falls into the clamping groove 61 to lock the hinge 6. In the prior art, various structures for locking the unfolding arm exist, and compared with the prior art, the locking structure provided by the invention is simpler and more practical.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, but rather as the subject matter of the invention is to be construed in all aspects and as broadly as possible.

Claims (8)

1. A construction method of a multi-section unfolding arm of a space-borne mesh antenna is characterized by comprising the following steps
Establishing a standard reflecting surface under a global coordinate system (X, Y, Z) with a given focal length f and a given caliber D of a reflecting surface of the mesh antenna and an origin of coordinates O, and generating an offset reflecting surface according to an offset distance D' of the reflecting surface of the mesh antenna;
secondly, determining the network access of the mesh antenna under a global coordinate system according to the standard reflecting surface and the bias reflecting surfaceCoordinates of key nodes A and B of the surface, and calculating the height H of the mesh surface on the mesh antennaup(ii) a On the (XOZ) surface of the global coordinate system (X, Y, Z), two intersection points of the bias reflecting surface and the standard reflecting surface are key nodes A and B of the net-shaped antenna upper net surface;
step three, the height H of the lower net surface of the net-shaped antenna is givendownAnd the distance H' between the upper mesh surface and the lower mesh surface, calculating the overall height H of the mesh antenna;
step four, according to the overall height H of the mesh antenna obtained through calculation, under a global coordinate system, calculating the coordinates of a root node C of the offset reflecting surface, namely the tail end node of the unfolding arm;
step five, according to the feed source point coordinates F (0, 0, F) of the standard reflecting surface and the root node C coordinates of the offset reflecting surface obtained in the step four, the minimum total length of the unfolding arm is taken as a target, and the position constraints of the reflecting surface of the mesh antenna and the unfolding arm are combined to construct the number N and the arm length L of the multi-section unfolding armiAnd under the global coordinate system, the j-th node of the unfolding arm forms an included angle with the X axis
Figure FDA0003198614800000011
The optimization model of (1), wherein j 1.... N +1, and the included angle θ between two expansion arms is obtainedk；
Step six, constructing the multi-section unfolding arm according to the step five, wherein when the included angle between two sections of unfolding arms connected by the hinge is thetakAnd locking the joints of the unfolding arm to complete the construction of the unfolding arm.
2. The method for constructing a multi-section unfolding arm of a space-borne mesh antenna according to claim 1, wherein the step one of generating the offset reflecting surface specifically comprises:
taking a cylindrical axial direction D with an offset distance D' in the X axial direction of the (XOZ) surface of the global coordinate system (X, Y, Z)aAt said DaAnd D/2 is taken as the radius to generate a cylinder, and the intersecting line of the cylinder and the standard reflecting surface is the offset reflecting surface of the mesh antenna.
3. The method for constructing a multi-section unfolding arm of a space-borne mesh antenna as claimed in claim 2, wherein the second step is specifically as follows:
the standard reflecting surface can be expressed as an equation under a global coordinate system:
Figure FDA0003198614800000021
the focal length f of the antenna reflecting surface is the focal length of the reflecting surface;
under a global coordinate system, establishing the coordinate of a network key node A on the mesh antenna as (X)A,YA,ZA) And B has the coordinates of (X)B,YB,ZB)：
Figure FDA0003198614800000022
Y is Y since the world Wide Key Point coordinates are on the (XOZ) plane of the Global coordinate System (X, Y, Z)AAnd YBIs 0 and XAAnd XBCan be expressed as:
Figure FDA0003198614800000023
on said (XOZ) plane, the equation of the straight line AB is thus established, which can be expressed as:
ZAB＝KAB(XAB-XA)+ZA，
wherein KABThe slope of line AB can be expressed as:
Figure FDA0003198614800000024
in the global coordinate system, the distance between the node on the offset reflecting surface and the line segment AB is recorded as HNFrom point to lineThe distance formula can be found:
Figure FDA0003198614800000031
for the obtained HNThe function is derived and extremed, when X is d', HNObtaining a maximum value, and calculating to obtain:
Figure FDA0003198614800000032
namely, the height H of the upper net surface is obtainedup。
4. The method as claimed in claim 3, wherein the second step further comprises calculating the height H of the mesh surface of the mesh antennaupThe integrity verification step of (1): according to key nodes A and B of the upper net surface of the mesh antenna, taking the cylindrical axis D with the offset distance as DaAnd an intersection point o with the line segment AB is an origin, the tangential direction and the normal direction of the point are the axial directions of a local coordinate system x and a local coordinate system z, a local coordinate system (x, y, z) of the offset reflecting surface is established, and the projections of the upper mesh surface and the lower mesh surface in the (xoy) plane in the local coordinate system are completely overlapped, so that the integrity of the mesh antenna is ensured.
5. The method for constructing a multi-section unfolding arm of a space-borne mesh antenna according to claim 1, wherein the third step is specifically as follows:
the overall height H of the mesh antenna may be expressed as:
H＝Hup+Hdown+H′。
6. the method for constructing a multi-section unfolding arm of a space-borne mesh antenna as claimed in claim 1, wherein the fourth step is specifically as follows:
coordinates (X) of the deployment arm end node CC,YC,ZC) Since the C point coordinates are on the (XOZ) plane of the global coordinate system (X, Y, Z), Y isCIs 0, according to the geometric relationship, XCAnd ZCCan be expressed as:
Figure FDA0003198614800000041
i.e. the coordinates of point C on the (XOZ) plane of the global coordinate system (X, Y, Z).
7. The method for constructing a multi-section unfolding arm of a space-borne mesh antenna as claimed in claim 1, wherein the step five is specifically as follows:
according to the feed source point coordinates F (0, 0, F) and the expansion arm tail end node C coordinates, the expansion arm length connected with the point C is longer than the whole height H of the mesh antenna, P is the distance from the key node A to the expansion arm connected with the point C, and the distance is between the numerical valuePAnd
Figure FDA0003198614800000042
in the number of the unfolded arms N and the length of the unfolded arms LiWherein i 1, 1.... N, and the angle between the jth node of the deployment arm and the X-axis
Figure FDA0003198614800000043
To design variables, where j 1...., N +1, with the goal of minimizing the sum of all rod lengths, the following optimization model was built:
Figure FDA0003198614800000044
Figure FDA0003198614800000045
Figure FDA0003198614800000046
Figure FDA0003198614800000047
Figure FDA0003198614800000048
Figure FDA0003198614800000049
Figure FDA00031986148000000410
wherein d is a design variable, L is the sum of the lengths of the unfolding arms, and X1And Z1Respectively an X coordinate and a Z coordinate of the F point under the global coordinate system, XN+1And ZN+1Respectively are the X coordinate and the Z coordinate of the C point under the global coordinate system,
Figure FDA00031986148000000411
is the largest loadable dimension of the fairing,kand
Figure FDA0003198614800000051
the upper limit and the lower limit of the slope of the connection line between the nth node and the (N + 1) th node are respectively expressed as follows:
Figure FDA0003198614800000052
the angle between the two arms is denoted as θkN-1, where k is 1.
Figure FDA0003198614800000053
8. The method for constructing a multi-section unfolding arm of a space-borne mesh antenna as claimed in any one of claims 1 to 7, wherein the multi-section unfolding arm locks the unfolding arm joint through a locking mechanism, the unfolding arm joint is a hinge (6) arranged between every two single-section arms (8) of the unfolding arm, the locking mechanism comprises a clamping groove (61) arranged on the hinge (6) and a connecting rod (7), one end of the connecting rod (7) is connected to the unfolding arm, the other end of the connecting rod (7) is provided with a cross rod (71) perpendicular to the connecting rod (7), when the hinge (6) rotates freely, the connecting rod (7) and the hinge (6) do not form a constraint relationship, and when two unfolding arms connected by the hinge (6) form a thetakWhen the hinge is used, the cross rod (71) falls into the clamping groove (61) to lock the hinge (6).
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