CN109101747B - Method and device for determining cable net structure of annular net-shaped reflector - Google Patents

Method and device for determining cable net structure of annular net-shaped reflector Download PDF

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CN109101747B
CN109101747B CN201810997475.0A CN201810997475A CN109101747B CN 109101747 B CN109101747 B CN 109101747B CN 201810997475 A CN201810997475 A CN 201810997475A CN 109101747 B CN109101747 B CN 109101747B
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CN109101747A (en
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范叶森
马小飞
李欢笑
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Xian Institute of Space Radio Technology
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Abstract

The invention provides a method and a device for determining a cable net structure of an annular net-shaped reflector, and belongs to the technical field of structural design of aerospace vehicles. The method comprises the following steps: determining a front tension net structure parameter and the tension of each tension rope in a corresponding tension array according to the reflector structure parameter, determining an XOY plane coordinate of each second node forming a rear tension net according to the three-dimensional position coordinate of each first node, determining the force density of each second rope section according to the force density of each first rope section, and determining the three-dimensional position coordinate of each second node forming a rear tension net according to the plane coordinate of each second node, the force density of each second rope section and the tension of each tension rope; and determining the length of each tension rope according to the three-dimensional position coordinates of the first node and the three-dimensional position coordinates of the second node so as to determine the whole cable net structure. The invention effectively solves the possible problems of post-tensioned net ropes when the length of the truss vertical rod is lower, and obtains the stable and reliable rope net structure which meets the electrical performance requirement.

Description

Method and device for determining cable net structure of annular net-shaped reflector
Technical Field
The invention relates to a method and a device for determining a cable net structure of an annular net-shaped reflector, and belongs to the technical field of structural design of aerospace craft.
Background
In order to detect and receive the micro-power signals, a new generation of mobile communication satellites, electronic detection satellites, data relay satellites and the like put forward an urgent need for a large-caliber deployable antenna reflector. The annular truss type expandable antenna reflector (also called peripheral truss type expandable antenna) has the characteristics of simple structure form, high reliability and large spreading-receiving ratio, the structure form of the antenna reflector cannot be changed by increasing the caliber within a certain range, the quality cannot be increased in proportion, and the annular truss type expandable antenna reflector is the most ideal structure form of the existing large satellite-borne expandable antenna reflector.
As shown in fig. 1, the annular reflector mainly comprises five parts, namely a front tension net 1, a metal reflection net 2, a tension array 3, an annular expandable truss 4 and a rear tension net 5. Wherein, the front tension net 1, the tension array 3 and the rear tension net 5 form a cable net structure together, and the metal reflection net 2 is attached on the front tension net 1. The annular expandable truss 4 is a main force bearing mechanism and a contraction and expansion mechanism, is a closed polygonal ring consisting of a plurality of parallelogram units with completely the same structure, and provides rigid support for a cable net structure; the front tension net 1 is parabolic after the annular expandable truss 4 is expanded, the front tension net 1 and the metal net 2 are combined together to form a reflecting surface, the front tension net 1 and the rear tension net 5 are connected through the tension array 3, and the shapes of the cable net structure and the reflecting surface are fixed. In order to have a stable and reliable shape of the reflecting surface, the rope tension must be positive and no slack rope can occur.
Currently, the method for determining the cable net structure includes: the structure of the front tension net 1 is determined according to the structural parameters of the reflector, and then the positive feed net surface is made according to the structure of the front tension net 1, so that the structures of the rear tension net 5 and the tension array 3 are determined, wherein the tension array is parallel to the z axis. The satellite generally puts strict requirements on the folded volume of the loop antenna due to the limitation of the satellite platform structure and the effective volume of the load bin. To meet this requirement, the length of the vertical rods of the truss must be reduced. The existing cable net structure determination method has certain requirements on the total height of the arc depth of the front tension net 1 and the rear tension net 5, when the length of the vertical rod of the truss is smaller than a certain value, the existing algorithm cannot find a full positive solution of the rope, and the problem that the cable net structure shown in fig. 2 cannot keep balance can occur.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the invention provides a method and a device for determining a cable net structure of an annular net-shaped reflector, which overcome the defects of the prior art, effectively solve the possible problems of post-tensioned cables when the length of a vertical rod of a truss is lower, and obtain the stable and reliable cable net structure meeting the electrical performance requirement.
The technical scheme adopted by the invention is as follows:
a method for determining a cable net structure of an annular net reflector, comprising:
determining a front tension net structure parameter and the tension of each tension rope in a corresponding tension array according to a reflector structure parameter, wherein the front tension net structure parameter comprises a three-dimensional position coordinate of each first node forming the front tension net and the force density of each first rope section forming the front tension net between two adjacent first nodes;
determining XOY plane coordinates of each second node forming the back tension net according to the three-dimensional position coordinates of each first node;
determining the force density of each second rope segment forming the post-tensioning net according to the force density of each first rope segment;
determining the three-dimensional position coordinates of each second node forming the back tension net according to the plane coordinates of each second node, the force density of each second rope section and the tension of each tension rope;
and determining the length of each tension rope according to the three-dimensional position coordinate of the first node and the three-dimensional position coordinate of the second node so as to determine the whole cable net structure.
In an alternative embodiment, said determining a force density of said second rope segments based on a force density of said first rope segments comprises:
determining a second rope segment corresponding to the first rope segment ij according to the following formula
Figure GDA0004015022240000021
Force density of (2):
Figure GDA0004015022240000022
wherein:
Figure GDA0004015022240000031
is the force density of the first rope section ij @>
Figure GDA0004015022240000032
A second rope section ij corresponding to the first rope section ij, and xi is the first rope section ij and the corresponding second rope section->
Figure GDA0004015022240000033
The ratio of the force density of (a).
In an alternative embodiment, the determining three-dimensional position coordinates of each second node forming the back tension net according to the plane coordinates of each second node, the force density of each second rope segment and the tension of each tension rope comprises:
determining Z-direction coordinate values of the second nodes according to the following formula;
determining the three-dimensional position coordinates of each second node according to the plane coordinates of each second node and the Z-direction coordinate values;
Figure GDA0004015022240000034
s.t.T i ＞0；
Figure GDA0004015022240000035
Figure GDA0004015022240000036
wherein: s.t as constraint, T i Is the tension of the tension rope i in the tension matrix,
Figure GDA0004015022240000037
is the Z coordinate value of the first node i, is greater than or equal to>
Figure GDA0004015022240000038
Second node/for the first node i>
Figure GDA0004015022240000039
Z coordinate value of (2), Z B For the Z-direction coordinate vectors of all other second nodes except the second node connected with the truss in the back tension net, and->
Figure GDA00040150222400000310
Is the Z-direction coordinate vector of the second node connected with the truss in the post-tension net, and T is the tension of each tension rope in the tension arrayVector, D = C T QC，D f ＝C T QC f Q is a diagonalized matrix of the force density of the second rope sections, C is a topological matrix of all second nodes of the post-tensioning network except the second nodes connected to the truss, C f Topology matrix of second nodes connected to the truss for the post-tension network, i and->
Figure GDA00040150222400000311
Are all positive integers, are selected>
Figure GDA00040150222400000312
The allowable value of the length of the shortest tension rope in the tension array.
In an alternative embodiment, the determining the front tension net structure parameter and the tension of each tension rope in the corresponding tension array according to the reflector structure parameter includes:
step 1, generating an initial geometric grid of a front tension net according to structural parameters of a reflector;
step 2, determining a tension matrix of a tension array corresponding to a plurality of nodes forming the geometric grid according to a force balance equation, wherein the tension matrix comprises tension corresponding to each tension rope forming the tension array;
step 3, determining adjustable nodes and corresponding adjustment quantities according to electrical performance requirements;
step 4, adjusting the adjustable nodes according to the corresponding adjustment quantity to form a new geometric grid;
repeating the steps 2-4 based on the formed new geometric grid until each node in the finally formed geometric grid is in a balanced state and the maximum tension and the minimum tension in the corresponding tension matrix are within a preset ratio range;
determining the three-dimensional position coordinates of each first node forming the front tension net according to the three-dimensional position coordinates of each node in the finally formed geometric grid;
determining the force density of each first rope segment forming the front tension net and the tension of each tension rope of the tension matrix corresponding to the front tension net according to a force balance equation.
In an optional embodiment, in step 3, the adjustment amount corresponding to the adjustable node is determined according to the following formula
Figure GDA0004015022240000041
In the above formula, Δ p is the adjustable node adjustment vector, T v The tension vector of the tension rope corresponding to the adjustable node is shown, and h is the adjustment step length.
In an alternative embodiment, the predetermined ratio is in the range of [1,6].
In an alternative embodiment, the ratio of the maximum value to the minimum value of the tension of each of the first rope segments is in the range of [1,3], and the ratio of the maximum value to the minimum value of the tension of each of the second rope segments is in the range of [1,3 ].
An apparatus for determining a cable net structure of a toroidal mesh reflector, comprising:
the front tension net determining module is used for determining a front tension net structure parameter and the tension of each tension rope in the corresponding tension array according to the reflector structure parameter, wherein the front tension net structure parameter comprises a three-dimensional position coordinate of each first node forming the front tension net and the force density of each first rope section forming the front tension net between every two adjacent first nodes;
the second node plane coordinate determination module is used for determining XOY plane coordinates of each second node forming the back tension net according to the three-dimensional position coordinates of each first node;
a second rope segment force density determination module for determining a force density of each second rope segment based on the force density of each first rope segment;
the second node three-dimensional coordinate determination module is used for determining the three-dimensional position coordinates of each second node forming the rear tension net according to the plane coordinates of each second node, the force density of each second rope section and the tension of each tension rope;
and the tension rope length determining module is used for determining the length of each tension rope according to the three-dimensional position coordinate of the first node and the three-dimensional position coordinate of the second node so as to determine the whole cable net structure.
In an alternative embodiment, the second rope segment force density determination module is to:
determining a second rope segment corresponding to the first rope segment ij according to the following formula
Figure GDA0004015022240000051
The force density of (2):
Figure GDA0004015022240000052
wherein:
Figure GDA0004015022240000053
is the force density of the first rope section ij @>
Figure GDA0004015022240000054
Second rope portion ^ corresponding to the first rope portion ij>
Figure GDA0004015022240000055
Force density ξ is the first rope segment ij and the corresponding second rope segment->
Figure GDA0004015022240000056
The ratio of the force density of (a).
In an optional embodiment, the second node three-dimensional coordinate determination module is configured to:
determining Z-direction coordinate values of the second nodes according to the following formula;
determining the three-dimensional position coordinates of each second node according to the plane coordinates of each second node and the Z-direction coordinate values;
Figure GDA0004015022240000057
/>
s.t.T i ＞0；
Figure GDA0004015022240000058
Figure GDA0004015022240000059
wherein: s.t as constraint, T i Is the tension of the tension cord i in the tension matrix,
Figure GDA00040150222400000510
is the Z coordinate value of the first node i, is greater than or equal to>
Figure GDA00040150222400000511
Second node/for the first node i>
Figure GDA00040150222400000512
Z coordinate value of (2), Z B For the Z-direction coordinate vectors of all other second nodes except the second node connected with the truss in the back tension net, and->
Figure GDA00040150222400000513
Is a Z-direction coordinate vector of a second node connected with the truss in the rear tension net, T is a tension vector of each tension rope in the tension array, and D = C T QC，D f ＝C T QC f Q is a diagonalized matrix of the force density of the second rope sections, C is a topological matrix of all second nodes of the post-tensioning network except the second nodes connected to the truss, C f A topological matrix of second nodes connected with the truss by the post-tension net, i and->
Figure GDA00040150222400000514
Are all positive integers, are combined>
Figure GDA00040150222400000515
The allowable value of the length of the shortest tension rope in the tension array.
Compared with the prior art, the invention has the advantages that:
the method for determining the cable net structure of the annular net-shaped reflector comprises the steps of determining structural parameters of a front tension net and tension of each tension rope in a tension array, determining XOY plane coordinates of each node in the tension net according to three-dimensional coordinates of each node in the front tension net, determining force density of each node in a rear tension net according to force density of each cable section in the front tension net, determining the length of each cable in the tension array according to the tension of each tension rope (namely the load borne by each node in the rear tension net), the XOY coordinates of each node in the rear tension net and the force density, obtaining a balanced cable net structure with all the nodes stabilized at theoretical positions, and avoiding the problem that when the length of a truss vertical rod is smaller than a certain value, a cable net structure cannot be balanced because all the cables cannot be found.
Drawings
FIG. 1 is an exploded view of a toroidal mesh reflector;
fig. 2 is a schematic diagram of a coordinate system of a cable net structure according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a reflector structure obtained by a conventional algorithm;
fig. 4 is a flowchart of a method for determining a cable net structure of an annular mesh reflector according to an embodiment of the present invention;
fig. 5 is a schematic tension diagram of a first rope segment, a second rope segment and a tension rope in a cable network structure according to an embodiment of the present invention;
fig. 6 is a schematic view of a device for determining a cable net structure of an annular mesh reflector according to an embodiment of the present invention;
fig. 7 shows the determination result of the cable net structure of the annular net-shaped reflector according to an embodiment of the present invention.
Fig. 8 shows the mechanical analysis results of the cable net structure according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention will be made with reference to the accompanying drawings.
Referring to fig. 4, an embodiment of the present invention provides a method for determining a cable net structure of an annular mesh reflector, including:
step 101: determining a front tension net structure parameter and the tension of each tension rope in a corresponding tension array according to a reflector structure parameter, wherein the front tension net structure parameter comprises a three-dimensional position coordinate of each first node forming the front tension net and the force density of each first rope section forming the front tension net between two adjacent first nodes;
specifically, in the embodiment of the present invention, the structural parameters of the reflector include a focal length F of the reflecting surface, an operating frequency F, a requirement for a gain G of the reflector, an aperture D of the reflector, a center offset distance D of the reflector, and the like, where a ratio (F/D) between the focal length of the reflecting surface and the aperture of the reflector is generally: 0.3-1.5; the above parameters are typically determined by the mission requirements, flight trajectory, performance requirements, etc. of the satellite; in the embodiment of the invention, when the structural parameters of the reflector are known, the structural parameters of the front tension net can be determined according to various electromagnetic simulation software (such as GRASP) and the like;
as shown in fig. 1, currently, a front tension net design curved surface (a continuous paraboloid) is generally discretized into a polyhedral approximate curved surface composed of a large number of triangular meshes, and the meshes forming the polyhedral approximate curved surface are the geometric meshes corresponding to the front tension net; as shown in fig. 1, a first node 1a in the geometric mesh is an apex of each triangle, and a first line segment 1b is an edge of each triangle;
as shown in fig. 2, in the coordinate system provided in the embodiment of the present invention, the center of the annular surface of the reflector truss is taken as the origin of coordinates, the z-axis points to the opening direction of the reflective surface, and the x-axis points to the far end of the reflector;
in an alternative embodiment, in order to ensure that the reflector reflecting surface geometry meets the requirement of electrical performance and that the whole cable-mesh structure has excellent mechanical properties and thermal deformation resistance, step 101 specifically comprises the following steps:
step 1, generating an initial geometric grid of a front tension net according to structural parameters of a reflector;
step 2, determining a tension matrix of a tension array corresponding to a plurality of nodes forming the geometric grid according to a force balance equation, wherein the tension array matrix comprises tension corresponding to each tension rope forming the tension array;
in particular, to maintain balance, the total forces in all three directions experienced by each node (the initial first node) forming the front tension net must be zero. Because the resultant force of the front tension net rope acting on each node in the z direction can be balanced by the tension in the Zhang Lizhen tension rope connected with the node, the tension of each rope section in the front tension net can ensure that each node is balanced in the x direction and the y direction, and each node is in a stable state; the equilibrium equation of each node i in the x-direction and the y-direction is:
Figure GDA0004015022240000081
in the formula (1), j represents the j-th node number connected with the node i, e is the total number of the rope segments connected with the node i, and l ij Representing the length of the rope section between the j-th nodes connected by node i, T ij Representing the tension in the cable segment between the j-th nodes connected by node i, the equilibrium equations for all nodes in the x-and y-directions can be expressed by equation (2),
Figure GDA0004015022240000082
in equation (2), U is the coefficient matrix of the force balance equation, T is the vector of the tensions of the rope sections forming the front tension net, n s R is the number of rope segments forming the front tension net;
based on the basic principle of the minimum norm method for optimizing the tension of the plane cable net structure, the optimal solution T of the tension of each rope section in a group of front tension nets can be obtained by combining the analysis * Is composed of
T * ＝T 0 +W + (b-WT 0 ) (3)
In the formula (3), the reaction mixture is,
Figure GDA0004015022240000083
W + is a generalized inverse matrix of W and,
Figure GDA0004015022240000084
Figure GDA0004015022240000085
the average tension of the rope portions forming the front tension net. />
In the calculation using equation (3), a set of tensions for balancing the front tension net in the x-direction and the y-direction can be obtained by specifying the average tension of the rope segments forming the front tension net (initial first rope segment) according to the engineering requirements, and the balancing in the z-direction is achieved by appropriately arranging the tension matrix tension rope tensions.
Referring to fig. 5, in order to keep each node i of the front tension net in a balanced state, the tension of the tension ropes in the tension matrix connected with the node i must be reasonably configured
Figure GDA0004015022240000086
To allow node i to balance in the z-direction, be>
Figure GDA0004015022240000087
Must be equal to the resultant z-direction force of the rope segments on the front tension net acting on the node i, i.e. the tension rope tension is determined according to equation (4):
Figure GDA0004015022240000091
step 3, determining adjustable nodes and corresponding adjustment quantities according to electrical performance requirements;
generally, the closer the nodes of the truss and the larger the allowable adjustment amount of the corresponding rope sections are, the better the force distribution condition of the whole net surface is improved; specifically, an adjustable node and a corresponding adjustment amount can be determined on the premise of ensuring that the electrical property meets the technical requirements according to electrical property simulation results such as gain requirements of an antenna service area and the service area, antenna pointing and the like through electromagnetic field simulation software; for the annular mesh antenna in the embodiment of the invention, the adjustment optimization of the geometric shape of the front tension net can be achieved only by adjusting the Z-direction coordinate value of the adjustable node.
Step 4, adjusting the adjustable nodes according to the corresponding adjustment quantity to form a new geometric grid;
in step 4, in order to ensure that the tension rope is not loosened and the rope tension ratio meets the technical requirements, the adjustment amount corresponding to the adjustable node can be determined according to (5):
Figure GDA0004015022240000092
in the above equation (5), Δ p is an adjustable node adjustment amount vector, T v Is the tension vector of the tension rope corresponding to the adjustable node, h is the adjustment step length, h is preferably [0.1,0.3 ]]mm。
Repeating the steps 2-4 based on the formed new geometric grid until each node in the finally formed geometric grid is in a balanced state and the maximum tension and the minimum tension in the corresponding tension matrix are within a preset ratio range; wherein the preset ratio range is preferably [1,6] so as to ensure that the whole cable net structure has excellent mechanical properties and heat deformability.
Determining the three-dimensional position coordinates of each first node forming the front tension net according to the three-dimensional position coordinates of each node in the finally formed geometric grid;
determining the force density of each first rope segment forming the front tension net and the tension of each tension rope of the tension matrix corresponding to the front tension net according to a force balance equation. Wherein the force density is the ratio of the tension of the rope section to the length of the rope section.
Step 102: determining XOY plane coordinates of each second node forming the back tension net according to the three-dimensional position coordinates of each first node;
the extending direction of each tension rope in the tension array is parallel to the Z-axis direction, the first nodes 1a correspond to the second nodes 5a one by one, and the second nodes 5a are the mapping positions of the corresponding first nodes 1a on the XOY plane and are superposed;
step 103: determining a force density of each second rope segment according to the force density of each first rope segment;
in particular, a second rope segment corresponding to the first rope segment ij is determined according to equation (6)
Figure GDA0004015022240000101
Force density of (2):
determining a second rope portion corresponding to the first rope portion ij according to equation (6)
Figure GDA0004015022240000102
Force density of (2):
Figure GDA0004015022240000103
wherein:
Figure GDA0004015022240000104
is the force density of the first rope section ij @>
Figure GDA0004015022240000105
Second rope portion ^ corresponding to the first rope portion ij>
Figure GDA0004015022240000106
Force density xi is a first rope section ij and a corresponding second rope section +>
Figure GDA0004015022240000107
The force density is the ratio of the rope segment tension to the rope segment length.
Step 104: determining the three-dimensional position coordinates of each second node forming the back tension net according to the plane coordinates of each second node, the force density of each second rope section and the tension of each tension rope;
in an optional embodiment, the Z-direction coordinate value of each second node is determined according to the optimization model shown in formula (7);
determining the three-dimensional position coordinates of each second node according to the plane coordinates of each second node and the Z-direction coordinate values;
Figure GDA0004015022240000108
wherein: find xi is to Find the optimal xi function value, s.t is the constraint condition,
Figure GDA0004015022240000109
is the tension of the tension rope i in the tension matrix, is greater or less>
Figure GDA0004015022240000111
Is the Z coordinate value of the first node i, is greater than or equal to>
Figure GDA0004015022240000112
A second node + +that is corresponding to the first node i>
Figure GDA0004015022240000113
Z coordinate value of (2), Z B For the Z-direction coordinate vectors of all other second nodes except the second node connected with the truss in the back tension net, and->
Figure GDA0004015022240000114
Is a Z-direction coordinate vector of a second node connected with the truss in the rear tension net, T is a tension vector of each tension rope in the tension array, and D = C T QC，D f ＝C T QC f Q is a diagonal matrix of the force density of the second rope sections, C is a topological matrix of all second nodes of the post-tensioned network except the second node connected to the truss, C f Topology matrix of second nodes connected to the truss for the post-tension network, i and->
Figure GDA0004015022240000115
Are all positive integers, are selected>
Figure GDA0004015022240000116
Is the shortest of the tension matrixThe length of the tensile cord is allowed.
Step 105: and determining the length of each tension rope according to the three-dimensional position coordinate of the first node and the three-dimensional position coordinate of the second node so as to determine the whole cable net structure.
In an alternative embodiment, the ratio of the maximum value to the minimum value of the tension of each first rope segment is in the range of [1,3], and the ratio of the maximum value to the minimum value of the tension of each second rope segment is in the range of [1,3], so that the net surface has excellent heat deformation resistance.
The method for determining the cable net structure of the annular net-shaped reflector comprises the steps of determining structural parameters of a front tension net and tension of each tension rope in a tension array, determining XOY plane coordinates of each node in the tension net according to three-dimensional coordinates of each node in the front tension net, determining force density of each node in a rear tension net according to force density of each cable section in the front tension net, determining the length of each cable in the tension array according to the tension of each tension rope (namely the load borne by each node in the rear tension net), the XOY coordinates of each node in the rear tension net and the force density, obtaining a balanced cable net structure with all the nodes stabilized at theoretical positions, and avoiding the problem that when the length of a truss vertical rod is smaller than a certain value, a cable net structure cannot be balanced because all the cables cannot be found.
Referring to fig. 6, an embodiment of the present invention further provides a device for determining a cable net structure of an annular mesh reflector, including:
a front tension net determining module 10, configured to determine, according to a reflector structure parameter, a front tension net structure parameter and tension of each tension rope in a corresponding tension array, where the front tension net structure parameter includes a three-dimensional position coordinate of each first node forming the front tension net and a force density of each first rope segment forming the front tension net and located between two adjacent first nodes;
a second node plane coordinate determination module 20, configured to determine, according to the three-dimensional position coordinate of each first node, an XOY plane coordinate of each second node forming the back tension network;
a second rope segment force density determination module 30 for determining a force density of each second rope segment based on the force density of each first rope segment;
a second node three-dimensional coordinate determination module 40, configured to determine, according to the plane coordinates of each second node, the force density of each second rope segment, and the tension of each tension rope, three-dimensional position coordinates of each second node forming the back tension network;
a tension rope length determining module 50, configured to determine lengths of the tension ropes according to the three-dimensional position coordinates of the first node and the three-dimensional position coordinates of the second node, so as to determine an entire cable-net structure.
In an alternative embodiment, the second rope segment force density determination module 30 is configured to:
determining a second rope portion corresponding to the first rope portion ij according to equation (6)
Figure GDA0004015022240000121
Force density of (2):
Figure GDA0004015022240000122
wherein:
Figure GDA0004015022240000123
is the force density of the first rope section ij @>
Figure GDA0004015022240000124
Second rope portion ^ corresponding to the first rope portion ij>
Figure GDA0004015022240000125
Force density xi is a first rope section ij and a corresponding second rope section +>
Figure GDA0004015022240000126
The ratio of the force density of (a).
In an optional embodiment, the second node three-dimensional coordinate determination module 40 is configured to:
determining Z-direction coordinate values of the second nodes according to the formula (1);
determining the three-dimensional position coordinates of each second node according to the plane coordinates of each second node and the Z-direction coordinate values;
Figure GDA0004015022240000127
wherein: s.t as a constraint,
Figure GDA0004015022240000128
is the tension of the tension rope i in the tension matrix, is greater or less>
Figure GDA0004015022240000129
Is a Z coordinate value of the first node i->
Figure GDA00040150222400001210
Second node/for the first node i>
Figure GDA00040150222400001211
Z coordinate value of (2), Z B For the Z-direction coordinate vectors of all other second nodes except the second node connected with the truss in the back tension net, and->
Figure GDA0004015022240000131
Is a Z-direction coordinate vector of a second node connected with the truss in the rear tension net, T is a tension vector of each tension rope in the tension array, and D = C T QC，D f ＝C T QC f Q is a diagonalized matrix of the force density of the second rope sections, C is a topological matrix of all second nodes of the post-tensioning network except the second nodes connected to the truss, C f Topology matrix of second nodes connected to the truss for the post-tension network, i and->
Figure GDA0004015022240000132
Are all positive integers, are selected>
Figure GDA0004015022240000133
The allowable length of the shortest tension rope in the tension array.
The embodiments of the apparatus and the method of the present invention correspond to each other, and for the specific description, reference is made to the embodiments of the method, which are not described herein again.
The following is a specific embodiment of the present invention:
take a ring-shaped mesh antenna with 30 parallelogram units in the truss and 10m expansion caliber of the truss as an example. The antenna aperture is 10m, the focal length of the front tension net is 10m, the offset distance of the reflecting surface is 6m, the average pre-tension of a rope section forming the front tension net is 20N, the front tension net and the rear tension net are both net-shaped structures formed by triangular meshes, and the height of the truss is 1m.
And (3) determining the result: the length of the shortest tension rope in the tension matrix is 173mm, the tension mean of the rope sections forming the front tension net is 20N, the maximum and minimum tension ratio of the rope sections forming the front tension net is 2.5, the tension mean of the rope sections forming the back tension net is 49.7N, and the maximum and minimum tension ratio of the rope sections forming the back tension net is 2.5. As shown in fig. 7, the determination result is imported into ANSYS for balance analysis, and the calculation result shows that the maximum node displacement is 0.228 × 10 -8 mm, all nodes are stable in the theoretical position.
Parts of the description which are not described in detail are within the common general knowledge of a person skilled in the art.

Claims (8)

1. A method for determining a cable net structure of an annular net reflector, comprising:
determining structural parameters of a front tension net and tension of each tension rope in a corresponding tension array according to structural parameters of a reflector, wherein the structural parameters of the front tension net comprise three-dimensional position coordinates of each first node forming the front tension net and force density of each first rope section which is positioned between two adjacent first nodes and forms the front tension net;
determining XOY plane coordinates of each second node forming the back tension net according to the three-dimensional position coordinates of each first node;
determining the force density of each second rope segment forming the post-tensioning net according to the force density of each first rope segment; the method comprises the following steps:
determining a second rope segment corresponding to the first rope segment ij according to the following formula
Figure FDA0004015022230000011
Force density of (2):
Figure FDA0004015022230000012
wherein:
Figure FDA0004015022230000013
for the force density of the first rope section ij>
Figure FDA0004015022230000014
Second rope portion ^ corresponding to the first rope portion ij>
Figure FDA0004015022230000015
Force density ξ is the first rope segment ij and the corresponding second rope segment->
Figure FDA0004015022230000016
The ratio of the force densities of (a);
determining the three-dimensional position coordinates of each second node forming the back tension net according to the plane coordinates of each second node, the force density of each second rope section and the tension of each tension rope; the method comprises the following steps:
determining Z-direction coordinate values of the second nodes according to the following formula;
determining the three-dimensional position coordinates of each second node according to the plane coordinates of each second node and the Z-direction coordinate values;
Figure FDA0004015022230000017
s.t.T i ＞0；
Figure FDA0004015022230000018
Figure FDA0004015022230000019
wherein: s.t as constraint, T i Is the tension of the tension rope i in the tension matrix,
Figure FDA00040150222300000110
is the Z coordinate value of the first node i,
Figure FDA00040150222300000111
second node/for the first node i>
Figure FDA00040150222300000112
Z coordinate value of (2), Z B For the Z-direction coordinate vectors of all other second nodes except the second node connected with the truss in the back tension net, and->
Figure FDA0004015022230000021
Is a Z-direction coordinate vector of a second node connected with the truss in the rear tension net, T is a tension vector of each tension rope in the tension array, and D = C T QC，D f ＝C T QC f Q is a diagonal matrix of the force density of the second rope sections, C is a topological matrix of all second nodes of the post-tensioned network except the second node connected to the truss, C f Topology matrix of second nodes connected to the truss for the post-tension network, i and->
Figure FDA0004015022230000022
Are all positive integers, are selected>
Figure FDA0004015022230000023
The length allowable value of the shortest tension rope in the tension array is obtained;
and determining the length of each tension rope according to the three-dimensional position coordinate of the first node and the three-dimensional position coordinate of the second node so as to determine the whole cable net structure.
2. The method for determining the cable net structure of a toroidal mesh reflector according to claim 1, wherein said determining the front tension net structure parameters and the tension of each tension rope in the corresponding tension matrix according to the reflector structure parameters comprises:
step 1, generating an initial geometric grid of a front tension net according to structural parameters of a reflector;
step 2, determining a tension matrix of a tension array corresponding to a plurality of nodes forming the geometric grid according to a force balance equation, wherein the tension matrix comprises tension corresponding to each tension rope forming the tension array;
step 3, determining adjustable nodes and corresponding adjustment quantities according to electrical performance requirements;
step 4, adjusting the adjustable nodes according to the corresponding adjustment quantity to form a new geometric grid;
repeating the steps 2-4 based on the formed new geometric grid until each node in the finally formed geometric grid is in a balanced state and the maximum tension and the minimum tension in the corresponding tension matrix are within a preset ratio range;
determining the three-dimensional position coordinates of each first node forming the front tension net according to the three-dimensional position coordinates of each node in the finally formed geometric grid;
determining the force density of each first rope segment forming the front tension net and the tension of each tension rope of the tension matrix corresponding to the front tension net according to a force balance equation.
3. The method for determining cable net structure of annular mesh reflector according to claim 2, wherein the adjustment amount corresponding to the adjustable node is determined in step 3 according to the following formula
Figure FDA0004015022230000031
In the above formula, Δ p is the adjustable node adjustment vector, T v The tension vector of the tension rope corresponding to the adjustable node is shown, and h is the adjustment step length.
4. The method of claim 2, wherein the predetermined ratio is in the range of [1,6].
5. The method as claimed in claim 1, wherein the ratio of the maximum value to the minimum value of the tension of each first rope segment is in the range of [1,3] and the ratio of the maximum value to the minimum value of the tension of each second rope segment is in the range of [1,3 ].
6. The apparatus for determining the cable net structure of a toroidal mesh reflector according to claim 1, comprising:
the front tension net determining module is used for determining front tension net structural parameters and tension of each tension rope in the corresponding tension array according to the structural parameters of the reflector, wherein the front tension net structural parameters comprise three-dimensional position coordinates of each first node forming the front tension net and force density of each first rope section which is positioned between two adjacent first nodes and forms the front tension net;
the second node plane coordinate determination module is used for determining XOY plane coordinates of each second node forming the back tension net according to the three-dimensional position coordinates of each first node;
a second rope segment force density determination module for determining a force density of each second rope segment based on the force density of each first rope segment;
the second node three-dimensional coordinate determination module is used for determining the three-dimensional position coordinates of each second node forming the rear tension net according to the plane coordinates of each second node, the force density of each second rope section and the tension of each tension rope;
and the tension rope length determining module is used for determining the length of each tension rope according to the three-dimensional position coordinate of the first node and the three-dimensional position coordinate of the second node so as to determine the whole cable net structure.
7. The apparatus of claim 6, wherein the second rope segment force density determining module is configured to:
determining a second rope segment corresponding to the first rope segment ij according to the following formula
Figure FDA0004015022230000041
Force density of (2):
Figure FDA0004015022230000042
wherein:
Figure FDA0004015022230000043
is the force density of the first rope section ij @>
Figure FDA0004015022230000044
Second rope portion ^ corresponding to the first rope portion ij>
Figure FDA0004015022230000045
Force density ξ is the first rope segment ij and the corresponding second rope segment->
Figure FDA0004015022230000046
The ratio of the force density of (a). />
8. The apparatus for determining cable net structure of annular net-shaped reflector according to claim 6 or 7, wherein the second node three-dimensional coordinate determining module is configured to:
determining Z-direction coordinate values of the second nodes according to the following formula;
determining the three-dimensional position coordinates of each second node according to the plane coordinates of each second node and the Z-direction coordinate values;
Figure FDA0004015022230000047
s.t.T i ＞0；
Figure FDA0004015022230000048
Figure FDA0004015022230000049
wherein: s.t as constraint, T i Is the tension of the tension rope i in the tension matrix,
Figure FDA00040150222300000410
is the Z coordinate value of the first node i,
Figure FDA00040150222300000411
is the Z-direction coordinate value of a second node i corresponding to the first node i, Z B For the Z-direction coordinate vectors of all other second nodes except the second node connected with the truss in the back tension net, and->
Figure FDA00040150222300000412
Is a Z-direction coordinate vector of a second node connected with the truss in the rear tension net, T is a tension vector of each tension rope in the tension array, and D = C T QC，D f ＝C T QC f Q is a diagonalized matrix of the force density of the second rope sections, C is a topological matrix of all second nodes of the post-tensioning network except the second nodes connected to the truss, C f Topology matrix of second nodes connected to the truss for the post-tension network, i and->
Figure FDA00040150222300000413
Are all positive integers, are selected>
Figure FDA00040150222300000414
The allowable value of the length of the shortest tension rope in the tension array. />
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