CN108598716A - The simple and easy method that rope net antenna reflective face rope net generates - Google Patents
The simple and easy method that rope net antenna reflective face rope net generates Download PDFInfo
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- CN108598716A CN108598716A CN201810348177.9A CN201810348177A CN108598716A CN 108598716 A CN108598716 A CN 108598716A CN 201810348177 A CN201810348177 A CN 201810348177A CN 108598716 A CN108598716 A CN 108598716A
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- 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
- H01Q15/141—Apparatus or processes specially adapted for manufacturing reflecting surfaces
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- 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
- H01Q15/16—Reflecting surfaces; Equivalent structures curved in two dimensions, e.g. paraboloidal
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Abstract
The invention discloses the simple and easy methods that a kind of rope net antenna reflective face rope net generates, and have following steps:It generates and refers to spherical surface, six duplicate subsurfaces will be divided into reference to spherical surface, take one of subsurface, two main ropes of its both sides are angularly divided equally, generate the initial coordinate C of one group of rope net node0=[x0y0z0], according to each cable elements and standard cable elements length lsBetween gap generate free node coordinate modification transposed matrix, and then generate the node coordinate of revised free node, it obtains revised subsurface rope net and the total rope of subsurface rope net is long, judge the difference of the total rope length of subsurface rope net twice, the difference of the total rope length of front and back grid twice is made to be less than convergence threshold by successive ignition amendment, by obtained subsurface rope net around the paraboloid of revolution center axis rotation angles of π/3, entire reflecting surface rope net is generated.Compared to common sciagraphy and geodesic method, the reflecting surface rope net unit length that the present invention generates is more uniformly distributed, especially in the case where focal length bore is smaller.
Description
Technical field
The present invention relates to rope net antenna design techniques field more particularly to a kind of combination equilateral triangle characteristics, pass through section
The simple and easy method of point coordinates grey iterative generation rope net antenna reflective face rope net geometric configuration.
Background technology
In recent years, earth observation satellite, communications satellite, survey of deep space spacecraft etc. receive energy to the gain of antenna and signal
Power proposes increasingly higher demands, heavy caliber, one of the main direction of development for becoming satellite antenna in high precision.Due to carrier rocket
Carrying capacity and loading space limitation, traditional solid surface antenna cannot be satisfied design requirement.Deployable antenna becomes current
Realize the effective form of large aperture antenna under rocket carrying capacity, main Types include solid face deployable antenna, paraballon and
Rope net antenna, wherein rope net antenna because its folding storage than the features such as high, light weight obtains the extensive concern of engineering research personnel,
And as the preferred antenna form of numerous space tasks.
Rope net antenna includes mainly support construction, reflecting surface rope net, back rope net, longitudinal drag-line etc., wherein reflecting surface rope
The online metal mesh being attached with for reflection electromagnetic wave.In space microgravity environment, cable elements under the action of pretightning force at
In tensioning state, so antenna reflective face is by being largely spliced by the facet on vertex of rope net node.However, by a large amount of
Inevitably there is certain error between the facet paraboloid of revolution being spliced and ideally-reflecting face.This error quilt
The referred to as errors of principles of reflecting surface rope net, mainly by rope net configuration (node topology relationship), sizing grid and rope net node position
Set decision.Therefore, the design of reflecting surface rope net directly determines the electromagnetic performance of rope net antenna, is the important of rope net Antenna Design
One step.
In terms of reflecting surface rope net grid generation, projection mapping method is a kind of common method.This method is generally divided into two
Step:First, according to the rope net configuration and sizing grid of selection, the plane cable net under static balancing state is generated in bore plane
Structure;Then plane cable net is mapped to along paraboloid of revolution axis direction on the ideal paraboloid of revolution vertically, to obtain most
Whole reflecting surface cable net structure.Projection mapping method generation grid process is simple, but when reflecting surface focal length-bore ratio is smaller
(such as f/D<0.5) the element length uniformity that, projection mapping method obtains is poor.Another common grid generation method is geodetic
Collimation method.Geodesic curve is the shortest path of point-to-point transmission on space curved surface, is based on this geodesic property, and geodetic wire grid wishes profit
With shortest total rope length structure reflecting surface rope net.But it is existing all comparatively laborious based on geodesic grid generation method, and
And what is generated is also all quasi- geodetic wire grid.
Invention content
According to technical problem set forth above, and provide a kind of simple and easy method that rope net antenna reflective face rope net generates.Institute
Method combination equilateral triangle characteristic is stated, node coordinate grey iterative generation rope net antenna reflective face rope net is passed through.It is small flat in triangle
In face, equilateral triangle is gathered around there are two significant advantage:(1) identical perimeter, the area that equilateral triangle surrounds is maximum, (2)
The maximum side of identical perimeter, equilateral triangle is most short.And the maximal side of cable elements determines the precision of reflecting surface, thus it is right
In given network topology form, equilateral triangle grid can utilize shortest total rope length to realize highest surface accuracy.For
Simplify geodesic method grid generating process, obtains the better reflecting surface rope net of performance, the present invention goes out from the characteristic of equilateral triangle
Hair, provides a kind of simple and easy method by node coordinate grey iterative generation reflecting surface rope net geometric configuration.
The technological means that the present invention uses is as follows:
A kind of simple and easy method that rope net antenna reflective face rope net generates, has following steps:
S1:Generated according to the bore D of the paraboloid of revolution and focal length f and refer to spherical surface, with reference to the vertex of spherical surface and bore circle with
The vertex of the paraboloid of revolution and bore circle overlap;
S2:By six mistakes with reference to the main rope (geodesic curve) on the vertex of spherical surface, six complete one will be divided into reference to spherical surface
The subsurface of sample takes one of subsurface, and two main ropes of its both sides are angularly divided equally, subsurface main rope node is obtained,
Wherein, that angularly divides equally divides angle, θ equallysAnd its corresponding chord length lsBy type face precision (root-mean-square error) δ of reflecting surface rope netrms
It determines, wherein enable lsFor standard cable elements length;
S3:Based on obtained subsurface main rope node, using three-way grid formula node topology relationship subsurface throwing
Then grid division in shadow face is projected using the projection normal direction paraboloid of revolution, generates the initial coordinate C of one group of rope net node0=
[x0y0z0], rope net node includes subsurface main rope node, subsurface internal node and subsurface fringe node, the side of subsurface
The fringe node of node between edge node i.e. two main rope on circular arc, initial subsurface can be according to the fringe node of subsurface
Number (being obtained by the topological relation between node) obtained (as angularly divided equally) by certain rule, remove adjacent subsurface main rope
It outside node, is connected by cable elements according to topological relation between other rope net nodes, obtains subsurface rope net and subsurface rope net is total
The long L of rope0, the sum of two main ropes of the total Suo Changwei of subsurface rope net and whole cable elements length;
S4:Subsurface main rope node is considered as stationary nodes, the fringe node of subsurface and subsurface internal node are regarded
For moveable free node, according to each cable elements and standard cable elements length lsBetween gap generate free node coordinate modification
Transposed matrix, and then generate the node coordinate of revised free node, obtain revised subsurface rope net and subsurface
The long L of the total rope of rope net1;
S5:The long L of the total rope of subsurface rope net that judgment step S3 is obtained0The long L of the total rope of subsurface rope net obtained with step S41
Difference, if more than the threshold value L of settingtol, then it is initial sit with the node coordinate of the obtained revised free nodes of step S4
Mark, iteration execute the node coordinate that step S4 corrects free node, until difference is less than convergence threshold;If satisfied, then executing step
Rapid S6;
S6:The subsurface rope net that step S5 is obtained generates entire reflection around the paraboloid of revolution center axis rotation angles of π/3
Face rope net.
In the step S1, it is given by with reference to spherical radius:
In the step S2, the corresponding central angle of main rope is θ=arcsin (D/2R), divides angle, θ equallys=2arcsin (ls/
2R), wherein wherein, R is with reference to spherical radius;
lsWith δrmsRelationship be:
To ensure that the precision of rope net antenna reflective face meets design requirement, the segments n that main rope is angularly divided equallyrIt should meet
Formula:
The subsurface main rope node obtained on reference to spherical surface is projected on the paraboloid of revolution, to generate subsurface master
Socket point.
In the step S4, for a certain free node i, during at it, node coordinate is corrected each time, according to each cable elements
With standard cable elements length lsBetween gap correct node i node coordinate, to reduce the length difference between each cable elements, node i
Position correction amount along the x-axis direction is represented by:
Wherein, xi,xjFor node i and the x-axis coordinate of coupled node j, lijFor connecting node i's and node j
Cable elements length, by the position correction amount composition of vector matrix Δ x of all free nodes along the x-axis direction, then revised freedom
The x-axis coordinate of node is
The y-axis coordinate that revised free node can similarly be obtained is
For the fringe node of subsurface, they can only be moved on bore circle, therefore also need to meet following restriction relation:
The z-axis coordinate of revised free node meets following formula:
The node coordinate that revised free node can be obtained above is
Compared with prior art, the beneficial effects of the invention are as follows:
1. compared to common sciagraphy and geodesic method, the reflecting surface rope net unit length that the present invention generates is more equal
It is even, especially in the case where focal length-relative aperture (f/D) is smaller.
2. the characteristic based on equilateral triangle, the present invention can obtain that the total rope length of grid is shorter, and type face precision is higher anti-
Penetrate face cable net structure.
3. the present invention is derived without complicated geometrical relationship, the setting of some empirical parameters is avoided, generating process is simple
Reliably, it is easily programmed realization.
The present invention can be widely popularized in rope net antenna reflective face rope net design field based on the above reasons.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to do simply to introduce, it should be apparent that, the accompanying drawings in the following description is this hair
Some bright embodiments for those of ordinary skill in the art without having to pay creative labor, can be with
Obtain other attached drawings according to these attached drawings.
Fig. 1 be the present invention specific implementation mode in reference to spherical surface etc. divide schematic diagram.
Fig. 2 be the present invention specific implementation mode in main rope angularly divide schematic diagram equally.
Fig. 3 be the present invention specific implementation mode in rope net node topology relation schematic diagram.
Fig. 4 be the present invention specific implementation mode in a certain coupled node j of subsurface internal node i topology close
It is schematic diagram.
Fig. 5 is the specific implementation mode interior joint coordinate iterative process figure of the present invention.
Fig. 6 is that the rope net of quasi- geodesic method in the embodiment of the present invention generates result front view.
Fig. 7 is that the rope net for the simple and easy method that rope net antenna reflective face rope net generates in the embodiment of the present invention is generating result just
View.
Specific implementation mode
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
The every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
As shown in Fig. 1-Fig. 7, a kind of simple and easy method that rope net antenna reflective face rope net generates has following steps:
S1:Generated according to the bore D of the paraboloid of revolution and focal length f and refer to spherical surface, with reference to the vertex of spherical surface and bore circle with
The vertex of the paraboloid of revolution and bore circle overlap, and are given by with reference to spherical radius:
S2:By six mistakes with reference to the main rope (geodesic curve) on the vertex of spherical surface, six complete one will be divided into reference to spherical surface
The subsurface of sample takes one of subsurface, and two main ropes of its both sides are angularly divided equally as shown in Figure 2, obtain subsurface
Main rope node, wherein O are the centre of sphere with reference to spherical surface, and the corresponding central angle of main rope is θ=arcsin (D/2R), divides angle, θ equallys=
2arcsin(ls/ 2R), that angularly divides equally divides angle, θ equallysAnd its corresponding chord length lsIt is (square by the type face precision of reflecting surface rope net
Root error) δrmsIt determines, wherein enable lsFor standard cable elements length;
lsWith δrmsRelationship be:
To ensure that the precision of rope net antenna reflective face meets design requirement, the segments n that main rope is angularly divided equallyrIt should meet
Formula:
The subsurface main rope node obtained on reference to spherical surface is projected on the paraboloid of revolution, to generate subsurface master
Socket point.
S3:Based on obtained subsurface main rope node, using three-way grid formula node topology relationship subsurface throwing
Grid division in shadow face generates the initial seat of one group of rope net node as shown in figure 3, being projected using the projection normal direction paraboloid of revolution
Mark C0=[x0y0z0], rope net node includes subsurface main rope node, subsurface internal node and subsurface fringe node, removes phase
Outside adjacent subsurface main rope node, connected by cable elements according to topological relation between other rope net nodes, obtain subsurface rope net and
The long L of the total rope of subsurface rope net0, the sum of two main ropes of the total Suo Changwei of subsurface rope net and whole cable elements length;
S4:Subsurface main rope node is considered as stationary nodes, the fringe node of subsurface and subsurface internal node are regarded
For moveable free node.For a certain free node i, the topological relation with surroundings nodes is as shown in figure 4, each at its
In minor node coordinate modification, according to each cable elements and standard cable elements length lsBetween gap correct node i node coordinate, section
The position correction amounts of point i along the x-axis direction are represented by:
Wherein, xi,xjFor node i and the x-axis coordinate of coupled node j, lijFor connecting node i's and node j
Cable elements length, by the position correction amount composition of vector matrix Δ x of all free nodes along the x-axis direction, then revised freedom
The x-axis coordinate of node is
The y-axis coordinate that revised free node can similarly be obtained is
For the fringe node of subsurface, following restriction relation is also needed to meet:
The z-axis coordinate of revised free node meets following formula:
The node coordinate that revised free node can be obtained above isObtain revised subsurface
Rope net and the long L of the total rope of subsurface rope net1;
S5:The long L of the total rope of subsurface rope net that judgment step S3 is obtained0The long L of the total rope of subsurface rope net obtained with step S41
Difference, if more than the threshold value L of settingtol, then with the node coordinate of the obtained revised free nodes of step S4For initial coordinate, iteration executes the node coordinate that step S4 corrects free node, until difference is less than convergence threshold
Value;If satisfied, the node coordinate of free node isS6 is thened follow the steps, node coordinate iterative process is as schemed
Shown in 5;
S6:The subsurface rope net that step S5 is obtained rotates the angles of π/3 around paraboloid of revolution central shaft (i.e. Z axis), generates
Entire reflecting surface rope net.
To better illustrate the advantage and validity of the present invention, retouched below by one embodiment and in conjunction with attached drawing
It states.
Embodiment:
Select the reflecting surface of bore D=10m, focal length f=5m to implement example, main rope is divided into 10 sections, quasi- survey is respectively adopted
Ground collimation method and method proposed by the present invention generate reflecting surface rope net, as shown in Figure 6 and Figure 7.The rope that table 1 is generated by two methods
Network parameters compare two methods, and the rope net that the present invention generates is either in the total rope length of grid, cable elements uniformity or reflecting surface
Precision δrmsEtc. in terms of parameters, the quasi- geodesic method being superior in document.Further it is proposed that method without complicated several
What relation derivation, generating process are more simple.
Table 1 generates the comparison of rope network parameters
Note:Quasi- geodesic method bibliography (Shi, Hang, Sichen Yuan, and Bingen Yang. " New
Methodology of Surface Mesh Geometry Design for Deployable Mesh Reflectors."
Journal of Spacecraft and Rockets(2017):1-16.)
Finally it should be noted that:The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations;To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, it will be understood by those of ordinary skill in the art that:Its according to
So can with technical scheme described in the above embodiments is modified, either to which part or all technical features into
Row equivalent replacement;And these modifications or replacements, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (4)
1. the simple and easy method that a kind of rope net antenna reflective face rope net generates, it is characterised in that have following steps:
S1:It is generated according to the bore D of the paraboloid of revolution and focal length f and refers to spherical surface, with reference to the vertex of spherical surface and bore circle and rotation
Paraboloidal vertex and bore circle overlap;
S2:By six mistakes with reference to the main rope on the vertex of spherical surface, it will be divided into six duplicate subsurfaces with reference to spherical surface, take
Two main ropes of its both sides are angularly divided equally, obtain subsurface main rope node, wherein angularly put down by one of subsurface
That divides divides angle, θ equallysAnd its corresponding chord length lsBy the type face precision δ of reflecting surface rope netrmsIt determines, wherein enable lsFor standard Suo Dan
First length;
S3:Based on obtained subsurface main rope node, using three-way grid formula node topology relationship on the perspective plane of subsurface
Then interior grid division is projected using the projection normal direction paraboloid of revolution, generates the initial coordinate C of one group of rope net node0=[x0 y0
z0], rope net node includes subsurface main rope node, subsurface internal node and subsurface fringe node, removes adjacent subsurface master
It outside socket point, is connected by cable elements according to topological relation between other rope net nodes, obtains subsurface rope net and subsurface rope net
The long L of total rope0, the sum of two main ropes of the total Suo Changwei of subsurface rope net and whole cable elements length;
S4:Subsurface main rope node is considered as stationary nodes, the fringe node of subsurface and subsurface internal node are considered as can
Mobile free node, according to each cable elements and standard cable elements length lsBetween gap generate free node coordinate modification position
Matrix is moved, and then generates the node coordinate of revised free node, obtains revised subsurface rope net and subsurface rope net
The long L of total rope1;
S5:The long L of the total rope of subsurface rope net that judgment step S3 is obtained0The long L of the total rope of subsurface rope net obtained with step S41Difference
Value, if more than the threshold value L of settingtol, then using the node coordinate of the obtained revised free nodes of step S4 as initial coordinate,
Iteration executes the node coordinate that step S4 corrects free node, until difference is less than convergence threshold;If satisfied, thening follow the steps
S6;
S6:The subsurface rope net that step S5 is obtained generates entire reflecting surface rope around the paraboloid of revolution center axis rotation angles of π/3
Net.
2. the simple and easy method that rope net antenna reflective face rope net according to claim 1 generates, it is characterised in that:The step
In S1, it is given by with reference to spherical radius:
3. the simple and easy method that rope net antenna reflective face rope net according to claim 1 generates, it is characterised in that:The step
In S2, the corresponding central angle of main rope is θ=arcsin (D/2R), divides angle, θ equallys=2arcsin (ls/ 2R), wherein wherein, R
To refer to spherical radius;
lsWith δrmsRelationship be:
The segments n that main rope is angularly divided equallyrFormula should be met:
The subsurface main rope node obtained on reference to spherical surface is projected on the paraboloid of revolution, to generate subsurface main rope section
Point.
4. the simple and easy method that rope net antenna reflective face rope net according to claim 1 generates, it is characterised in that:The step
In S4, for a certain free node i, during at it, node coordinate is corrected each time, according to each cable elements and standard cable elements length
lsBetween gap correct the node coordinate of node i, the position correction amount of node i along the x-axis direction is represented by:
Wherein, xi,xjFor node i and the x-axis coordinate of coupled node j, lijFor the cable elements of connecting node i and node j
Length, by the position correction amount composition of vector matrix Δ x of all free nodes along the x-axis direction, then the x of revised free node
Axial coordinate is
The y-axis coordinate that revised free node can similarly be obtained is
For the fringe node of subsurface, following restriction relation is also needed to meet:
The z-axis coordinate of revised free node meets following formula:
The node coordinate that revised free node can be obtained above is
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CN112531319A (en) * | 2020-11-30 | 2021-03-19 | 西北工业大学 | Construction method of multisection expansion arm of satellite-borne mesh antenna |
CN112927371A (en) * | 2021-03-03 | 2021-06-08 | 深圳市创想三维科技有限公司 | Image processing method, image processing device, computer equipment and storage medium |
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CN112531319A (en) * | 2020-11-30 | 2021-03-19 | 西北工业大学 | Construction method of multisection expansion arm of satellite-borne mesh antenna |
CN112927371A (en) * | 2021-03-03 | 2021-06-08 | 深圳市创想三维科技有限公司 | Image processing method, image processing device, computer equipment and storage medium |
CN114970254A (en) * | 2022-05-16 | 2022-08-30 | 西安电子科技大学 | Cable net antenna profile precision adjusting method based on key cable selection criterion |
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