CN108090306A - A kind of deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain - Google Patents
A kind of deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain Download PDFInfo
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Abstract
The invention discloses a kind of deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain, including：Determine the position and number of dual reflector antenna interarea, minor face and back frame structure parameter, working frequency and material properties and strain transducer distribution；It extracts the measured value of strain transducer in antenna minor face and establishes the finite element model of antenna；Determine the node at antenna minor face target point and its corresponding Mode Shape matrix；Determine the node in antenna minor face at strain transducer and its corresponding strain mode vibration shape matrix；Calculate the generalized Modal coordinate of dual reflector antenna；Calculate the modal displacement of antenna minor face target point；According to the modal displacement of antenna minor face target point, the ideal position of combining target point calculates the deformed position of antenna minor face target point, so as to which quick reconfiguration goes out deformed aerial minor face pattern.The present invention can fast and effeciently reconstruct deformed aerial minor face pattern, be conducive to the index request that dual reflector antenna meets electrical property.
Description
Technical field
The invention belongs to antenna technical fields, and in particular to the deformed aerial minor face pattern based on minor face structural strain is quick
Reconstructing method.The present invention can be used for, in the case where dual reflector antenna minor face generates strain, fast and effeciently calculating antenna
The displacement of minor face target point, and then minor face pattern after deformation is reconstructed, be conducive to the index that dual reflector antenna meets electrical property
It is required that it is optimal Antenna Operation performance.
Background technology
As large-scale antenna is increasingly applied in astronomical observation, Satellite Tracking and is communicated etc., double-reflecting face day
The bore of line, frequency range are also being constantly increasing, this brings many challenges to the structure design of antenna, will to the electrical property of antenna
Ask also higher and higher.
Dual reflector antenna is due to being chronically exposed in natural environment, and minor face is easily conducted oneself with dignity and wind, sleet, too
The influence of the environmental factors such as sun irradiation, these can all make antenna minor face generate strain, minor face pattern is caused to change, and then is made
The electrical performance indexes of antenna deteriorate.Thus, it quick and precisely calculates dual reflector antenna minor face and generates minor face pattern after strain, be
Ensure that dual reflector antenna meets the key of its electrical performance indexes requirement, be conducive to Antenna Operation performance and be optimal.
At present, the related academic research in relation to dual reflector antenna subreflector is mainly the position by adjusting subreflector
Posture is put to ensure that the high performance requirements for meeting antenna, such as Yao build great waves, Zeng Daxing, Hou Yulei wait large-scale radio telescopes day
Line subreflector adjusts system design and experimental study [J] manned space flights, 2016 (1):69-73 looks in the distance to meet large-scale radio
During mirror antenna movement caused by gravity deformation antenna performance variation, determine and optimize " 65 meters of Shanghai radio
The configuration of telescopic system " antenna subreflector adjustment mechanism.Minor face compensation of the Bai Yaojun based on large aperture antenna malformation
Research [D] the Xian Electronics Science and Technology University of method, using the geometrical relationship between major-minor reflecting surface in 2013., by calculating
Subreflector adjustment amount is come the electrical loss of energy caused by compensating when primary reflection surface deforms.But these all do not account for it is double anti-
It penetrates surface antenna minor face and causes the changed situation of minor face pattern due to military service load acts on and generates strain, so as to directly or indirectly
On cause inaccuracy to antenna electric performance index compensation.
Therefore, when being compensated to dual reflector antenna working performance, it is necessary to take into account generate the feelings of strain in minor face
The displacement of antenna minor face target point under condition, and then quick reconfiguration goes out minor face pattern after deformation, is conducive to improve to double-reflecting face day
The accuracy that line electrical property compensates is optimal Antenna Operation performance.
The content of the invention
It, should based on minor face structure it is an object of the invention to provide one kind to solve drawbacks described above in the prior art
The deformed aerial minor face pattern method for fast reconstruction of change, in the case where dual reflector antenna minor face generates strain, quickly and effectively
Ground calculates the displacement of antenna minor face target point, and then quick reconfiguration goes out minor face pattern after deformation, is conducive to dual reflector antenna
Meet the index request of electrical property, be optimal Antenna Operation performance.
To achieve these goals, the deformed aerial minor face pattern provided by the invention based on minor face structural strain quickly weighs
Structure method, includes the following steps：
(1) determine dual reflector antenna interarea, minor face and backrest etc. structural parameters, working frequency and material properties and
The position of strain transducer distribution and number；
(2) strain transducer measured value in antenna minor face is extracted, and the dual reflector antenna is established in ANSYS softwares
Finite element model；
(3) antenna minor face destination node and its corresponding Mode Shape matrix are determined according to finite element model；
(4) determine that node in antenna minor face at strain transducer and its corresponding strain mode are shaken according to finite element model
Type matrix；
(5) strain transducer in antenna minor face in strain transducer measured value and step (4) in (2) according to the step of obtaining
Locate the corresponding strain mode vibration shape matrix of node, calculate the generalized Modal coordinate of dual reflector antenna；
(6) the antenna pair in the generalized Modal coordinate of dual reflector antenna minor face and step (3) in (5) according to the step of obtaining
The corresponding Mode Shape matrix of appearance punctuation node calculates the displacement of antenna minor face target point；
(7) displacement of antenna minor face destination node in the step of basis obtains (6), with reference to the ideal position of tie point, meter
The deformed position of antenna minor face destination node is calculated, so as to the minor face pattern of quick reconfiguration deformed aerial.
The scheme that the present invention further limits includes：
The structural parameters of the dual reflector antenna include reflecting surface bore, the structural unit arrangement situation of minor face；It is described
The material properties of dual reflector antenna include interarea, the density of minor face and backrest material, elasticity modulus and Poisson's ratio.
In the step (2), strain transducer measured value is { ε }={ ε in antenna minor face1,ε2,...,εn}。
Antenna minor face destination node and its corresponding Mode Shape square are determined according to finite element model in the step (3)
Battle array, comprises the following steps：
(3a) carries out finite element analysis, N (N=n) rank Mode Shape before extraction in ANSYS softwares to finite element model
βj, wherein 1≤j≤N：
In formula, S is total node number of the finite element model；
(3b) determines m target point of antenna minor face, is respectively p1,p2,...,pm, extracted successively from N number of Mode Shape
This corresponding value of m node, and combine and form this corresponding Mode Shape matrix { β } of m antenna minor face destination nodem：
Node in antenna minor face at strain transducer and its corresponding is determined according to finite element model in the step (4)
Strain mode vibration shape matrix, comprises the following steps：
(4a) carries out finite element analysis in ANSYS softwares to finite element model, and N (N=n) rank strain mode is shaken before extraction
Type γj：
In formula, S is total node number of the finite element model；
(4b) determines in antenna minor face corresponding n node at strain transducer, is respectively q1,q2,...,qn, successively from N
This corresponding value of n node is extracted in a strain mode vibration shape, and combines to be formed in this n antenna minor face and be saved at strain transducer
The corresponding strain mode vibration shape matrix { γ } of pointn：
The generalized Modal coordinate of dual reflector antenna is calculated in the step (5), is comprised the following steps：
The n antenna obtained in the strain value { ε } and step (4) that are measured according to the strain transducer obtained in step (2)
The corresponding strain mode vibration shape matrix { γ } of node at strain transducer in minor facen, the generalized Modal coordinate { r } of antenna can be obtained
={ r1,r2,…,rN}：
{ r }=(({ γ }n)T({γ}n))-1({γ}n)T{ε} (1)。
The displacement of antenna minor face target point is calculated in the step (6), is comprised the following steps：
According to antenna minor face mesh in the generalized Modal coordinate { r } of dual reflector antenna in (5) the step of obtaining and step (3)
The corresponding Mode Shape matrix { β } of node at punctuatem, displacement { χ }={ χ of antenna minor face target point can be obtained1,χ2,…,
χi,…,χm},1≤i≤m：
{ χ }={ β }m{r} (2)。
The step (7) comprises the following steps：
(7a) assumes that the ideal position of m target point in minor face is (xi,yi,zi), and according to day in (6) the step of obtaining
Displacement { χ }={ χ of line minor face destination node1,χ2,…,χi,…,χm, 1≤i≤m obtains deformed position after vector addition
Put (xi',yi',zi')；
(7b) according to the position coordinates of target point after obtained deformation, using the griddata interpolating functions in MATLAB into
Row interpolation calculates, so as to obtain reconstructing deformed aerial minor face pattern.
Compared with prior art, the present invention it has the characteristics that：
1. in research gravity and external environment load when causing malformation to dual reflector antenna, with other invention phases
Consider wherein, the shadow that antenna minor face structural strain generates minor face pattern can be eliminated than the strain that the present invention generates antenna minor face
It rings, the accuracy of antenna electric performance index compensation can be improved.
2. the present invention can quickly calculate the displacement of antenna minor face target point using seldom strain transducer, without big
The factors such as scale modeling analysis gravity and external environment load to antenna arrange structure influence, have it is at low cost, method is simple
And calculating cycle it is short the advantages of.
Description of the drawings
Fig. 1 is the flow chart of the deformed aerial minor face pattern method for fast reconstruction the present invention is based on minor face structural strain；
Fig. 2 is the ANSYS Whole structure model figures of the dual reflector antenna；
Fig. 3 is the ANSYS minor face structural model figures of the dual reflector antenna；
Fig. 4 is the distributing position figure of strain transducer in the dual reflector antenna minor face；
Fig. 5 is the distributing position figure of the dual reflector antenna minor face target point；
Fig. 6 is dual reflector antenna deformation minor face pattern reconstruct image.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawings and examples, but is not intended as appointing the present invention
The foundation of what limitation.
With reference to Fig. 1, the present invention is the deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain, specific to walk
It is rapid as follows：
Step 1, structural parameters, working frequency and the material properties of dual reflector antenna interarea, minor face and backrest etc. are determined,
And position and the number of strain transducer distribution.
The structural parameters of the dual reflector antenna include reflecting surface bore, the structural unit arrangement situation of minor face；It is described
The material properties of dual reflector antenna include interarea, the density of minor face and backrest material, elasticity modulus and Poisson's ratio etc..
Determine the position of strain transducer distribution and number n.
Step 2, the strain value of strain transducer measurement in antenna minor face is extracted, and this pair is established instead in ANSYS softwares
Penetrate the finite element model of surface antenna.
Strain transducer measured value is { ε }={ ε in antenna minor face1,ε2,...,εn}。
Step 3, antenna minor face destination node and its corresponding Mode Shape matrix are determined.
3.1. finite element analysis, N (N=n) rank Mode Shape before extraction are carried out to finite element model in ANSYS softwares
βj, wherein 1≤j≤N：
In formula, S is total node number of the finite element model；
3.2. determine m target point of antenna minor face, be respectively p1,p2,...,pm, extracted successively from N number of Mode Shape
This corresponding value of m node, and combine and form this corresponding Mode Shape matrix { β } of m antenna minor face destination nodem：
Step 4, the node in antenna minor face at strain transducer and its corresponding strain mode vibration shape matrix are determined.
4.1. finite element analysis, N (N=n) the rank strain mode vibration shape before extraction are carried out to structural model in ANSYS softwares
γj：
In formula, S is total node number of the finite element model；
4.2. corresponding n node, respectively q at strain transducer are determined in antenna minor face1,q2,...,qn, successively from N
This corresponding value of n node is extracted in a strain mode vibration shape, and combines to be formed in this n antenna minor face and be saved at strain transducer
The corresponding strain mode vibration shape matrix { γ } of pointn：
Step 5, the generalized Modal coordinate of dual reflector antenna is calculated.
The n antenna minor face obtained in the strain value { ε } and step 4 that are measured according to the strain transducer obtained in step 2
The corresponding strain mode vibration shape matrix { γ } of node at upper strain transducern, can be obtained the generalized Modal coordinate { r } of antenna=
{r1,r2,…,rN}：
{ r }=(({ γ }n)T({γ}n))-1({γ}n)T{ε} (1)
Step 6, the displacement of antenna minor face target point is calculated.
According to antenna minor face target point in the generalized Modal coordinate { r } of dual reflector antenna in obtained step 5 and step 3
The corresponding Mode Shape matrix { β } of nodem, displacement { χ }={ χ of antenna minor face target point can be obtained1,χ2,…,χi,…,χm},1
≤i≤m：
{ χ }={ β }m{r} (2)
Step 7, the deformed position of antenna minor face destination node, the minor face pattern of quick reconfiguration deformed aerial are calculated.
7.1. the ideal position for assuming m target point in minor face is (xi,yi,zi), and according to antenna in obtained step 6
Displacement { χ }={ χ of minor face destination node1,χ2,…,χi,…,χm, 1≤i≤m obtains deformed position after vector addition
(xi',yi',zi')；
7.2. according to the position coordinates of target point after obtained deformation, using the griddata interpolating functions in MATLAB into
Row interpolation calculates, so as to obtain reconstructing deformed aerial minor face pattern.
Advantages of the present invention can be further illustrated by following emulation experiment：
1st, structural parameters, working frequency and the material properties of dual reflector antenna and the position of strain transducer distribution are determined
It puts and number, and establishes ANSYS models.
In the present embodiment, instance analysis, center operating frequency f=115GHz are carried out with 110 meters of dual reflector antennas.
Respectively as shown in Figure 2,3, minor face uses shell unit, cell type shell63 for ANSYS Whole structure models and minor face model,
Thickness is 40mm, elasticity modulus 2E+05MPa, Poisson's ratio 0.3, density 7.8e+03kg/m3.It strains and passes in antenna minor face
The distributing position of sensor is as shown in figure 4, node coordinate is as shown in table 1.
Node coordinate at 1 strain transducer position of table
2nd, the modal displacement at antenna minor face target point is calculated
The distributing positions of 2.1 antenna minor face target points is soft using ANSYS as shown in figure 5, its node coordinate is as shown in table 2
Part carries out free mesh and model analysis, and determines its corresponding preceding 8 rank Mode Shape matrix according to step (3).
Node coordinate at 2 antenna minor face target point of table
2.2 antenna model in ANSYS softwares ideally, which is in, refers to level state, to its structural finite element model
Apply gravitational load, antenna is only as shown in table 3 by the strain value that strain transducer measures in antenna minor face during gravitational load, and root
Its corresponding preceding 8 rank strain mode vibration shape matrix is determined according to step (4).
2.3, according to formula (1) and step (5), obtain generalized Modal coordinate, as shown in table 4.
2.4 according to formula (2) and step (6), calculates the modal displacement of antenna minor face target point, as shown in table 5.By table 5
It understands, the deformation of the lower minor face target point of gravitational load effect in the Y direction is more than it in the deformation of X-direction, Z-direction, and Y-direction is most
Aximal deformation value reaches -168.7239mm.
The strain value of 3 strain transducer of table measurement
4 generalized Modal coordinate of table
5 antenna minor face target point displacement of table
3rd, reconstruct deformation aft antenna minor face pattern
According to step (7), calculate the deformed position of antenna minor face, and using MATLAB griddata interpolating functions into
Row interpolation calculates, and reconstructs deformed aerial minor face pattern as shown in fig. 6, so as to obtain any point in deformation aft antenna minor face
Position coordinates.
4th, analysis result
Above-mentioned experiment can be seen that can have using the present invention by arranging a small amount of strain transducer in antenna minor face
Effect ground calculates the modal displacement of antenna minor face target point, and then quick reconfiguration goes out to deform aft antenna minor face pattern, is conducive to instruct
The malformation compensation of dual reflector antenna and electrical property compensation, make it meet the index request of electrical property, have important
Art meaning and engineering application value.
Claims (8)
1. the deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain, which is characterized in that include the following steps：
(1) structural parameters, working frequency and the material properties and strain for determining dual reflector antenna interarea, minor face and backrest pass
The position of sensor distribution and number；
(2) strain transducer measured value in antenna minor face is extracted, and the limited of the dual reflector antenna is established in ANSYS softwares
Meta-model；
(3) antenna minor face destination node and its corresponding Mode Shape matrix are determined according to finite element model；
(4) node in antenna minor face at strain transducer and its corresponding strain mode vibration shape square are determined according to finite element model
Battle array；
(5) saved according to the step of obtaining in (2) in strain transducer measured value and step (4) in antenna minor face at strain transducer
The corresponding strain mode vibration shape matrix of point calculates the generalized Modal coordinate of dual reflector antenna；
(6) the antenna minor face mesh in the generalized Modal coordinate of dual reflector antenna minor face and step (3) in (5) according to the step of obtaining
The corresponding Mode Shape matrix of punctuation node calculates the displacement of antenna minor face target point；
(7) displacement of antenna minor face destination node in the step of basis obtains (6) with reference to the ideal position of tie point, calculates day
The deformed position of line minor face destination node, so as to the minor face pattern of quick reconfiguration deformed aerial.
2. the deformed aerial minor face pattern method for fast reconstruction according to claim 1 based on minor face structural strain, special
Sign is that the structural parameters of the dual reflector antenna include reflecting surface bore, the structural unit arrangement situation of minor face；It is described double
The material properties of reflector antenna include interarea, the density of minor face and backrest material, elasticity modulus and Poisson's ratio.
3. the deformed aerial minor face pattern method for fast reconstruction according to claim 1 based on minor face structural strain, special
Sign is, in step (2), strain transducer measured value is { ε }={ ε in antenna minor face1,ε2,…,εn}。
4. the deformed aerial minor face pattern method for fast reconstruction according to claim 1 based on minor face structural strain, special
Sign is that step (3) carries out according to the following procedure：
(3a) carries out finite element analysis, N ranks Mode Shape β before extraction in ANSYS softwares to finite element modelj, wherein, 1≤j
≤ N, N=n：
<mrow>
<msub>
<mi>&beta;</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mi>j</mi>
<mn>1</mn>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mi>j</mi>
<mn>2</mn>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&beta;</mi>
<mi>j</mi>
<mi>S</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
In formula, S is total node number of the finite element model；
(3b) determines m target point of antenna minor face, is respectively p1,p2,…,pm, this m are extracted from N number of Mode Shape successively
The corresponding value of node, and combine and form this corresponding Mode Shape matrix { β } of m antenna minor face destination nodem：
5. the deformed aerial minor face pattern method for fast reconstruction according to claim 1 based on minor face structural strain, special
Sign is that step (4) carries out according to the following procedure：
(4a) carries out finite element analysis, N ranks strain mode vibration shape γ before extraction in ANSYS softwares to finite element modelj, wherein,
N=n：
<mrow>
<msub>
<mi>&gamma;</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>&gamma;</mi>
<mi>j</mi>
<mn>1</mn>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&gamma;</mi>
<mi>j</mi>
<mn>2</mn>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&gamma;</mi>
<mi>j</mi>
<mi>S</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
In formula, S is total node number of the finite element model；
(4b) determines in antenna minor face corresponding n node at strain transducer, is respectively q1,q2,…,qn, answered successively from N number of
Become in Mode Shape and extract this corresponding value of n node, and combination forms in this n antenna minor face node pair at strain transducer
The strain mode vibration shape matrix { γ } answeredn：
6. the deformed aerial minor face pattern method for fast reconstruction according to claim 1 based on minor face structural strain, special
Sign is, step (5), according to the strain value { ε } that the strain transducer obtained in step (2) measures and the n that is obtained in step (4)
The corresponding strain mode vibration shape matrix { γ } of node at strain transducer in a antenna minor facen, the generalized Modal of antenna can be obtained
Coordinate { r }={ r1,r2,…,rN}：
{ r }=(({ γ }n)T({γ}n))-1({γ}n)T{ε} (1)。
7. the deformed aerial minor face pattern method for fast reconstruction according to claim 6 based on minor face structural strain, special
Sign is that step (6) carries out according to the following procedure：
According to antenna minor face target point in the generalized Modal coordinate { r } of dual reflector antenna in (5) the step of obtaining and step (3)
Locate the corresponding Mode Shape matrix { β } of nodem, displacement { χ }={ χ of antenna minor face target point can be obtained1,χ2,…,χi,…,
χm},1≤i≤m：
{ χ }={ β }m{r} (2)。
8. the deformed aerial minor face pattern method for fast reconstruction according to claim 1 based on minor face structural strain, special
Sign is that step (7) carries out according to the following procedure：
(7a) assumes that the ideal position of m target point in minor face is (xi,yi,zi), and according to antenna pair in (6) the step of obtaining
Displacement { χ }={ χ of Area Objects node1,χ2,…,χi,…,χm, 1≤i≤m obtains deformed position after vector addition
(xi',yi',zi')；
(7b) is inserted according to the position coordinates of target point after obtained deformation using the griddata interpolating functions in MATLAB
Value calculates, so as to obtain reconstructing deformed aerial minor face pattern.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109543227A (en) * | 2018-10-22 | 2019-03-29 | 西安电子科技大学 | Charming appearance and behaviour error in pointing method for real-time measurement, the radar antenna of large-scale reflector antenna |
| CN109506582A (en) * | 2018-12-11 | 2019-03-22 | 上海航天控制技术研究所 | A kind of three-dimensional configuration inversion method based on optical measurement |
| CN109737886A (en) * | 2019-02-28 | 2019-05-10 | 重庆邮电大学 | A kind of array photoelectric system for the reflecting surface connection point deformation measuring radio telescope primary antenna |
| CN114065580A (en) * | 2021-11-15 | 2022-02-18 | 西安电子科技大学 | Active phased array antenna array plane reconstruction method based on least square method |
| CN114065580B (en) * | 2021-11-15 | 2022-09-13 | 西安电子科技大学 | Active phased array antenna array plane reconstruction method based on least square method |
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