CN102968532B  The dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore  Google Patents
The dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore Download PDFInfo
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 CN102968532B CN102968532B CN201210466403.6A CN201210466403A CN102968532B CN 102968532 B CN102968532 B CN 102968532B CN 201210466403 A CN201210466403 A CN 201210466403A CN 102968532 B CN102968532 B CN 102968532B
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Abstract
The invention discloses a kind of dynamoelectric integral design method of 65 meters of largescale reflector antennas, mainly solve problem dynamoelectric integrated in largescale antenna design.The steps include: based on antenna structure finite element analysis, obtain distorted reflector posterior nodal point displacement information; According to coordinate spatial relation after node Theoretical Design coordinate and distortion, calculate theoretical coordinate and the displacement of triangular element center of mass point; Phase error on the optical path difference of computational reflect face triangular element center of mass point and corresponding bore face thereof; By cell projection on bore face, calculate far field Electric Field Distribution, obtain unit for electrical property parameters; With antenna structure parameter for design variable, antenna electric performance parameter optimum is target, sets up Optimized model; Adopt Sequential Quadratic Programming method solvingoptimizing model, obtain optimum mechanical electromagnetic comprehensive Design scheme, realize the dynamoelectric Integrated design of reflector antenna.The present invention can be used for instructing the structural design of largescale reflector antenna and to the antenna electrical and mechanical comprehensive performance analysis and evaluation under different operating mode.
Description
Technical field
The invention belongs to antenna technical field, specifically the dynamoelectric integral design method of the largescale reflector antenna structure of a kind of 65m bore, is used to guide the structural design of 65m bore largescale antenna, make its mechanical property and electrical property allround excellent.
Background technology
Along with the development of radar communication, survey of deep space and radio astronomy cause, reflector antenna is to high band, bigbore future development.Largescale reflector antenna is typical electromechanical integration equipment, and its mechanical property and electrical property influence each other, mutually restrict.In engineering, Electrical Engineer proposes Design of Mechanical Structure requirement, and structural engineer can only distribute the design accuracy of each building block by rule of thumb.There are two kinds of situations in result, one is that the latter has used up all ways, used best process equipment and means, still cannot meet the demands; Two is in actual production, and what manufacturing accuracy was high not can meet electrical performance indexes, and some manufacturing accuracy so not high instead can meet electrical performance indexes.Result causes antenna manufacturing cost high, and the lead time is long, and its performance cannot fundamentally ensure.
Due to largescale reflector antenna design, manufacture and testing expense very high, therefore require that its design should oneshot forming.But reaching tens meters because of the bore of largescale antenna, its weight reaches kiloton on hundreds of, brings great difficulty to structural design; Deform because this largescale antenna structure is fairly subject to external environment condition effect simultaneously, antenna electric performance is affected.As malformation makes antenna gain decline, minor level rising etc.When the operating frequency of antenna of high band reaches Ka frequency range, antenna structure distortion on the impact of antenna electric performance by even more serious.Due to the quantitative relationship between structural parameters and electromagnetic parameter cannot be determined in existing reflector antenna designing technique, cause during Antenna Construction Design, certainly existing the dynamoelectric problem be separated.
At present, the method solving the dynamoelectric separate design problem of antenna both at home and abroad the most frequently used has several as follows:
(1) carry out integrated analysis from comprehensive angle to antenna, by the thought of Optimization Modeling, the designing requirement of the subjects such as each machinery, electromagnetism is carried out unifying to consider, this method considers the benefit of electrical and mechanical comprehensive design.As Liu Jingsheng etc. the method that adopts be exactly this comprehensive optimization method.But it is how to affect antenna electric performance that the method does not fundamentally analyze antenna structure distortion, namely the scheme providing under electrical performance indexes prerequisite and reduce structural design difficulty can not met.
(2) antennareflected facial disfigurement distribution function is utilized, obtain the contribution of each node to antenna far field electric field, thus the antenna electric performance situation of change analyzed in different distortion situation, as at K.Bahadori, Y.Rahmatsamii.Characterization ofeffects of periodic and aperiodic surface distortions on membrane reflector antennas.IEEE Trans.Antennas and Propagation, VOL.53, the method adopted in NO.9, September 2005 is exactly this method.The method is only that hypothesis distorted reflector meets certain trigonometric function distribution, but in reality, malformation is difficult to provide with a certain concrete function.The electromechanical properties of the method are comprehensively analyzed simultaneously is be based upon on the basis of malformation shape hypothesis, can not reflect the true impact relation between antenna structure distortion and antenna electric performance.
(3) measurement point on the antenna deformation curved surface in Practical Project is adopted, and as calculating object after theoretical node simulation analysis distortion, analyze antenna deformation to the impact of antenna electric performance, as just adopted in this way in " modern radar " the 1st phase in 1994 " a kind of approximating method of antenna deformation curved surface " (Hua Mulin) document.The method engineer applied is worth large, but key is the antenna that will have actual processing, assemble, and need carry out Measurement and analysis on antenna material object.The antenna electric performance of general Antenna Construction Design personnel under the design of Simulation stage needs to know current structure, and judge whether accordingly need change or redesign antenna structure, and can not determine at antenna structure, reflecting surface shapes, assemble also in completed situation, then analyzes mechanical property and the electrical property of antenna.
Summary of the invention
The object of the invention is the deficiency avoiding abovementioned art methods, for certain 65 meters of largescale reflector antenna of bore, a kind of dynamoelectric integral design method of antenna structure is proposed, instruct the Electromechanical Design of the largescale reflector antenna structure of 65m bore, to reduce design cost, the machinery improving antenna and electromagnetism combination property.
The technical scheme realizing the object of the invention is, based on the largescale reflector antenna structural finite element analysis of 65m bore, obtain the nodal displacement after distorted reflector, according to Theoretical Design coordinate and the distortion recoil target spatial relation of reflecting surface node, the aperture field phase error that computational reflect face nodal displacement causes, and calculate antenna far field Electric Field Distribution on this basis, draw the directional diagram of antenna far field electric field, obtain antenna gain, minor level and beam angle, with antenna structure size, the parameters such as shape and topology are design variable, antenna electric performance parameter optimum is target, set up Optimized model, dynamoelectric Integrated design is carried out to antenna structure.Detailed process is as follows:
(1) according to the largescale reflector antenna structure of 65m bore and form parameter, determine antenna structure finite element model, obtain reflecting surface triangular element, and the theoretical coordinate of triangular element node
with
${P}_{n,3}({x}_{n,3}^{P},{y}_{n,3}^{P},{z}_{n,3}^{P});$
(2) utilize structural finite element analysis software, static analysis is carried out to the largescale reflector antenna structural finite element model of 65m bore, the displacement of each triangular element node after obtaining distorted reflector
with
(3) each triangular element of the largescale reflector antenna of 65m bore obtained according to structural finite element analysis software and the corresponding relation of node thereof, calculate the theoretical coordinate of each triangular element center of mass point
and displacement
$\mathrm{\ΔM}({\mathrm{\Δx}}_{n}^{M},{\mathrm{\Δy}}_{n}^{M},{\mathrm{\Δz}}_{n}^{M});$
(4) 2, space distance computing formula is utilized, each triangular element barycenter node after obtaining distorted reflector
optical path difference ε
_{n}, and calculate the phase error δ that each triangular element barycenter nodal displacement causes in bore face
_{n};
(5) 65m bore largescale reflector antenna bore face field distribution of amplitudes Q (ρ) is determined, the phase error δ caused in bore face according to each triangular element barycenter nodal displacement
_{n}, by antenna far field Electric Field Distribution function, calculate antenna electric performance parameter;
(6) with size, shape and topological parameter in antenna structure for design variable, optimum for target with antenna electric performance parameter, setting up optimized mathematical model, obtaining mechanical property and the allround excellent largescale reflector antenna organization plan of 65m bore of electrical property by solving this model;
Described step (4) is carried out according to the following procedure:
(4a) set the coordinate of feed phase center as F (x
_{f}, y
_{f}, z
_{f}), before distortion, feed is to reflecting surface nth triangular element center of mass point
light path
for:
(4b) the nth triangular element center of mass point after feed to distorted reflector
light path d
_{n}for:
In formula,
for the deflection of the nth triangular element center of mass point in x direction after feed to distorted reflector under Oxyz coordinate,
for the deflection of the nth triangular element center of mass point in y direction after feed to distorted reflector under Oxyz coordinate,
for the deflection of the nth triangular element center of mass point in z direction after feed to distorted reflector under Oxyz coordinate;
(4c) by (4a) and (4b) obtain electromagnetic wave before and after distorted reflector arrive the nth triangular element center of mass point the optical path difference ε of process
_{n}for:
(4d) electromagnetic wave of feed radiation is parallel to focal axis after reflective surface, and by (4a), (4b) and (4c) obtain the phase error δ of the nth triangular element that the displacement of units centre of mass point causes in bore face
_{n}for:
In formula, k=2 π/λ is propagation constant, and λ is wavelength;
Described step (5) is carried out according to the following procedure:
(5a) obtaining antenna aperture field distribution of amplitudes Q (ρ) according to following formula is:
In formula, B and C is edge taper pin parameter, and B+C=1, P are Aperture field distribution parameter, and a is reflector antenna radius;
(5b) by reflecting surface cell projection on bore face, the phase error δ of each units centre of mass point
_{n}as the phase error in this cell projection territory;
(5c) according to Heron's formula, with
with
the nth triangular element for apex coordinate projects the area Δ s of deltashaped region on bore face
_{n}' be:
In formula,
${l}_{n,1}=\sqrt{{({x}_{n,2}^{P}{x}_{n,1}^{P})}^{2}+{({y}_{n,2}^{P}{y}_{n,1}^{P})}^{2}},$ ${l}_{n,2}=\sqrt{{({x}_{n,3}^{P}{x}_{n,2}^{P})}^{2}+{({y}_{n,3}^{P}{y}_{n,2}^{P})}^{2}},$ ${l}_{n,3}=\sqrt{{({x}_{n,1}^{P}{x}_{n,3}^{P})}^{2}+{({y}_{n,1}^{P}{y}_{n,3}^{P})}^{2}}$ Three length of sides of projected triangle respectively,
$p=\frac{{l}_{n,1}+{l}_{n,2}+{l}_{n,3}}{2}$ It is intermediate variable;
(5d) according to abovementioned aperture field distribution of amplitudes and phase distribution parameters, by following formulae discovery antenna far field Electric Field Distribution E be:
In formula,
for aperture field sampling point vector;
for aperture field sampled point radius; Q (n)=Q (ρ
_{n}) be Aperture field distribution parameter;
for far field observation point is to the distance vector of initial point; N is triangular element sum;
(5e) by antenna far field Electric Field Distribution function, antenna electric performance parameter is calculated according to antenna far field Electric Field Distribution.
Described step (5e) calculates antenna electric performance parameter according to antenna far field Electric Field Distribution, draws antenna far field direction of an electric field figure, obtains the gain G of antenna, minor level SLL and beam angle θ from the direction of an electric field figure of antenna far field;
Described step (6) is carried out according to the following procedure:
(6a) set up the dynamoelectric Integrated Optimization Model of the largescale reflector antenna structure of following 65m bore and calculate optimal structural design parameter:
Find:A,Z,m
_{a}
s.t.:W≤W
_{0}
j＝1,2,....,NE
s＝1,2,...,NS
In formula, A=(A
_{i}), (i=1,2 ..., NA) for prototype structure backrest cell crosssection amass, Z=(Z
_{i}), (i=1,2 ..., NZ) be back frame structure lowerchord panel point longitudinal coordinate value, m
_{a}for the counterweight of unit area on pitching gear, Δ G
_{s}be the gain loss under s operating mode, α
_{s}for the weights of this operating mode, W is general assembly (TW), W
_{0}for the quality upper limit, Z
_{p}for the position of entire physical center of gravity,
for the design height of elevation axis of antenna,
for the von Mises stress value of a jth unit under s operating mode,
for largest unit stress value under certain operating mode, NE is unit sum, and NS is operating mode sum;
(6b) Sequential Quadratic Programming method (SQPDONLP) is adopted to solve the dynamoelectric Integrated Optimization Model of the largescale reflector antenna structure of 65m bore, and utilize finite difference method to carry out the sensitivity of objective function and constraint function in calculation optimization model, judge whether the electrical parameters of antenna calculated meets the demands, if met the demands, Antenna Construction Design scheme is qualified; Otherwise, Amending design variatevalue, and repeat step (1) to step (6), until be met the structural design scheme of mechanical property and electrical performance indexes.
In step (1), antenna structure comprises centrosome, backrest and Reflector Panel size.
The theoretical coordinate of described step (1) triangular element node is
with
after step (2) distorted reflector, the displacement of each triangular element node is
with
the theoretical coordinate of each triangular element center of mass point of step (3) is
and displacement
after step (4) distorted reflector, each triangular element barycenter node is
in, n be greater than 1 natural number.
Described step (3) is carried out according to the following procedure:
(3a) three of the nth triangular element node coordinates are established to be respectively
with
obtain this triangular element center of mass point coordinate
(3b) three of this nth triangular element nodal displacements are established to be respectively
with
obtain this triangular element center of mass point displacement
$\mathrm{\ΔM}({\mathrm{\Δx}}_{n}^{M},{\mathrm{\Δy}}_{n}^{M},{\mathrm{\Δz}}_{n}^{M}):$
Compared with prior art, tool has the following advantages in the present invention:
1. utilize antenna feed phase center to the air line distance of reflecting surface triangular element center of mass point, before and after computational reflect facial disfigurement electromagnetic wave the optical path difference of process, thus the bore face phase error that accurate Calculation units centre of mass point is corresponding;
2. triangular element on reflecting surface is projected to bore face, each units centre of mass point phase error represents the phase place change of this unit, antenna far field Electric Field Distribution is calculated by integrating the aperture field, obtain electrical parameters of antenna, antenna structure parameter and electromagnetic parameter are closely connected, avoid and only use reflector precision to judge the deficiency of antenna performance, realize the electrical and mechanical comprehensive analysis of antenna;
3., by setting up and solvingoptimizing mathematical model, under the prerequisite meeting the constraint of certain mechanical property, obtaining the optimum electrical property of antenna, avoid and carry out Antenna Construction Design by rule of thumb, achieve the dynamoelectric Integrated design of 65m bore largescale reflector antenna structure.
Accompanying drawing explanation
Fig. 1 is the dynamoelectric Integrated design process flow diagram of the largescale reflector antenna of 65m bore of the present invention;
Fig. 2 is triangular element and node coordinate schematic diagram on reflecting surface of the present invention;
Fig. 3 is reflecting surface triangular element center of mass point of the present invention and projected area schematic diagram;
Fig. 4 is bore face of the present invention phase error schematic diagram;
Fig. 5 is reflector antenna unit for electrical property parameters calculation flow chart of the present invention;
Fig. 6 is 65m bore largescale reflector antenna geometric parameter schematic diagram;
Fig. 7 is the largescale reflector antenna finite element model of 65m bore;
Fig. 8 is antenna radiation pattern contrast before and after dynamoelectric integrated optimization under 20 ° of elevation angle operating modes;
Fig. 9 is antenna radiation pattern contrast before and after dynamoelectric integrated optimization under 70 ° of elevation angle operating modes.
Embodiment
Referring to accompanying drawing, the present invention is described in further detail.
With reference to Fig. 1, concrete steps of the present invention are as follows:
Step one, sets up the largescale reflector antenna finite element model of 65m bore.
According to given antenna aperture D, focal distance f, Reflector Panel, radiation beam, ring beam, centrosome basic parameter, determine antenna structure finite element model, and obtain reflecting surface triangular element under rectangular coordinate Oxyz, and the theoretical coordinate of triangular element node
with
n be greater than 1 natural number, as shown in Figure 2, wherein A is reflecting surface, and B is triangular element node, and C is triangular element, and determine the coordinate h of reflecting surface summit in model coordinate systems, the present invention takes Zdirection height simultaneously.
Step 2, carries out static analysis to antenna structure finite element model, obtains the cell node information after being out of shape.
Utilize structural finite element analysis software, under deadweight, wind lotus, temperature operating mode different from ice and snow load, static analysis is carried out to antennareflected body structure, the displacement of each triangular element node obtain distorted reflector under rectangular coordinate Oxyz after
with
Step 3, calculates triangular element center of mass point coordinate, displacement and cell projection area.
With reference to Fig. 3, wherein A is reflecting surface, and B is bore face, and C is reflecting surface triangular element, and D is bore face projected triangle, P
_{n, 1}, P
_{n, 2}, P
_{n, 3}be respectively three nodes of the nth triangular element, M is this triangular element center of mass point, P
_{n, 1}', P
_{n, 2}', P
_{n, 3}' three summits of respectively the nth projected triangle, l
_{n, 1}, l
_{n, 2}, l
_{n, 3}be respectively the length on three limits of the nth projected triangle, Δ s
_{n}' be the area of the nth triangular element in bore Mian Shang view field.The concrete steps of computational reflect face triangular element center of mass point coordinate and displacement are as follows:
1) three of the nth triangular element node coordinates are established to be respectively
with
obtain this triangular element center of mass point coordinate
2) three of the nth triangular element nodal displacements are established to be respectively
with
obtain this triangular element center of mass point displacement
$\mathrm{\ΔM}({\mathrm{\Δx}}_{n}^{M},{\mathrm{\Δy}}_{n}^{M},{\mathrm{\Δz}}_{n}^{M}):$
Step 4, calculates the phase error in bore face.
With reference to Fig. 4, under rectangular coordinate Oxyz, A is bore face, and F is feed phase center,
for feed before distorted reflector is to the light path of reflecting surface nth triangular element center of mass point M, d
_{n}for feed after distorted reflector is to the light path of reflecting surface nth triangular element center of mass point M',
for the axial displacement of reflecting surface nth triangular element center of mass point, δ
_{n}be the phase error that the nth triangular element center of mass point displacement causes in bore face, ρ
_{n}for aperture field sampled point radius.The computation process of bore face phase error is as follows:
1) set the coordinate of feed phase center as F (x
_{f}, y
_{f}, z
_{f}), before distortion, feed is to reflecting surface nth triangular element center of mass point
light path
for:
2) the nth triangular element center of mass point after feed phase center to distorted reflector
light path d
_{n}for:
In formula,
for the deflection of the nth triangular element center of mass point in x direction after feed to distorted reflector under Oxyz coordinate,
for the deflection of the nth triangular element center of mass point in y direction after feed to distorted reflector under Oxyz coordinate,
for the deflection of the nth triangular element center of mass point in z direction after feed to distorted reflector under Oxyz coordinate;
3) before and after distorted reflector electromagnetic wave arrive the nth triangular element center of mass point the optical path difference ε of process
_{n}for:
4) electromagnetic wave of feed radiation is parallel to focal axis after reflective surface, the phase error δ that the nth triangular element center of mass point displacement causes in bore face
_{n}for:
In formula, k=2 π/λ is propagation constant, and λ is wavelength.
Step 5, calculates antenna electric performance parameter.
With reference to Fig. 5, the calculation procedure of antenna electric performance parameter is as follows:
1) calculating aperture field distribution of amplitudes Q (ρ) is:
In formula, B and C is edge taper pin parameter, and B+C=1, and select suitable B, namely obtain different edge illumination level, P is Aperture field distribution parameter, and be used for controlling the shape of Aperture field distribution, a is the largescale reflector antenna radius of 65m bore;
2) by reflecting surface cell projection on bore face, the phase error δ of each units centre of mass point
_{n}as the phase error in this cell projection region;
3) the nth triangular element is still triangle in bore Mian Shang view field, and its apex coordinate is respectively
with
as shown in Figure 3, three length of sides of the nth projected triangle are obtained:
According to Heron's formula, obtain the area Δ s of the nth triangular element in bore Mian Shang view field
_{n}':
In formula,
be intermediate variable, Heron's formula utilizes the long method asking for triangle area of three sides of a triangle;
4) according to abovementioned aperture field distribution of amplitudes and phase distribution parameters, by following formulae discovery antenna far field Electric Field Distribution:
In formula,
for aperture field sampling point vector;
for aperture field sampled point radius; Q (n)=Q (ρ
_{n}) be Aperture field distribution parameter;
for observation point is to the vector of unit length of initial point; N is triangular element sum;
5) calculate antenna electric performance parameter according to antenna far field Electric Field Distribution, draw antenna far field direction of an electric field figure, from the direction of an electric field figure of antenna far field, obtain the gain G of antenna, minor level SLL and beam angle θ.
Step 6, sets up and solvingoptimizing model.
The Optimization Solution step of antenna structure parameter is as follows:
1) set up the dynamoelectric integrated optimization mathematical model of the largescale reflector antenna structure of following 65m bore, calculate optimal structural design parameter:
Find:A,Z,m
_{a}
s.t.:W≤W
_{0}
j＝1,2,....,NE
s＝1,2,...,NS
In formula, A=(A
_{i}), (i=1,2 ..., NA) for prototype structure backrest cell crosssection amass; Z=(Z
_{i}), (i=1,2 ..., NZ) be back frame structure lowerchord panel point longitudinal coordinate value; m
_{a}for the counterweight of unit area on pitching gear; Δ G
_{s}it is the gain loss under s operating mode; α
_{s}for the weights of this operating mode; W is general assembly (TW); W
_{0}for the quality upper limit; Z
_{p}for the position of entire physical center of gravity;
for the design height of elevation axis of antenna;
for the von Mises stress value of a jth unit under s operating mode;
for largest unit stress value under certain operating mode; NE is unit sum; NS is operating mode sum.
2) Sequential Quadratic Programming method (SQPDONLP) is adopted to solve the dynamoelectric Integrated Optimization Model of the largescale reflector antenna structure of 65m bore, finite difference method is utilized to carry out the sensitivity of objective function and constraint function in calculation optimization model, judge whether the electrical parameters of antenna calculated meets the demands, if met the demands, Antenna Construction Design scheme is qualified; Otherwise, amendment parameter of structure design, and repeat step one to step 6, until be met the structural design scheme of mechanical property and electrical performance indexes.Sequential Quadratic Programming method (SQPDONLP) is the method solving general nonlinearity restricted problem, be applicable to solving general optimal control problem on a small scale, the precision of this solution is relevant with the interstitial content of analytical structure, is applicable to solving of the largescale reflector antenna problem of 65m bore.
Advantage of the present invention further illustrates by following emulation experiment:
1. simulated conditions
Dynamoelectric for 65m bore of the present invention largescale reflector antenna structure integral design method is applied on the largescale reflector antenna of 65m bore, carries out antenna reflector structural design and electrical property prognostic experiment.As shown in Figure 6, wherein, A is antenna main reflector, primary reflection surface bore is 65000mm, primary reflection surface height is 13826.44mm, primary reflection surface centrosome internal diameter is 6000mm, primary reflection surface bore is 14169.32mm to feed phase center distance, B is subreflector, and subreflector bore is 6100m, and subreflector height is 1773.91mm, subreflector bore is 19134.01mm to primary reflection surface vertex distance, subreflector half angle is 79.61 °, and feed half angle is 8.9 °, and equivalent burnt footpath ratio is 0.30.
Application structure finite element analysis software ANSYS sets up the finite element model of antennareflected body structure.This antenna reflective face is real template, and backrest belongs to rigid frame class.Antenna reflective face radial direction is divided into nine circles, has 544 pieces of panels.Every block panel adopts rigid panel structural design, is riveted formed by stretching covering and the shaping longitudinal rib of drawn, hoop muscle.The material of monolith surface board member all adopts duralumin metal plate LY12M, is considered as shell unit when finite element analysis, is Shell63 at ANSYS choice of software cell type, and whole reflecting surface has divided 42883 triangle shell units altogether.Antenna back frame centrally body even circumferential is furnished with 16 radiation beams, 48 annular girders.Whole backrest is alloy pipe and is welded, and each steel pipe is considered as beam element in finite element, selects cell type to be Beam188 in Ansys software, has 15607 beam elements.
Working frequency range is S frequency range and X frequency range, and this S band gain requires to be not less than 58.1dB, and this X band gain requires to be not less than 70.5dB.Secondary lobe envelope meets CCIR.5802 requirement, and work wind speed is 20m/s, and existence wind speed is 55m/s, and operating ambient temperature range is45 DEG C to 60 DEG C, and surface accuracy index is 0.6mm, whole antenna reflector construction weight≤300 ton.Utilize the dynamoelectric integral design method of antenna structure of the present invention, 65m antenna reflector construction weight is reduced to 276 tons from 300 tons, and antenna efficiency is brought up to 60%.Antenna irradiation taper is10dB, and Aperture field distribution parameter equals 1, and frequency of operation is 8GHz.
2. simulation result
Above condition is utilized to emulate the antenna structure model set up, as shown in Figure 7.Emulation, under antenna Gravitative Loads, during the different operating elevation angle, optimizes antenna electric performance parameter, as shown in table 1.Be that under the operating mode of 20 °, antenna electric performance optimizes front and back antenna radiation pattern distribution as shown in Figure 8 at the angle of pitch; Be that under the operating mode of 70 °, antenna electric performance optimizes front and back antenna radiation pattern distribution as shown in Figure 9 at the angle of pitch.
Front and back Comparative result optimized by table 1
From table 1, data can be found out, initial design identical precision under the angle of pitch is the operating mode of 20 ° is 0.6945, and gain loss is 0.0494; Be that under the operating mode of 70 °, identical precision is 0.6961 at the angle of pitch, gain loss is 0.1295.Precision of coincideing under the angle of pitch is the operating mode of 20 ° after dynamoelectric integrated optimization is 0.6193, and gain loss is 0.0493; Be that under the operating mode of 70 °, identical precision is 0.6440 at the angle of pitch, gain loss is 0.0900.Based on the antenna structure that the dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore of the present invention is set up, the antenna gain under the angle of pitch is 20 ° and 70 ° of two operating mode is lost all at below 0.1dB, meets design requirement.
By the experimental result of this case, prove to adopt method of the present invention to can be used for carrying out the largescale reflector antenna structural design of 65m bore and electrical property is predicted.
Claims (4)
1. the dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore, it is characterized in that, the method comprises following process:
(1) according to the largescale reflector antenna structure of 65m bore and form parameter, determine antenna structure finite element model, obtain reflecting surface triangular element, and the theoretical coordinate of triangular element node
with
n be greater than 1 natural number;
(2) utilize structural finite element analysis software, static analysis is carried out to the largescale reflector antenna structural finite element model of 65m bore, the displacement of each triangular element node after obtaining distorted reflector
with
(3) each triangular element of the largescale reflector antenna of 65m bore obtained according to structural finite element analysis software and the corresponding relation of node thereof, calculate the theoretical coordinate of each triangular element center of mass point
and displacement
(4) 2, space distance computing formula is utilized, each triangular element barycenter node after obtaining distorted reflector
optical path difference ε
_{n}, and calculate the phase error δ that each triangular element barycenter nodal displacement causes in bore face
_{n};
(5) 65m bore largescale reflector antenna bore face field distribution of amplitudes Q (ρ) is determined, the phase error δ caused in bore face according to each triangular element barycenter nodal displacement
_{n}, by antenna far field Electric Field Distribution function, calculate antenna electric performance parameter;
(6) with size, shape and topological parameter in antenna structure for design variable, optimum for target with antenna electric performance parameter, setting up optimized mathematical model, being met the organization plan of the largescale reflector antenna of 65m bore of mechanical property and electrical performance indexes by solving this model;
Described step (4) is carried out according to the following procedure:
(4a) set the coordinate of feed phase center as F (x
_{f}, y
_{f}, z
_{f}), before distortion, feed is to reflecting surface nth triangular element center of mass point
light path
for:
(4b) the nth triangular element center of mass point after feed to distorted reflector
light path d
_{n}for:
In formula,
for the deflection of the nth triangular element center of mass point in x direction after feed to distorted reflector under Oxyz coordinate,
for the deflection of the nth triangular element center of mass point in y direction after feed to distorted reflector under Oxyz coordinate,
for the deflection of the nth triangular element center of mass point in z direction after feed to distorted reflector under Oxyz coordinate;
(4c) by (4a) and (4b) obtain electromagnetic wave before and after distorted reflector arrive the nth triangular element center of mass point the optical path difference ε of process
_{n}for:
(4d) electromagnetic wave of feed radiation is parallel to focal axis after reflective surface, and by (4a), (4b) and (4c) obtain the phase error δ of the nth triangular element that the displacement of units centre of mass point causes in bore face
_{n}for:
In formula, k=2 π/λ is propagation constant, and λ is wavelength;
Described step (5) is carried out according to the following procedure:
(5a) obtaining antenna aperture field distribution of amplitudes Q (ρ) according to following formula is:
In formula, B and C is edge taper pin parameter, and B+C=1, P are Aperture field distribution parameter, and a is reflector antenna radius;
(5b) by reflecting surface cell projection on bore face, the phase error δ of each units centre of mass point
_{n}as the phase error in this cell projection territory;
(5c) according to Heron's formula, with
with
the nth triangular element for apex coordinate projects the area Δ s of deltashaped region on bore face
_{n}' be:
In formula,
${l}_{n,1}=\sqrt{{({x}_{n,2}^{P}{x}_{n,1}^{P})}^{2}+{({y}_{n,2}^{P}{y}_{n,1}^{P})}^{2}},{l}_{n,2}=\sqrt{{({x}_{n,3}^{P}{x}_{n,2}^{P})}^{2}+{({y}_{n,3}^{P}{y}_{n,2}^{P})}^{2}},$ ${l}_{n,3}=\sqrt{{({x}_{n,1}^{P}{x}_{n,3}^{P})}^{2}+{({y}_{n,1}^{P}{y}_{n,3}^{P})}^{2}}$ Three length of sides of projected triangle respectively,
$p=\frac{{l}_{n,1}+{l}_{n,2}+{l}_{n,3}}{2}$ It is intermediate variable;
(5d) according to abovementioned aperture field distribution of amplitudes and phase distribution parameters, by following formulae discovery antenna far field Electric Field Distribution E be:
In formula,
for aperture field sampling point vector;
for aperture field sampled point radius; Q (n)=Q (ρ
_{n}) be Aperture field distribution parameter;
for far field observation point is to the distance vector of initial point; N is triangular element sum;
(5e) by antenna far field Electric Field Distribution function, antenna electric performance parameter is calculated according to antenna far field Electric Field Distribution;
Described step (5e) calculates antenna electric performance parameter according to antenna far field Electric Field Distribution, draws antenna far field direction of an electric field figure, obtains the gain G of antenna, minor level SLL and beam angle θ from the direction of an electric field figure of antenna far field;
Described step (6) is carried out according to the following procedure:
(6a) set up the dynamoelectric Integrated Optimization Model of the largescale reflector antenna structure of following 65m bore and calculate optimal structural design parameter:
Find:A,Z,m
_{a}
s.t.:W≤W
_{0}
j＝1,2,....,NE
s＝1,2,...,NS
In formula, A=(A
_{i}), (i=1,2 ..., NA) for prototype structure backrest cell crosssection amass, Z=(Z
_{i}), (i=1,2 ..., NZ) be back frame structure lowerchord panel point longitudinal coordinate value, m
_{a}for the counterweight of unit area on pitching gear, Δ G
_{s}be the gain loss under s operating mode, α
_{s}for the weights of this operating mode, W is general assembly (TW), W
_{0}for the quality upper limit, Z
_{p}for the position of entire physical center of gravity,
for the design height of elevation axis of antenna,
for the von Mises stress value of a jth unit under s operating mode,
for largest unit stress value under certain operating mode, NE is unit sum, and NS is operating mode sum;
(6b) Sequential Quadratic Programming method (SQPDONLP) is adopted to solve the dynamoelectric Integrated Optimization Model of the largescale reflector antenna structure of 65m bore, and utilize finite difference method to carry out the sensitivity of objective function and constraint function in calculation optimization model, judge whether the electrical parameters of antenna calculated meets the demands, if met the demands, Antenna Construction Design scheme is qualified; Otherwise, Amending design variatevalue, and repeat step (1) to step (6), until be met the structural design scheme of mechanical property and electrical performance indexes.
2. the dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore according to claim 1, is characterized in that in step (1), antenna structure comprises centrosome, backrest and Reflector Panel size.
3. the dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore according to claim 1, is characterized in that the theoretical coordinate of described step (1) triangular element node
with
after step (2) distorted reflector, the displacement of each triangular element node is
with
the theoretical coordinate of each triangular element center of mass point of step (3) is
and displacement
after step (4) distorted reflector, each triangular element barycenter node is
in, n be greater than 1 natural number.
4. the dynamoelectric integral design method of the largescale reflector antenna structure of 65m bore according to claim 1, it is characterized in that, described step (3) is carried out according to the following procedure:
(3a) three of the nth triangular element node coordinates are established to be respectively
with
obtain this triangular element center of mass point coordinate
(3b) three of this nth triangular element nodal displacements are established to be respectively
with
obtain this triangular element center of mass point displacement
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Citations (4)
Publication number  Priority date  Publication date  Assignee  Title 

CN101267062A (en) *  20080430  20080917  西安电子科技大学  Method for predicting antenna electric performance based on simulated distortion reflective side 
CN101308177A (en) *  20080711  20081119  西安电子科技大学  Initiative reflecting plane antenna electrical behavior prediction method 
CN101344564A (en) *  20080814  20090114  西安电子科技大学  Active phase array antenna electrical property prediction method based on mechanical, electric and thermal threefield coupling 
CN102253290A (en) *  20110329  20111123  王从思  Method for predicting electrical properties of deformed logperiodic antennae based on electromechanical coupling model 

2012
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Patent Citations (4)
Publication number  Priority date  Publication date  Assignee  Title 

CN101267062A (en) *  20080430  20080917  西安电子科技大学  Method for predicting antenna electric performance based on simulated distortion reflective side 
CN101308177A (en) *  20080711  20081119  西安电子科技大学  Initiative reflecting plane antenna electrical behavior prediction method 
CN101344564A (en) *  20080814  20090114  西安电子科技大学  Active phase array antenna electrical property prediction method based on mechanical, electric and thermal threefield coupling 
CN102253290A (en) *  20110329  20111123  王从思  Method for predicting electrical properties of deformed logperiodic antennae based on electromechanical coupling model 
NonPatent Citations (1)
Title 

大型反射面天线机电场耦合模型及其在65m口径天线设计中的应用;冷国俊;《2011年机械电子学学术会议论文集》;20110901;全文 * 
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