CN101267062B - Method for predicting antenna electric performance based on simulated distortion reflective side - Google Patents

Abstract

The present invention provides a prediction method of the antenna electrical property based on the fitting deformation reflector, mainly resolving the problem of electro-mechanical separation in the antenna design. The method includes following steps: obtaining a node displacement after the deforming of the reflector based on the finite element analysis of the antenna structure; designing the space position relationship of the coordination and the deformed coordinate according to the theory of the reflector node, processing fit to the deformed reflector; calculating the normal error of the antenna surface and the phase error caused by the normal error by utilizing the fitting reflector; calculating antenna far fields electric field distribution according to the amplitude and the phase parameter of the antenna aperture; calculating antenna far fields electrical pattern according to the antenna far fields electric field distribution, obtaining the electrical parameter from the direction pattern, realizing the electrical property prediction of the reflector antenna structure displacement field and the electromagnetic field coupling. The invention can guide the structure design of the antenna, and comprehensively analyzes and assesses the antenna electromechanical properties under different conditions.

Description

Method for predicting antenna electric performance based on the match distortion reflective side

Technical field

The invention belongs to antenna technical field, specifically is a kind of method for predicting antenna electric performance based on the match distortion reflective side.Be used in reference to structural design, the performance simulation A+E of lead antenna.

Background technology

Along with the development of communication, radio astronomy cause, surface antenna develops to high band, bigbore direction.Large-scale surface antenna structure is typical electromechanical integrated structure, and its mechanical performance and electrical property influence each other, mutual restriction.In the engineering, the Electrical Engineer proposes the Design of Mechanical Structure requirement, and the structural engineer can only distribute the design accuracy of each building block by rule of thumb.Two kinds of situation appear in the result, and the one, the latter has used up all ways, has used best process equipment and means, still can't meet the demands; The 2nd, in actual production, what the accuracy of manufacture was high is not to satisfy electrical performance indexes, and some accuracy of manufacture and so high instead can not satisfy electrical performance indexes.The result causes the antenna manufacturing cost high, and the lead time is long, and its performance can't fundamentally guarantee.

Because design, manufacturing and the testing expense of large-scale surface antenna are very high, so require its design should one-shot forming.But because of the bore of large-scale antenna reaches tens meters, nearly 100 tons of its weight are brought great difficulty to structural design; Deform owing to this large-scale antenna structure is vulnerable to the external environment condition effect very much simultaneously, antenna electric performance is affected.As malformation make antenna efficiency reduce, minor level uprises, directivity variation etc.When the operating frequency of antenna of high band reaches the Ka frequency range, antenna structure distortion to the influence of antenna electric performance with even more serious.Owing to can't confirm the quantitative relationship between antenna structure distortion and the electrical property in the prior art, certainly exist dynamo-electric problem of separating when causing the antenna structure design.

At present, solve the most frequently used method of the dynamo-electric separate design problem of antenna both at home and abroad and have following several kinds:

(1) from comprehensive angle antenna is carried out integrated analysis, unify the requirement of subject design such as each machinery, electromagnetism to consider with the thought of Modeling optimization, this method has been considered the benefit of electrical and mechanical comprehensive design.As at J.S.Liu; L.Hollaway.Integrated structure-electromagnetic optimization of large reflector antenna systems.Structuraland Multidisciplinary Optimization; VOL.16; NO.1, the method that is adopted among the July1998 is exactly this comprehensive optimization method.But it is how to influence antenna electric performance that this method is not fundamentally analyzed the antenna structure distortion, promptly can not satisfy the scheme that provides reduction structural design difficulty under the electrical performance indexes prerequisite.

(2) utilize the antenna reflective face warping function; Obtain of the contribution of each node to the antenna electric field; Thereby analyze the antenna electric performance situation of change under the different distortion situation; As at K.Bahadori, Y.Rahmat-samii.Characterization of effects ofperiodic and aperiodic surface distortions on membrane reflector antennas.IEEE Trans.Antennas and Propagation, VOL.53; NO.9, the method that is adopted among the September 2005 is exactly this method.This method only is that the hypothesis distorted reflector satisfies certain trigonometric function distribution, but malformation is difficult to provide with a certain concrete function in the reality.The electromechanical properties analysis-by-synthesis of this method is to be based upon on the basis of malformation shape hypothesis simultaneously, can not reflect the true influence relation between antenna structure distortion and the antenna electric performance.

(3) measurement point on the antenna deformation curved surface in the actual engineering of employing; And theoretical node simulation analysis distortion back is as calculating object; Analyze the influence of antenna deformation, as (Hua Mulin) just adopting this method in the document in " modern radar " 1994 the 1st phases " a kind of approximating method of antenna deformation curved surface " to antenna electric performance.The method practical applications is worth big, but key is the antenna that actual processing will be arranged, assemble, and needs on the antenna material object, to carry out Measurement and analysis.General antenna structure designer need know the antenna electric performance under the current structure in the design of Simulation stage; And judge whether to need change or designing antenna structure again in view of the above; And can not confirm at antenna structure, reflecting surface shapes, assembles under the also completed situation, analyzes the electromechanical properties of antenna again.

Summary of the invention

The objective of the invention is to avoid the deficiency of above-mentioned art methods, propose a kind of method for predicting antenna electric performance, instruct the Electromechanical Design of antenna structure, to reduce design cost, to improve antenna electrical and mechanical comprehensive performance based on the match distortion reflective side.

The technical scheme that realizes the object of the invention is, based on the antenna structure finite element analysis, obtains the modal displacement after the distorted reflector; Design Theory coordinate and distortion recoil target spatial relation according to the reflecting surface node; Distortion reflective side is carried out match, and calculate the phase error of the bore face that antenna surface normal error and this method phase error cause, calculate antenna far field Electric Field Distribution; Draw the directional diagram of antenna far field electric field, carry out surface antenna electromechanical properties analysis-by-synthesis.Detailed process is following:

(1) according to Reflector Panel, back of the body frame, the centerbody structural parameters of antenna, confirms the antenna structure FEM model, obtain the theoretical coordinate P (x of reflecting surface sampling node _i, y _i, z _i);

(2) utilize finite element software, the antenna reflective face structure is carried out finite element analysis, obtain displacement P (the Δ x of distorted reflector post-sampling node _i, Δ y _i, Δ z _i), and carry out Coordinate Conversion through the structural model coordinate system, obtain the new coordinate system of antenna reflective face;

(3) in new coordinate system, utilize distorted reflector posterior nodal point coordinate and the minimum difference that is out of shape the front nodal point coordinate, construct the paraboloidal equation group of match, obtain the equation of match distortion reflective side;

(4) utilize match distortion reflective side equation, obtain distorted reflector posterior nodal point P (x _i+ Δ x _i, y _i+ Δ y _i, z _i+ Δ z _i) normal direction cosine and normal direction deviation ε _i, calculate the phase error δ that each node causes at the bore face _i

(5) the antenna opening diametric plane is divided into N ring territory, calculates n the K on the ring territory _nThe bore face phase error that individual node is corresponding obtains n the corresponding phase error δ in ring territory _n, n=1 ..., N;

(6) confirm antenna opening diametric plane field distribution of amplitudes Q (ρ '), according to the phase error δ in each ring territory _n,, calculate the electrical quantity of antenna through antenna far field Electric Field Distribution function;

(7), judge whether the antenna electrical quantity that calculates meets the demands, if meet the demands then the antenna structure design is qualified according to the requirement on electric performance of Antenna Design; Otherwise, revise parameter of structure design, and repeating step (1) is to step (6), until meeting the demands.

Said step (3), undertaken by following process:

(3a) in new coordinate system, calculate the error of coordinate Δ r of practical distortion face and match distortion reflective side, Δ r=r (P ₁)-r (P ₀), in the formula, P ₁Be the coordinate of antenna deformation face up-sampling point, P ₀It is the coordinate of match distortion reflective side up-sampling point;

(3b) utilize practical distortion to face the error of coordinate Δ r of match distortion reflective side, according to the principle of least square and integration extreme value theorem, equationof structure group A β=H,

A is a coefficient,

$A=\begin{array}{c}\left[\begin{array}{cccccc}\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}\frac{x_i^2}{2f}& \mathrm{\Σ}\frac{x_i{y}_i}{2f}& -\mathrm{\Σ}{x}_i& -\mathrm{\Σ}{x}_i{y}_i& \mathrm{\Σ}{x}_i^2& \mathrm{\Σ}\frac{x_i{z}_i}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}\frac{x_i{y}_i}{2f}& \mathrm{\Σ}\frac{y_i^2}{2f}& -\mathrm{\Σ}{y}_i& -\mathrm{\Σ}{y}_i^2& \mathrm{\Σ}{x}_i{y}_i& \mathrm{\Σ}\frac{y_i{z}_i}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}\frac{x_i{z}_i}{2f}& \mathrm{\Σ}\frac{y_i{z}_i}{2f}& -\mathrm{\Σ}{z}_i& -\mathrm{\Σ}{y}_i{z}_i& \mathrm{\Σ}{x}_i{z}_i& \mathrm{\Σ}\frac{z_i^2}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}\frac{x_i}{2f}& \mathrm{\Σ}\frac{y_i}{2f}& -n& -\mathrm{\Σ}{y}_i& \mathrm{\Σ}{x}_i& \mathrm{\Σ}\frac{z_i}{f}\end{array}\right]\end{array}$

β is the paraboloidal parameter of match, β=(Δ x Δ y Δ z φ _xφ _yΔ f) ^T,

$H={\left(\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}(z_i-{z_i}^{\′})x_i\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}(z_i-{z_i}^{\′})y_i\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}(z_i-{z_i}^{\′})z_i\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\Σ}}}(z_i-{z_i}^{\′})\right)}^T;$

(3c) find the solution above-mentioned equation group, obtain the paraboloidal parameter beta of match, be i.e. Δ x, Δ y, Δ z, φ _x, φ _yAnd Δ f, wherein Δ x, Δ y, Δ z are the parabolic displacement of summit in former coordinate system of match, φ _x, φ _yBe respectively the corner of the paraboloidal focal axis of match around former reference axis x, y, Δ f is the focal length variations amount;

(3d), obtain the equation of match distortion reflective side with in the paraboloidal parameter substitution of the match match reflecting surface formula:

$z=\frac{{(x-\mathrm{\Δx})}^2+{(y-\mathrm{\Δy})}^2}{4(f+\mathrm{\Δf})}+\mathrm{\Δz}+y{\mathrm{\φ}}_x-{\mathrm{x\φ}}_y$

In the formula, f is the focal length of distortion front-reflection face.

Said step (4), undertaken by following process:

(4a) the paraboloidal normal direction cosine of match is equaled the parabolic normal direction cosine of going up the relevant position of former design, obtain the node P (x after the distorted reflector according to the distortion posterior nodal point _i+ Δ x _i, y _i+ Δ y _i, z _i+ Δ z _i) normal direction cosine (l _i, m _i, n _i):

$l_i=\frac{-x_i}{2\sqrt{f(f+z_i)}},$ $m_i=\frac{-y_i}{2\sqrt{f(f+z_i)}},$ $n_i=\sqrt{\frac{f}{f+z_i}};$

(4b) by distortion front nodal point P (x _i, y _i, z _i) normal direction cosine, obtain through node P ₁(x ₀, y ₀, z ₀) normal equation:

$\frac{x-x_0}{l}=\frac{y-y_0}{m}=\frac{z-z_0}{n};$

(4c) find the solution normal equation, must be the normal direction straight line of actual node and the z coordinate of the parabolic intersection point of match, and the node P after the distortion ₁(x ₀, y ₀, z ₀) the intersection point P of the paraboloidal normal direction of corresponding match ₀(x ' ₀, y ' ₀, z ' ₀) coordinate;

(4d) through following formula, calculate the node P of distortion reflective side ₁With respect to the parabolic node P of match ₀Normal direction deviation ε _i:

${\mathrm{\&epsiv;}}_i=\sqrt{{(x_0-{x_0}^{\&prime;})}^2+{(y_0-{{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">y</figure-callout>}}_0}^{\&prime;})}^2+{(z_0-{{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">z</figure-callout>}}_0}^{\&prime;})}^2};$

(4e) calculate new focus and focal axis, obtain new focal distance f;

(4f) according to the normal direction deviation ε of each node _i, calculate the phase error δ that each node causes at the antenna opening diametric plane _i:

${\mathrm{\&delta;}}_i=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{\&epsiv;}}_i\cos {\mathrm{\&xi;}}_i$

Wherein: λ is the antenna operation wavelength, tan ξ _i=ρ _i'/2f, ρ _i' be node P ₁Respective radii at the bore face.

Said step (6), undertaken by following process:

(6a) calculate antenna aperture field distribution of amplitudes Q (ρ) according to following formula:

$Q\left(\mathrm{\&rho;}\right)=B+C{(1-\frac{{\mathrm{\&rho;}}^2}{a^2})}^P$

In the formula, B+C=1, P are the aperture field distributed constant, and a is the reflector antenna radius;

(6b) each piece territory phase error δ _jBe used as a constant, as the corresponding phase error in ring domain center;

(6c) according to above-mentioned aperture field distribution of amplitudes and phase distribution parameters, through antenna far field electric field formula $E={\&Integral;\&Integral;}_{A}Q\left({\mathrm{\&rho;}}^{\&prime;}\right)e^{\mathrm{J\&delta;}\left({\mathrm{\&rho;}}^{\&prime;}\right)}{e}^{\mathrm{Jk}{\stackrel{\&RightArrow;}{\mathrm{\&rho;}}}^{\&prime;}\&CenterDot;\hat{r}}{\mathrm{Ds}}^{\&prime;},$ Calculate antenna far field Electric Field Distribution, ρ=ρ ' in the formula/a, ρ '=(a _N-1+ a _n)/2=(2n-1) a/2N, Be the distance vector of far field point of observation to initial point, k is a wave constant;

(6d) according to antenna far field Electric Field Distribution, calculate antenna far field direction of an electric field figure, from directional diagram, obtain the unit for electrical property parameters such as gain, minor level and lobe width of antenna.

The present invention compared with prior art has following advantage:

1. utilize distorted reflector posterior nodal point coordinate and the minimum difference that is out of shape the front nodal point coordinate, the paraboloidal equation of structure match simulates distortion reflective side, is easy to find normal direction of being out of shape node and the normal error that calculates this point through this match reflecting surface;

2. owing to be incorporated into the node normal error in the phase error of antenna opening diametric plane through optical path difference; Antenna structure displacement field and electromagnetic field are closely connected; Thereby avoided only using reflector precision to judge the deficiency of antenna performance, realize the electrical and mechanical comprehensive analysis of antenna;

3. through calculating antenna far field Electric Field Distribution; Obtain the antenna electrical quantity; And,, judge the reasonability of structural design through the prediction of the electrical property in the structured design process with electrical quantity that calculates and antenna electric performance requirement contrast; Avoid carrying out by rule of thumb the antenna structure design, realized the Electromechanical Design of antenna.

Description of drawings

Fig. 1 is a reflector antenna electrical property prediction flow chart of the present invention;

Fig. 2 is a match distortion reflective side flow chart of the present invention;

Fig. 3 is that the present invention calculates bore face phase error flow chart;

Fig. 4 is that the present invention calculates reflector antenna electrical quantity flow chart;

Fig. 5 is the sketch map that reflector antenna is in any pose;

Fig. 6 is the sketch map that reflector antenna is in the state of looking up to heaven;

Fig. 7 is that the paraboloidal geometric parameter of match concerns sketch map;

Fig. 8 is the normal error sketch map of distortion reflective side antenna;

Fig. 9 is that reflector antenna bore face divides the ring sketch map;

Figure 10 is the used 7.3m antenna structure threedimensional model sketch map of emulation of the present invention.

Embodiment

Followingly the present invention is described in further detail with reference to accompanying drawing.

With reference to Fig. 1, concrete steps of the present invention are following:

Step 1 is set up the reflector antenna FEM model.

According to given antenna aperture D, focal distance f, Reflector Panel, radiation beam, ring beam, centerbody basic parameter, confirm the antenna structure FEM model, obtain the theoretical coordinate P (x of reflecting surface sampling node _i, y _i, z _i).Simultaneously, confirm the coordinate h of reflecting surface summit in model coordinate systems, be generally Z to height.

Step 2 is analyzed FEM model, the sampling node information after obtaining being out of shape.

Utilize finite element software, the antenna-reflected body structure is carried out finite element analysis under deadweight, wind lotus, vibration, the different operating modes with the ice and snow load of temperature load, obtain displacement P (the Δ x of reflecting surface sampling node _i, Δ y _i, Δ z _i), and carry out Coordinate Conversion according to the coordinate system of structural model, and after obtaining being out of shape is initial point with the reflecting surface summit, and the antenna opening diametric plane is the XY plane, and focal axis is the new coordinate system of Z axle, its process such as Fig. 5 and shown in Figure 6.

Azimuth shown in Figure 5 and the angle of pitch are respectively the antenna of any pose of az and el, use the Coordinate Conversion formula: (x ^*y ^*z ^*1) R=(x y z 1) _y(90 °-az) R _x(el) R _x(90 °) convert the state of looking up to heaven as shown in Figure 6 into.In the formula, (x ^*, y ^*, z ^*) for be in assigned address (az, antenna el) is the coordinate among O '-x ' y ' z ' at the state coordinate of looking up to heaven, (x, y is z) for being in assigned address (az, the coordinate of antenna el) in coordinate system O-xyz, R _x(θ) and R _yAll be the coordinate transformation matrix (φ), they are respectively:

$R_x\left(\mathrm{\&theta;}\right)=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\&theta;}& \sin \mathrm{\&theta;}& 0\\ 0& -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}& 0\\ 0& 0& 0& 1\end{array}\right],$ $R_y\left(\mathrm{\&phi;}\right)=\left[\begin{array}{cccc}\cos \mathrm{\&phi;}& 0& -\sin \mathrm{\&phi;}& 0\\ 0& 1& 0& 0\\ \sin \mathrm{\&phi;}& -0& \cos \mathrm{\&phi;}& 0\\ 0& 0& 0& 1\end{array}\right]$

Step 3, the match distortion reflective side.

With reference to Fig. 2, the concrete steps of distortion reflective side match are following:

1) in new coordinate system, calculates the error of coordinate Δ r of practical distortion face and match distortion reflective side, Δ r=r (P ₁)-r (P ₀), in the formula, P ₁Be the coordinate of antenna deformation face up-sampling point, P ₀Be the coordinate of match distortion reflective side up-sampling point, this practical distortion face and match reflection relation of plane are as shown in Figure 7;

2) the eyeball P of employing deformation surface ₁With match face corresponding points P ₀Axial error come the structural environment equation, according to the principle of least square and integration extreme value theorem, obtain following equation group:

A·β＝H (1)

Wherein,

$A=\begin{array}{c}\left[\begin{array}{cccccc}\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="x\; i"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">x</figure-callout>}}_i^{}}{2f}& \mathrm{\&Sigma;}\frac{x_i{y}_i}{2f}& -\mathrm{\&Sigma;}{x}_i& -\mathrm{\&Sigma;}{x}_i{y}_i& \mathrm{\&Sigma;}{\mathrm{<figure-callout\; id="2"\; label="x\; i"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">x</figure-callout>}}_i^{}& \mathrm{\&Sigma;}\frac{x_i{z}_i}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i{y}_i}{2f}& \mathrm{\&Sigma;}\frac{y_i^2}{2f}& -\mathrm{\&Sigma;}{y}_i& -\mathrm{\&Sigma;}{y}_i^2& \mathrm{\&Sigma;}{x}_i{y}_i& \mathrm{\&Sigma;}\frac{y_i{z}_i}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i{z}_i}{2f}& \mathrm{\&Sigma;}\frac{y_i{z}_i}{2f}& -\mathrm{\&Sigma;}{z}_i& -\mathrm{\&Sigma;}{y}_i{z}_i& \mathrm{\&Sigma;}{x}_i{z}_i& \mathrm{\&Sigma;}\frac{z_i^2}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i}{2f}& \mathrm{\&Sigma;}\frac{y_i}{2f}& -n& -\mathrm{\&Sigma;}{y}_i& \mathrm{\&Sigma;}{x}_i& \mathrm{\&Sigma;}\frac{z_i}{f}\end{array}\right]\end{array}$

β＝(ΔxΔyΔzφ _xφ _yΔf) ^T

$H={\left(\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}(z_i-{z_i}^{\&prime;})x_i\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}(z_i-{z_i}^{\&prime;})y_i\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}(z_i-{z_i}^{\&prime;})z_i\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}(z_i-{z_i}^{\&prime;})\right)}^T;$

Wherein: num is the sampling node sum, (x _i, y _i, z _i') be node theoretical coordinate (x _i, y _i, z _i) at distortion reflective side corresponding nodes coordinate, Δ x, Δ y, Δ z are the parabolic displacement of summit in former coordinate system of match, φ _x, φ _yBe respectively the corner of the paraboloidal focal axis of match around former reference axis x, y, Δ f is the focal length variations amount, and f is the focal length of distortion front-reflection face;

3) find the solution above-mentioned equation group (1), obtain paraboloidal 6 the geometric parameter β undetermined of match, i.e. Δ x, Δ y, Δ z, φ _x, φ _yAnd Δ f;

4) with in the paraboloidal parameter substitution of the match match reflecting surface formula, obtain the equation of match distortion reflective side:

$z=\frac{{(x-\mathrm{\&Delta;x})}^2+{(y-\mathrm{\&Delta;y})}^2}{4(f+\mathrm{\&Delta;f})}+\mathrm{\&Delta;z}+y{\mathrm{\&phi;}}_x-{\mathrm{x\&phi;}}_y.---\left(2\right)$

Step 4, the phase error of calculating bore face.

With reference to Fig. 3, the computational process of bore face phase error is following:

1) according to the distortion posterior nodal point the paraboloidal normal direction cosine of match is equaled the parabolic normal direction cosine of going up the relevant position of former design, obtain the node P (x after the distorted reflector _i+ Δ x _i, y _i+ Δ y _i, z _i+ Δ z _i) normal direction cosine do

$l_i=\frac{-x_i}{2\sqrt{f(f+z_i)}},$ $m_i=\frac{-y_i}{2\sqrt{f(f+z_i)}},$ $n_i=\sqrt{\frac{f}{f+z_i}}---\left(3\right)$

Wherein: (l _i, m _i, n _i) be the normal direction cosine of node P.

2) by the node P (x after the distortion _i+ Δ x _i, y _i+ Δ y _i, z _i+ Δ z _i) normal direction cosine, obtain through node P ₁(x ₀, y ₀, z ₀) normal equation:

$\frac{x-x_0}{l}=\frac{y-y_0}{m}=\frac{z-z_0}{n}---\left(4\right)$

Point P (x _P, y _P, z _P) be the position before the distortion of reflecting surface node, put P ₁Be the physical location after the node P distortion, some P ₀Be node P ₁Along normal direction and the paraboloidal intersection point of match, as shown in Figure 8, Fig. 8 has described the geometry of the reflector antenna with surface error.

3) find the solution this equation (4), the node P after obtaining being out of shape ₁(x ₀, y ₀, z ₀) the intersection point P of the paraboloidal normal direction of corresponding match ₀(x ' ₀, y ' ₀, z ' ₀) coordinate is:

$\left\{\begin{array}{c}{x_0}^{\&prime;}=\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">c</figure-callout>}1\&CenterDot;z+c2\\ {{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">y</figure-callout>}}_0}^{\&prime;}=c3\&CenterDot;z+c4\\ {{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">z</figure-callout>}}_0}^{\&prime;}=\frac{1-s3-s4-\sqrt{{(s3+s4-1)}^2-4\&CenterDot;s2s5-4\&CenterDot;s2s6}}{2\&CenterDot;s2}\end{array}\right.---\left(5\right)$

In the formula:

$c1=\frac{l}{n},$ $\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">c</figure-callout>}2=-\frac{\mathrm{<figure-callout\; id="0"\; label="l\; n\; z"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">l</figure-callout>}}{n}{z}_{}{}_0+x_0,$ $c3=\frac{m}{n},$ $c4=-\frac{m}{n}{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">z</figure-callout>}}_0+{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">y</figure-callout>}}_0,$

s1＝4(f+Δf)， $\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">s</figure-callout>}2=\frac{{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">c</figure-callout>}1}^2+{c3}^2}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">s</figure-callout>}1},$ $s3=\frac{2[c1(c2-\mathrm{\&Delta;x})+c3(c4-\mathrm{\&Delta;y})]}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">s</figure-callout>}1},$

s4＝c3·φ _x-c1·φ _y， $s5=\frac{{(c2-\mathrm{\&Delta;x})}^2+{(c4-\mathrm{\&Delta;y})}^2}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">s</figure-callout>}1},$ s6＝Δz+c4·φ _x-c2·φ _y

4) the node P through distortion reflective side ₁Calculating this point with respect to the paraboloidal normal direction deviation of match is:

${\mathrm{\&epsiv;}}_i=\sqrt{{(x_0-{x_0}^{\&prime;})}^2+{(y_0-{{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">y</figure-callout>}}_0}^{\&prime;})}^2+{(z_0-{{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="S2008100181069E00051.png"\; state="\{\{state\}\}">z</figure-callout>}}_0}^{\&prime;})}^2}---\left(6\right)$

5) confirm the position of focal axis

Theoretical paraboloidal coordinate system is O-xyz, and the paraboloidal coordinate system of match is O '-x ' y ' z ', and wherein O and O ' are respectively their summit, and Oz and O ' z ' are respectively their focal axis.

Theoretical paraboloidal equation is: x ²+ y ²=4fz

The paraboloidal equation of match is: x ' ²+ y ' ²=4 (f+ Δ f) z '

Make again that φ z is the corner of coordinate system O '-x ' y ' z ' around former reference axis Oz.Because of φ _x, φ _y, φ _zBe trace, then can ignore their second order trace, so the Coordinate Conversion equation of two coordinate systems does

$\left\{\begin{array}{c}{x}_1=(x-\mathrm{\&Delta;x})-{\mathrm{z\&phi;}}_y+{\mathrm{y\&phi;}}_{\mathrm{<figure-callout\; id="1"\; label="z\; y"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">z</figure-callout>}}& \\ y_{}{}_1=(y-\mathrm{\&Delta;y})-{\mathrm{x\&phi;}}_z+{\mathrm{z\&phi;}}_{\mathrm{<figure-callout\; id="1"\; label="x\; z"\; filenames="S2008100181069E00061.png"\; state="\{\{state\}\}">x</figure-callout>}}& \\ z_{}{}_1=(z-\mathrm{\&Delta;z})-{\mathrm{y\&phi;}}_x+{\mathrm{x\&phi;}}_y\end{array}\right.---\left(7\right)$

Through type (2) can be known, the paraboloidal summit of match, and the coordinate of initial point in former coordinate system O-xyz of promptly new coordinate system be (Δ x, Δ y, Δ z), newly the coordinate of the focal point F of focal axis ' in O-xyz is (x _{F '}, y _{F '}, z _{F '}), the coordinate in new coordinate system O '-x ' y ' z ' is (0,0, f+ Δ f).Therefore, the coordinate of the initial point of former coordinate system O-xyz in new coordinate system O '-x ' y ' z ' is (Δ x ,-Δ y ,-Δ z), and its coordinate system is respectively-φ around the corner of new reference axis O ' x ', O ' y ', O ' z ' _x,-φ _yWith-φ _z, then can get the coordinate of new focus in former coordinate system O-xyz and do

$\left\{\begin{array}{c}{x}_{F^{\&prime;}}=\mathrm{\&Delta;x}+(f+\mathrm{\&Delta;f})\&CenterDot;{\mathrm{\&phi;}}_y\\ y_{F^{\&prime;}}=\mathrm{\&Delta;y}-(f+\mathrm{\&Delta;f})\&CenterDot;{\mathrm{\&phi;}}_x\\ z_{F^{\&prime;}}=f+\mathrm{\&Delta;f}+\mathrm{\&Delta;z}\end{array}\right..---\left(8\right)$

6) according to the normal direction deviation ε of each node _i, calculate the phase error δ that each node causes at the bore face _i

${\mathrm{\&delta;}}_i=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{\&epsiv;}}_i\cos {\mathrm{\&xi;}}_i---\left(9\right)$

Wherein: λ is the antenna operation wavelength, tan ξ _i=ρ _i'/2f, ρ _i' be node P ₁In the respective radii of bore face, f is new focal coordinates;

Step 5 is calculated the phase error in each ring territory.

As shown in Figure 9, the antenna actinal surface be divided into N the ring territory, n (n=1 ..., N) on the individual ring territory K is arranged _nIndividual node.Suppose to have on the antenna reflective face num impact point, then num and K _nSatisfy following relation:

$\mathrm{num}=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{K}_n---\left(10\right)$

Calculate K on n the ring territory according to formula (9) _nThe bore face phase error that individual node is corresponding obtains n the corresponding phase error δ in ring territory _nFor:

${\mathrm{\&delta;}}_n=\sqrt{\frac{1}{K_n}\underset{j=1}{\overset{K_n}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_j^2}---\left(11\right)$

Step 6 is calculated the antenna electrical quantity.

With reference to Fig. 4, antenna computation of electrical step is following:

1) calculating aperture field distribution of amplitudes Q (ρ) does

$Q\left(\mathrm{\&rho;}\right)=B+C{(1-\frac{{\mathrm{\&rho;}}^2}{a^2})}^P---\left(12\right)$

Wherein, B+C=1 selects suitable B, just can produce different caliber field edge irradiation level, and aperture field distributed constant P is used for controlling the shape that aperture field distributes;

2) each piece territory phase error δ _jBe used as a constant, as the corresponding phase error in ring domain center;

3) according to above-mentioned aperture field distribution of amplitudes and phase distribution parameters, the transformation for mula that distributes through bore calculates Electric Field Distribution:

$E=\&Integral;\underset{A}{\&Integral;}Q\left({\mathrm{\&rho;}}^{\&prime;}\right)e^{\mathrm{j\&delta;}\left({\mathrm{\&rho;}}^{\&prime;}\right)}{e}^{\mathrm{jk}{\stackrel{\&RightArrow;}{\mathrm{\&rho;}}}^{\&prime;}\&CenterDot;\hat{r}}d{s}^{\&prime;}---\left(13\right)$

Formula (13) is carried out discretization handle, to calculate the far field Electric Field Distribution of antenna:

$E=2\mathrm{\&pi;}{a}^2\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{E}_{n,n-1}{e}^{j{\mathrm{\&delta;}}_n}---\left(14\right)$

Wherein

E _{N, n-1}=E _n-E _N-1, $E_n={\&Integral;}_0^{n/N}Q\left(\mathrm{\&rho;}\right)J_0\left(\mathrm{U\&rho;}\right)\mathrm{\&rho;\; D\&rho;},$ ρ '=(a _N-1+ a _n)/2=(2n-1) a/2N, ρ=ρ '/a, u=kasin θ, a are the actinal surface radius, and k is the free space wave constant, and θ is the azimuth of far field impact point, J ₀(*) be first kind Bessel function.

4) according to antenna far field Electric Field Distribution, calculate antenna far field direction of an electric field figure, from directional diagram, obtain the unit for electrical property parameters such as gain, minor level and lobe width of antenna.

Step 7 according to the requirement on electric performance of Antenna Design, judges whether the antenna electrical quantity calculate meets the demands, if meet the demands then the antenna structure design is qualified; Otherwise, revise parameter of structure design, and repeating step (1) meets the demands until the antenna electrical quantity to step (6).

Advantage of the present invention can further specify through following emulation experiment:

1. simulated conditions

Antenna electromechanical properties comprehensive analysis method of the present invention is compiled to " reflector antenna electromechanical properties analysis-by-synthesis software ", on 7.3m bore boat-carrying parabolic antenna, carried out antenna reflector structural design and electrical property prognostic experiment.

This antenna reflective face is real template, and back of the body frame belongs to the truss class.The piece panel adopts the design of rigid panel structural shape, is riveted and is formed by longitudinal rib, the hoop muscle of stretching covering and drawn moulding.The material of monolith surface board member all adopts duralumin metal plate LY12-M, when finite element analysis, is regarded as shell unit, in ANSYS software, gets Shell63.Entire antenna radially is divided into three circles, is evenly distributed with 16 radiation beams along the centerbody circumference, 48 annular girders.Working frequency range is Ku frequency range and C frequency range, this Ku band gain requirement >=57.2dB, this C band gain requirement >=50.2dB.The secondary lobe envelope satisfies the CCIR.580-2 requirement, and work wind speed is 20m/s, and the existence wind speed is 55m/s, and operating ambient temperature range is-45 ℃ to 60 ℃, and the surface normal precision index is 0.5mm, entire antenna reflector structure weight≤1.5 tons.Utilize antenna structure displacement field of the present invention and electromagnetic field couples model, be reduced to 1.2 tons to 7.3m ship-board antenna reflector structure weight from 1.5 tons, and bring up to 58.76dB to antenna gain.Here getting the antenna irradiation taper is-10dB, and the aperture field distributed constant equals 1, and operating frequency is 14GHz.

2. simulation result

The antenna structure model that utilizes above condition emulation to be set up, shown in figure 10.Emulation is under deadweight and the effect of wind lotus, and during the different operating elevation angle, the antenna electric performance parameter of eight kinds of working conditions is as shown in table 1 altogether.

The antenna electric performance major parameter of table 1 emulation under the different operating situation

Data can be found out from table 1, and the antenna of setting up based on dynamo-electric integrated approach of the present invention is that the antenna gain under 90 ° the deadweight operating mode is 58.761dB at the angle of pitch, satisfy >=designing requirement of 57.2dB.

Through the experimental result of this software, prove and adopt method of the present invention to can be used for carrying out reflector antenna structural design and electrical property prediction.

Claims (4)

1. method for predicting antenna electric performance based on the match distortion reflective side comprises following process:

(1) according to Reflector Panel, back of the body frame, the centerbody structural parameters of antenna, confirms the antenna structure FEM model, obtain the theoretical coordinate P (x of reflecting surface sampling node _i, y _i, z _i);

(2) utilize finite element software, antenna structure is carried out finite element analysis, obtain displacement P (the Δ x of distorted reflector post-sampling node _i, Δ y _i, Δ z _i), and carry out Coordinate Conversion through the structural model coordinate system, obtain the new coordinate system of antenna reflective face;

(3) in new coordinate system, utilize the error of coordinate of practical distortion reflecting surface and match distortion reflective side, and make its minimum, construct the paraboloidal equation group of match, obtain the equation of match distortion reflective side;

(4) utilize match distortion reflective side equation, obtain distorted reflector posterior nodal point P ₁Normal direction cosine and normal direction deviation ε _i, calculate the phase error δ that each node causes at the bore face _i

(5) the antenna opening diametric plane is divided into N ring territory, calculates n the K on the ring territory _nThe bore face phase error that individual node is corresponding obtains n the corresponding phase error δ in ring territory _n, n=1 ..., N;

(6) confirm the antenna opening diametric plane the field distribution of amplitudes Q (ρ '), according to each the ring territory phase error δ _n,, calculate the electrical quantity of antenna through antenna far field Electric Field Distribution function;

(7), judge whether the antenna electrical quantity that calculates meets the demands, if meet the demands then the antenna structure design is qualified according to the requirement on electric performance of Antenna Design; Otherwise, revise parameter of structure design, and repeating step (1) is to step (6), until meeting the demands.

2. method for predicting antenna electric performance according to claim 1 is characterized in that step (3) undertaken by following process:

(3a) in new coordinate system, calculate the error of coordinate Δ r of practical distortion reflecting surface and match distortion reflective side, Δ r=r (P ₁)-r (P ₀), in the formula, P ₁Be the coordinate of antenna deformation reflecting surface up-sampling node, P ₀It is the coordinate of match distortion reflective side up-sampling node;

(3b) utilize the error of coordinate Δ r of practical distortion reflecting surface to the match distortion reflective side, according to the principle of least square and integration extreme value theorem, equationof structure group A β=H,

Wherein, A is a coefficient,

$A=\left[\begin{array}{cccccc}\underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i^2}{2f}& \mathrm{\&Sigma;}\frac{x_i{y}_i}{2f}& -\mathrm{\&Sigma;}{x}_i& -\mathrm{\&Sigma;}{x}_i{y}_i& \mathrm{\&Sigma;}{x}_i^2& \mathrm{\&Sigma;}\frac{x_i{z}_i}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i{y}_i}{2f}& \mathrm{\&Sigma;}\frac{y_i^2}{2f}& -\mathrm{\&Sigma;}{y}_i& -\mathrm{\&Sigma;}{y}_i^2& \mathrm{\&Sigma;}{x}_i{y}_i& \mathrm{\&Sigma;}\frac{y_i{z}_i}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i{z}_i}{2f}& \mathrm{\&Sigma;}\frac{y_i{z}_i}{2f}& -\mathrm{\&Sigma;}{z}_i& -\mathrm{\&Sigma;}{y}_i{z}_i& \mathrm{\&Sigma;}{x}_i{z}_i& \mathrm{\&Sigma;}\frac{z_i^2}{f}\\ \underset{i=1}{\overset{\mathrm{num}}{\mathrm{\&Sigma;}}}\frac{x_i}{2f}& \mathrm{\&Sigma;}\frac{y_i}{2f}& -n& -\mathrm{\&Sigma;}{y}_i& \mathrm{\&Sigma;}{x}_i& \mathrm{\&Sigma;}\frac{z_i}{f}\end{array}\right]$

β is the paraboloidal parameter of match, β=(Δ x Δ y Δ z φ _xφ _yΔ f) ^T,

(3c) find the solution above-mentioned equation group, obtain the paraboloidal parameter beta of match, be i.e. Δ x, Δ y, Δ z, φ _x, φ _yAnd Δ f, wherein Δ x, Δ y, Δ z are the parabolic displacement of summit in former coordinate system of match, φ _x, φ _yBe respectively the corner of the paraboloidal focal axis of match around former reference axis x, y, Δ f is the focal length variations amount;

(3d), obtain the equation of match distortion reflective side with in the paraboloidal parameter substitution of the match match distortion reflective side formula:

$z=\frac{{(x-\mathrm{\&Delta;x})}^2+{(y-\mathrm{\&Delta;y})}^2}{4(f+\mathrm{\&Delta;f})}+\mathrm{\&Delta;z}+y{\mathrm{\&phi;}}_x-x{\mathrm{\&phi;}}_y$

In the formula, f is the focal length of distortion front-reflection face.

3. method for predicting antenna electric performance according to claim 1 is characterized in that step (4), is undertaken by following process:

(4a) the paraboloidal normal direction cosine of match is equaled the parabolic normal direction cosine of going up the relevant position of former design, obtain the node P (x after the distorted reflector according to the distortion posterior nodal point _i+ Δ x _i, y _i+ Δ y _i, z _i+ Δ z _i) normal direction cosine (l _i, m _i, n _i):

$l_i=\frac{-x_i}{2\sqrt{f(f+z_i)}},m_i=\frac{-y_i}{2\sqrt{f(f+z_i)}},n_i=\sqrt{\frac{f}{f+z_i}};$

(4b) by distortion front nodal point P (x _i, y _i, z _i) normal direction cosine, obtain through the distortion after node P ₁(x ₀, y ₀, z ₀) normal equation:

$\frac{x-x_0}{l}=\frac{y-y_0}{m}=\frac{z-z_0}{n};$

(4c) find the solution normal equation, the straight line that obtains explaining and the z component of the parabolic intersecting point coordinate of match, and the node P after being out of shape through the normal equation of node after the distortion ₁(x ₀, y ₀, z ₀) the intersection point P of the paraboloidal normal direction of corresponding match ₀(x ' ₀, y ' ₀, z ' ₀) coordinate;

(4d) through following formula, calculate the intersection point P of the node P1 of distortion reflective side with respect to the paraboloidal normal direction of match ₀Normal direction deviation ε _i:

${\mathrm{\&epsiv;}}_i=\sqrt{{(x_0-{x_0}^{\&prime;})}^2+{(y_0-{y_0}^{\&prime;})}^2+{(z_0-{z_0}^{\&prime;})}^2};$

(4e) calculate new focus and focal axis, obtain new focal distance f;

(4f) according to the normal direction deviation ε of each node _i, calculate the phase error δ that each node causes at the antenna opening diametric plane _i:

${\mathrm{\&delta;}}_i=\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{\&epsiv;}}_i\cos {\mathrm{\&xi;}}_i$

Wherein: λ is the antenna operation wavelength, tan ξ _i=ρ _i'/2f, ρ _i' be node P ₁Respective radii at the bore face.

4. method for predicting antenna electric performance according to claim 1 is characterized in that step (6), is undertaken by following process:

(6a) calculate antenna opening diametric plane field distribution of amplitudes Q (ρ) according to following formula:

$Q\left(\mathrm{\&rho;}\right)=B+C{(1-\frac{{\mathrm{\&rho;}}^2}{a^2})}^P$

In the formula, B+C=1, P are bore face field distribution parameter;

(6b) each ring territory phase error δ _jBe used as a constant, as this corresponding phase error in ring center, territory;

(6c) according to the bore face field distribution of amplitudes in (6a) with (6b) in phase error, through antenna far field electric field formula

Calculate antenna far field Electric Field Distribution, ρ=ρ ' in the formula/a, ρ '=(a _N-1+ a _n)/2=(2n-1) a/2N,

Be the distance vector of far field point of observation to initial point, k is a wave constant;

(6d) according to antenna far field Electric Field Distribution, calculate antenna far field direction of an electric field figure, from directional diagram, obtain gain, minor level and three unit for electrical property parameters of lobe width of antenna.

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