CN108090306A - A kind of deformed aerial minor face pattern method for fast reconstruction based on minor face structural strain - Google Patents

Abstract

The invention discloses a method for quickly reconstructing the shape of a secondary surface of a deformed antenna based on the structural strain of the secondary surface. The location and number of distribution; extract the measured value of the strain sensor on the sub-surface of the antenna and establish the finite element model of the antenna; determine the nodes at the target point on the sub-surface of the antenna and the corresponding mode shape matrix; determine the strain on the sub-surface of the antenna The nodes at the sensor and their corresponding strain mode shape matrices; calculate the generalized modal coordinates of the dual-reflector antenna; calculate the node displacement of the target point on the sub-surface of the antenna; according to the node displacement of the target point on the sub-surface of the antenna, combined with the The ideal position calculates the deformed position of the target point on the sub-surface of the antenna, so as to quickly reconstruct the shape of the sub-surface of the deformed antenna. The invention can quickly and effectively reconstruct the shape of the secondary surface of the deformed antenna, which is beneficial for the double-reflection surface antenna to meet the index requirements of electrical performance.

Description

A Fast Reconstruction Method for Deformed Antenna Subsurface Shape Based on Subsurface Structural Strain

technical field

The invention belongs to the technical field of antennas, and in particular relates to a method for rapidly reconstructing the subsurface morphology of deformed antennas based on subsurface structural strain. The invention can be used to quickly and effectively calculate the displacement of the target point on the secondary surface of the antenna under the condition that the secondary surface of the double-reflector antenna is strained, and then reconstruct the shape of the secondary surface after deformation, which is beneficial to the electrical performance of the double-reflector antenna. Requirements of the index, so that the antenna performance can be optimized.

Background technique

As large antennas are widely used in astronomical observation, satellite tracking and communication, etc., the diameter and frequency band of dual-reflector antennas are also increasing, which brings many challenges to the structural design of the antenna and affects the electrical performance of the antenna. The requirements are also getting higher and higher.

Due to the long-term exposure of the double reflector antenna to the natural environment, its secondary surface is easily affected by its own weight and environmental factors such as wind, rain, snow, and sunlight. Deteriorate the electrical performance index of the antenna. Therefore, the fast and accurate calculation of the secondary surface morphology of the dual-reflector antenna after the secondary surface is strained is the key to ensure that the dual-reflector antenna meets the requirements of its electrical performance indicators, which is conducive to the optimal performance of the antenna.

At present, the relevant academic research on the sub-reflector of the dual-reflector antenna is mainly to ensure the high-performance requirements of the antenna by adjusting the position and attitude of the sub-reflector, such as Yao Jiantao, Zeng Daxing, Hou Yulei, etc. Adjusting the sub-reflector of a large radio telescope antenna System design and experimental research [J]. Manned Spaceflight, 2016 (1): 69-73, in order to meet the antenna performance changes caused by gravity deformation during the movement of large radio telescope antennas, the "Shanghai 65-meter The configuration of the adjustment mechanism of the antenna sub-reflector of the radio telescope system. Bai Yaojun. Research on sub-surface compensation method based on structural deformation of large-aperture antenna[D]. Xidian University, 2013. Using the geometric relationship between the main and sub-reflectors, calculating the adjustment amount of the sub-reflector to compensate for the main Loss of electrical performance due to deformation of reflective surfaces. However, these have not considered the situation that the secondary surface of the dual-reflector antenna changes due to the strain caused by the service load, which directly or indirectly leads to the inaccuracy of the compensation of the electrical performance index of the antenna.

Therefore, when compensating the working performance of the dual-reflector antenna, it is necessary to consider the displacement of the target point on the secondary surface of the antenna when the secondary surface is strained, so as to quickly reconstruct the shape of the secondary surface after deformation, which is beneficial to improve the performance of the dual-reflector antenna. The accuracy of the compensation for the electrical performance of the reflector antenna makes the antenna work performance optimal.

Contents of the invention

In order to solve the above-mentioned defects existing in the prior art, the object of the present invention is to provide a method for quickly reconstructing the sub-surface morphology of deformed antennas based on the structural strain of the sub-surface. Effectively calculate the displacement of the target point on the secondary surface of the antenna, and then quickly reconstruct the shape of the secondary surface after deformation, which is conducive to the double reflector antenna meeting the electrical performance index requirements and making the antenna work performance optimal.

In order to achieve the above object, the method for quickly reconstructing the sub-surface morphology of deformed antenna based on the structural strain of the sub-surface provided by the present invention includes the following steps:

(1) Determine the structural parameters, operating frequency and material properties of the main surface, secondary surface and back frame of the double-reflector antenna, as well as the location and number of strain sensor distribution;

(2) Extract the measured value of the strain sensor on the secondary surface of the antenna, and set up the finite element model of the double-reflector antenna in the ANSYS software;

(3) Determine the target node on the subsurface of the antenna and its corresponding mode shape matrix according to the finite element model;

(4) Determine the nodes at the strain sensor on the secondary surface of the antenna and their corresponding strain mode shape matrix according to the finite element model;

(5) calculate the generalized modal coordinates of the double-reflector antenna according to the strain sensor measurement values obtained in the step (2) and the corresponding strain mode shape matrix at the node at the strain sensor on the antenna secondary surface in the step (4);

(6) Calculate the displacement of the antenna sub-surface target point according to the obtained generalized modal coordinates of the dual-reflector antenna sub-surface in step (5) and the mode shape matrix corresponding to the target point node of the antenna sub-surface in step (3) ;

(7) According to the displacement of the target node on the sub-surface of the antenna obtained in step (6), combined with the ideal position of the connection point, calculate the deformed position of the target node on the sub-surface of the antenna, so as to quickly reconstruct the sub-surface morphology of the deformed antenna.

The scheme that the present invention is further limited comprises:

The structural parameters of the double-reflector antenna include the arrangement of the structural units of the reflector aperture and the secondary surface; the material properties of the double-reflector antenna include the density, elastic modulus, and Poisson Compare.

In the step (2), the measured value of the strain sensor on the secondary surface of the antenna is {ε}={ε ₁ ,ε ₂ ,...,ε _n }.

In said step (3), determining the antenna secondary surface target node and its corresponding mode shape matrix according to the finite element model includes the following steps:

(3a) Perform finite element analysis on the finite element model in ANSYS software, and extract the first N (N=n) order mode shape β _j , where 1≤j≤N:

In the formula, S is the total number of nodes of the finite element model;

(3b) Determine the m target points on the sub-surface of the antenna, which are respectively p ₁ , p2,...,p _m , extract the values corresponding to the m nodes from the N mode shapes in turn, and combine them to form the m The mode shape matrix {β} _m corresponding to the target node on the sub-surface of the antenna:

In said step (4), determine the node at the strain sensor place and its corresponding strain mode shape matrix on the secondary surface of the antenna according to the finite element model, including the following steps:

(4a) Perform finite element analysis on the finite element model in ANSYS software, and extract the first N (N=n) order strain mode shape γ _j :

In the formula, S is the total number of nodes of the finite element model;

(4b) Determine the n nodes corresponding to the strain sensor on the secondary surface of the antenna, respectively q ₁ , q ₂ ,...,q _n , and extract the values corresponding to the n nodes from the N strain mode shapes in turn , and combined to form the strain mode shape matrix {γ} _n corresponding to the nodes at the strain sensors on the n antenna sub-surfaces:

Calculating the generalized modal coordinates of the double-reflector antenna in the step (5) includes the following steps:

According to the strain value {ε} measured by the strain sensor obtained in step (2) and the strain mode shape matrix {γ} _n corresponding to the nodes of the strain sensor on n antenna sub-surfaces obtained in step (4), we can obtain The generalized modal coordinates of the antenna {r}={r ₁ ,r ₂ ,…,r _N }:

{r}=(({γ} _n ) ^T ({γ} _n )) ^-1 ({γ} _n ) ^T {ε} (1).

Calculating the displacement of the antenna secondary surface target point in the described step (6), comprises the following steps:

According to the generalized modal coordinates {r} of the dual-reflector antenna obtained in step (5) and the mode shape matrix {β} _m corresponding to the node at the target point on the antenna sub-surface in step (3), the antenna pair The displacement of the plane target point {χ}={χ ₁ ,χ ₂ ,…,χ _i ,…,χ _m }, 1≤i≤m:

{χ}={β} _m {r} (2).

Described step (7) comprises the following steps:

(7a) Assume that the ideal positions of m target points on the secondary surface are (xi _, y _i , zi ₎ , and according to the displacement {χ}={χ ₁ , χ2,…,χ _i ,…,χ _m }, 1≤i≤m, the vectors are added to get the deformed position (xi _' , y _i ', z _i ');

(7b) According to the obtained position coordinates of the deformed target point, the griddata interpolation function in MATLAB is used for interpolation calculation, so as to obtain the reconstructed deformed antenna secondary surface morphology.

Compared with the prior art, the present invention has the following characteristics:

1. When studying the structural deformation of the double-reflector antenna caused by gravity and external environmental loads, compared with other inventions, the present invention takes into account the strain generated by the secondary surface of the antenna, which can eliminate the structural strain of the secondary surface of the antenna that affects the shape of the secondary surface , which can improve the accuracy of antenna electrical performance index compensation.

2. The present invention can use few strain sensors to quickly calculate the displacement of the target point on the secondary surface of the antenna, without the need for large-scale modeling and analysis of the influence of factors such as gravity and external environmental loads on the antenna arrangement structure, and has the advantages of low cost, simple method and easy calculation Advantages of short cycle time.

Description of drawings

Fig. 1 is a flow chart of the method for quickly reconstructing the sub-surface morphology of deformed antenna based on sub-surface structural strain in the present invention;

Figure 2 is the ANSYS overall structure model diagram of the dual-reflector antenna;

Fig. 3 is the ANSYS sub-surface structure model diagram of the double-reflector antenna;

Fig. 4 is a distribution position diagram of the strain sensors on the secondary surface of the double-reflector antenna;

Fig. 5 is the distribution position figure of this double-reflector antenna subsurface target point;

Fig. 6 is a reconstructed view of the deformed secondary surface of the dual-reflector antenna.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments, but it is not used as a basis for any limitation of the present invention.

Referring to Fig. 1, the present invention is a rapid reconstruction method of deformed antenna sub-surface morphology based on sub-surface structural strain, and the specific steps are as follows:

Step 1, determine the structural parameters, operating frequency and material properties of the main surface, secondary surface and back frame of the dual-reflector antenna, as well as the location and number of strain sensors.

The structural parameters of the double-reflector antenna include the arrangement of the structural units of the reflector aperture and the secondary surface; the material properties of the double-reflector antenna include the density, elastic modulus, and Poisson than wait.

Determine the location and number n of strain sensor distribution.

Step 2, extract the strain value measured by the strain sensor on the secondary surface of the antenna, and establish the finite element model of the dual-reflector antenna in ANSYS software.

The measured value of the strain sensor on the secondary surface of the antenna is {ε}={ε ₁ ,ε ₂ ,...,ε _n }.

Step 3, determine the target node on the subsurface of the antenna and its corresponding mode shape matrix.

3.1. Perform finite element analysis on the finite element model in ANSYS software, and extract the first N (N=n) order mode shape β _j , where 1≤j≤N:

In the formula, S is the total number of nodes of the finite element model;

3.2. Determine the m target points on the secondary surface of the antenna, which are p ₁ , p ₂ ,..., p _m , and extract the values corresponding to the m nodes from the N mode shapes in turn, and combine them to form the m The mode shape matrix {β} _m corresponding to the target node on the sub-surface of the antenna:

Step 4: Determine the nodes at the strain sensors on the secondary surface of the antenna and their corresponding strain mode shape matrices.

4.1. Perform finite element analysis on the structural model in ANSYS software, and extract the first N (N=n) order strain mode shape γ _j :

In the formula, S is the total number of nodes of the finite element model;

4.2. Determine the n nodes corresponding to the strain sensor on the secondary surface of the antenna, respectively q ₁ , q ₂ ,...,q _n , and extract the values corresponding to these n nodes from the N strain mode shapes in turn, And combined to form the strain mode shape matrix {γ} _n corresponding to the nodes of the strain sensors on the n antenna sub-surfaces:

Step 5, calculate the generalized modal coordinates of the dual-reflector antenna.

According to the strain value {ε} measured by the strain sensor obtained in step 2 and the strain mode shape matrix {γ} _n corresponding to the nodes of the strain sensor on n antenna secondary surfaces obtained in step 4, the generalized Modal coordinates {r}={r ₁ ,r ₂ ,…,r _N }:

{r}＝(({γ} _n ) ^T ({γ} _n )) ^-1 ({γ} _n ) ^T {ε} (1)

Step 6, calculate the displacement of the target point on the secondary surface of the antenna.

According to the obtained generalized modal coordinates {r} of the dual-reflector antenna in step 5 and the mode shape matrix {β} _m corresponding to the target point node on the sub-surface of the antenna in step 3, the displacement of the target point on the sub-surface of the antenna can be obtained {χ}={χ ₁ ,χ ₂ ,…,χ _i ,…,χ _m }, 1≤i≤m:

{χ}={β} _m {r} (2)

Step 7: Calculate the deformed position of the target node on the sub-surface of the antenna, and quickly reconstruct the sub-surface morphology of the deformed antenna.

7.1. Assume that the ideal positions of m target points on the secondary surface are (xi _, y _i , _zi ), and according to the displacement {χ}={χ ₁ ,χ ₂ , …,χ _i ,…,χ _m }, 1≤i≤m, the vectors are added to get the deformed position (xi _' , y _i ', z _i ');

7.2. According to the obtained position coordinates of the deformed target point, use the griddata interpolation function in MATLAB to perform interpolation calculations, so as to obtain the reconstructed deformed antenna secondary surface morphology.

Advantages of the present invention can be further illustrated by following simulation experiments:

1. Determine the structural parameters, operating frequency and material properties of the dual-reflector antenna, as well as the location and number of strain sensors, and establish an ANSYS model.

In this embodiment, a 110-meter double-reflector antenna is used for example analysis, and the central operating frequency is f=115 GHz. The ANSYS overall structure model and subsurface model are shown in Figures 2 and 3 respectively. The subsurface adopts shell elements, the element type is shell63, the thickness is 40mm, the elastic modulus is 2E+05MPa, Poisson's ratio is 0.3, and the density is 7.8e +03kg/m3. The distribution positions of the strain sensors on the secondary surface of the antenna are shown in Figure 4, and the node coordinates are shown in Table 1.

Table 1 Node coordinates at the strain sensor locations

2. Calculate the node displacement at the target point on the sub-surface of the antenna

2.1 The distribution of target points on the sub-surface of the antenna is shown in Figure 5, and its node coordinates are shown in Table 2. Use ANSYS software for free mesh division and modal analysis, and determine the corresponding first 8 orders according to step (3). Mode shape matrix.

Table 2 Node coordinates at the target point on the antenna sub-surface

2.2 In the ANSYS software, the antenna model is ideally in a flat state, and a gravity load is applied to its structural finite element model. When the antenna is only subjected to gravity load, the strain values measured by the strain sensor on the antenna secondary surface are shown in Table 3, and According to step (4), determine the corresponding first 8-order strain mode shape matrix.

2.3 According to formula (1) and step (5), the generalized modal coordinates are obtained, as shown in Table 4.

2.4 According to the formula (2) and step (6), calculate the node displacement of the target point on the subsurface of the antenna, as shown in Table 5. It can be seen from Table 5 that under the action of gravity load, the deformation of the secondary surface target point in the Y direction is greater than its deformation in the X and Z directions, and the maximum deformation in the Y direction reaches -168.7239mm.

Table 3 Strain values measured by strain sensors

Table 4 Generalized modal coordinates

Table 5 Displacement of the target point on the sub-surface of the antenna

3. Reconstruct the shape of the antenna secondary surface after deformation

According to step (7), calculate the deformed position of the sub-surface of the antenna, and use the griddata interpolation function of MATLAB to perform interpolation calculation, reconstruct the appearance of the sub-surface of the deformed antenna as shown in Fig. The position coordinates of a point.

4. Analysis results

It can be seen from the above experiments that the application of the present invention can effectively calculate the node displacement of the target point on the antenna sub-surface by arranging a small number of strain sensors on the sub-surface of the antenna, and then quickly reconstruct the shape of the sub-surface of the antenna after deformation, which is beneficial to guide the The structural deformation compensation and electrical performance compensation of the reflector antenna make it meet the requirements of electrical performance indicators, which has important academic significance 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,…,ε_n}。

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 model_j, wherein, 1≤j ≤ N, N=n：

<mrow> <msub> <mi>&amp;beta;</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>&amp;beta;</mi> <mi>j</mi> <mn>1</mn> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;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>&amp;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,…,p_m, 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 node_m：

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 model_j, wherein, N=n：

<mrow> <msub> <mi>&amp;gamma;</mi> <mi>j</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>&amp;gamma;</mi> <mi>j</mi> <mn>1</mn> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>&amp;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>&amp;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,…,q_n, 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 } answered_n：

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 face_n, the generalized Modal of antenna can be obtained Coordinate { r }={ r₁,r₂,…,r_N}：

{ 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 node_m, displacement { χ }={ χ of antenna minor face target point can be obtained₁,χ₂,…,χ_i,…, χ_m},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 (x_i,y_i,z_i), and according to antenna pair in (6) the step of obtaining Displacement { χ }={ χ of Area Objects node₁,χ₂,…,χ_i,…,χ_m, 1≤i≤m obtains deformed position after vector addition (x_i',y_i',z_i')；

(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.