CN106229605A - A kind of massive phased array accurate installation method of antenna based on mathematical modeling - Google Patents

Abstract

The invention discloses a precise installation method of a large-scale phased array antenna based on mathematical modeling, which is suitable for the precise installation and commissioning of a single-wing or double-wing large-scale phased-array antenna with large size and high installation accuracy requirements, and belongs to the general assembly of microwave remote sensing design field. The method comprises the steps of: (1) establishing a star coordinate system; (2), fine-tuning the attitude of the star; (3) measuring the coordinates of the antenna and the installation point on the star; (4) establishing a mathematical model, and calculating the adjustment gasket; (5) Add spacers to install the antenna according to the calculation results; (6) Measure the comprehensive pointing of the plane and correct the spacers. The invention avoids the problem that repeated trial and error assembly and adjustment of large-scale phased array antennas affect the accuracy and efficiency of antenna installation, and has the advantages of strong engineering implementability, easy guarantee of installation accuracy, reduced number of installation and adjustment and precise measurement, and improved installation efficiency.

Description

A Precise Installation Method of Large Phased Array Antenna Based on Mathematical Modeling

technical field

The invention belongs to the field of overall assembly design of microwave remote sensing, and specifically relates to a method for realizing precise installation technology of large-scale phased array antennas based on mathematical modeling. Commissioning.

Background technique

In recent years, with the rapid development of spacecraft payload technology, large phased array antennas (plane phased array antennas with a length of more than 5 meters for a single wing and a plane phased array antenna with a length of more than 10 meters for both wings or parabolic antennas with a diameter of Ratio, multi-polarization, multiple working modes and other characteristics have been more and more applied in the field of microwave remote sensing. However, high-quality satellite image quality also puts forward higher requirements for the installation accuracy of large-scale phased array antennas. .

The installation accuracy of a large phased array antenna mainly includes the comprehensive planarity R (unit: mm) and the comprehensive pointing N (vector, including angles in three directions). The adjustment accuracy and the adjustment accuracy of the antenna deployment mechanism itself also depend on the adjustment accuracy during the assembly process of the antenna and the star, and even the precise adjustment of the deployment state of the large phased array antenna through the assembly link can obtain the required Expand the composite flatness and specific composite pointing accuracy.

At present, in the satellite assembly process, the traditional manual trial and error mode is generally adopted in the assembly and adjustment process of spaceborne equipment that requires installation accuracy. The main process is: first install the equipment, tighten the mounting screws, and then measure the installation position and angle accuracy of the equipment with precision measuring equipment (theodolite, etc.). , and then use precision measuring equipment to re-measure, after repeated commissioning, until the equipment installation accuracy meets the requirements. This type of method has the following disadvantages:

1) This type of method is only for the installation and adjustment process of small equipment (equipment with a length or radius less than 5 meters) that requires installation accuracy. The installation surface needs to be single, and the installation angle increases. There is no experience in China for the installation of large-scale phased array antennas with complex installation surfaces;

2) If this type of method is not properly assembled at one time, repeated attempts and adjustments will on the one hand cause the deformation of the equipment installation interface and reduce the interface accuracy, and on the other hand will also lead to a decrease in equipment installation efficiency. For large-scale planar phased array antennas with comprehensive pointing accuracy requirements, each repeated trial and error will bring a large workload, and only manual trial and error may not be able to achieve the required precise installation accuracy.

The title of the patent is "Automatic precision measurement method for satellite large-scale planar array SAR antenna" only involves automatic precision measurement of large-scale planar array SAR antenna, including the fitting algorithm of antenna array flatness and plane normal, but the patent is only theoretical Calculations cannot accurately guide the installation of large planar phased array antennas based on precision measurement data.

Contents of the invention

The technical solution of the present invention is to overcome the shortcomings of the traditional manual trial and error and repeated commissioning of equipment installation mode, and provide a precise installation method suitable for large-scale phased array antennas with complex installation surfaces. Based on the data, the commissioning process of the large-scale phased array antenna is transformed into a mathematical model, and the adjustment shim addition plan is calculated, and the shim is added according to the calculation result, so as to avoid the influence of repeated trial and adjustment of the large-scale phased array antenna on the installation of the antenna issues of precision and efficiency.

The technical solution of the present invention is: a method for accurately installing a large-scale phased array antenna based on mathematical modeling, the method includes the following steps:

(1), establish a star coordinate system, the coordinate origin O of the star coordinate system is the center point of the satellite-arrow separation plane, the positive direction of the X-axis is the flight direction of the satellite, the positive direction of the Z-axis is the direction to the ground, and the positive direction of the Y-axis is in line with X0Z The plane satisfies the right-hand law;

(2) Turn the installation surface on the star to the orientation of docking with the phased array antenna, and fine-tune the attitude of the star so that the attitude of the star in the three directions of pitch, yaw, and yaw is consistent with the X-axis, Y-axis, and Z-axis of the star coordinate system. The angle error is less than 0.1, and the deviation between the Y-axis coordinates of the three installation points on the star and the system requirements is less than 0.1mm;

(3), construct the three installation points of the antenna and the projection triangles of the three installation points on the star on the common vertical plane of the star installation surface and the antenna installation surface, adopt the method of plane geometry, and solve the position of each installation point by analytic trigonometric function. The thickness of the adjusting gasket;

(4) According to the calculation results obtained in step (3), add corresponding adjustment gaskets at the three installation points of the large phased array antenna to install the antenna on the star;

(5) Measure the comprehensive pointing of the antenna front plane after the antenna is installed on the star Nt0, solve the angle between the normal line of the antenna front and the X-axis, Y-axis and Z-axis of the star coordinate system, and judge the three included angles and the system requirements Whether the absolute values of the difference between the angles reached are all lower than the preset threshold, and if they are all lower, then the antenna installation process is ended, otherwise, go to step (6);

(6) When the difference between the normal line of the antenna front and the coordinate axis of the corresponding star coordinate system and the angle required by the system is +Δ, and Δ is a positive number, reduce the thickness of the gasket at the corresponding installation point, and the difference between the angle is -Δ, Δ is a positive number, increase the thickness of the gasket at the corresponding installation point;

(7) Repeat steps (5) to (6) until the absolute values of the differences between the angles between the normal of the antenna front and the X-axis, Y-axis, and Z-axis of the star coordinate system and the angles required by the system are all lower than the preset values. set threshold.

The docking azimuth of the phased array antenna is located in the flight direction of the satellite, that is, the positive direction of the X axis or the negative direction of the X axis.

When two phased array antennas are installed on the star, and the docking orientations of the antennas are respectively the positive direction of the X axis and the negative direction of the X axis, the method includes the following steps:

First, according to the above steps (1) to (7), replace the docking orientation of the phased array antenna in step (2) with the positive direction of the X-axis and the negative direction of the X-axis, and set the two phased arrays in the positive and negative directions of the X-axis The array antenna is installed on the star;

Then, measure the comprehensive pointing Nt of the whole-wing antenna front plane and the comprehensive flatness Rt of the whole-wing antenna;

Finally, it is judged whether the comprehensive direction of the whole-wing antenna array plane Nt or the comprehensive flatness Rt of the whole-wing antenna is less than the deviation range required by the system. At the same time, the requirements are met, that is, the star installation work of the double-flank antenna is completed.

The above step (3) constructs the three installation points of the antenna and the projection triangles of the three installation points on the star on the common vertical plane of the star installation surface and the antenna installation surface, adopts the method of plane geometry, and solves the position requirements of each installation point by analytic trigonometric function The detailed process of increasing the thickness of the shim is as follows:

(3.1), measure the coordinate values A1(xa ₁ ,ya ₁ ,za ₁ ), B1(xb ₁ ,yb ₁ ,zb ₁ ) of the three installation points of the antenna in the star coordinate system without adding the adjustment shim C1(xc ₁ ,yc ₁ ,zc ₁ ) and its fitting plane point to N1(cosα1, cosβ1, cosγ1) and the coordinates of the corresponding installation point on the star A2(xa ₂ ,ya ₂ ,za ₂ ), B2(xb ₂ , yb ₂ , zb ₂ ), C2(xc ₂ , yc ₂ , zc ₂ ) and their fitting plane point to N2(cosα2, cosβ2, cosγ2);

(3.2), the antenna installation surface and the star installation face are projected on the common vertical plane M, and the projection points A1, B1, C1 of the antenna installation points on the plane M are projected to obtain the projection points A1', B1', C1' and the star installation points at The projection point on the plane, translate the projection point of the star installation point on the plane to get A2', B2', C2', make the two closest installation points A2' and A1' coincide into one point, and eliminate A1 and A2, The public height difference between B1 and B2 and C1 and C2, and the projected triangle A1'C1'C2' is obtained;

(3.3), define the installation point with the largest distance between the antenna installation surface as C1, add the thickness of the adjusting gasket at C1 point: h _C = 0, no need to add gasket;

(3.4), calculate the value α' of ∠C1'A1'C2' of the projection triangle, α'=α, α is the vector angle between the star installation plane pointing to N1 and the antenna installation plane pointing to N2, and its calculation formula is:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

(3.5), according to the coordinate value of three installation points of star, calculate straight line vector A2B2, A2C2; Wherein, A2B2 vector is The A2C2 vector is

(3.6), calculate the included angles θ ₁ and θ ₂ between A2B2 and A2C2 and the common vertical plane M, obtained by the vector angle formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

(3.7) Define the installation point straight line vector A2B2 on the star installation surface, the projection lengths S ₁ and S ₂ of A2C2 on the common vertical plane M, and calculate |A ₂ 'B ₂ '| and |A ₂ ' in the projection triangle according to the following formula C ₂ '|:

|A ₂ 'B ₂ '|＝S ₁ ＝|A ₂ B ₂ |×sinθ ₁ , |A ₂ 'C ₂ '|＝S ₂ ＝|A ₂ C ₂ |×sinθ ₂ ;

(3.8) Calculate the thickness of the adjusting shim added at point A1 as: d ₁ ＝h _A ＝|A ₂ 'C ₂ '|×tgα', and the thickness of adding the adjusting shim at point B1 as: h _B ＝h _A -h ₁ ＝( |A ₂ 'C ₂ '|-|A ₂ 'B ₂ '|)×tgα'.

The adjusted installation point described in the above step (7) is determined by the following principle: when B1 and C1 are installation points installed on the antenna front at the same time, when the angle between the normal of the antenna front and the X-axis of the star coordinate system and When the absolute value of the difference between the angle required by the system exceeds the preset threshold, adjust the antenna installation point at A1; when the angle difference between the normal line of the antenna array and the Z axis of the star coordinate system and the angle required by the system When the absolute value of exceeds the preset threshold, adjust the antenna installation point at B1 or C1.

The increase or decrease _adjustment amount h of gasket thickness described in the above step (7) is:

h _{adjustment amount} = tg (Δ) × L

When the adjusted installation point is A1, L is the distance of A1D1, when the adjusted installation point is B1 or C1, L is the distance of B1D1 or C1D1; D1 is the vertical foot of A1 to B1C1.

The above-mentioned large-scale phased array antenna is parked on the air flotation platform (5) through the air foot (6), and zero-gravity installation of the phased array antenna is realized through the air foot (6) and the air flotation platform (5).

The beneficial effect of the present invention compared with prior art is:

1) The project of the present invention has strong implementability. It can use precise measuring instruments to test and analyze the trend of star installation results, and calculate and analyze the adjustment of the gasket addition plan through mathematical models. Compared with manual experience and trial and error, it has more directionality and effective adjustment. sex.

2) The installation accuracy of the antenna in the present invention is easy to guarantee, and the calculation and analysis of the mathematical model can make the installation accuracy reach or approach the target value as quickly as possible within a limited number of commissioning times. The control array antenna can be installed and adjusted in place at one time, and its unfolded comprehensive flatness reaches 3mm, and its comprehensive pointing accuracy reaches 0.02°.

3) The antenna installation efficiency of the present invention is high. According to the actual satellite installation test verification, the calculated thickness of the adjustment gasket can be the fastest to install and adjust the antenna in place at one time, reducing the number of times of installation and adjustment, and improving the efficiency of star installation. In addition, if the antenna is not properly installed and adjusted at one time, the correction scheme of the present invention can be used to correct the adjustment spacer and calculate the adjustment amount, avoiding the blindness of manual trial and error, and quickly converging the adjustment trend to the expected direction.

4) The present invention realizes the zero-gravity installation of the phased array antenna through the air foot and the air flotation platform. The installation scheme of the air foot and the air flotation platform realizes the zero gravity of the antenna. 10m or less, it can meet the zero-gravity installation requirements of the antenna; in addition, because the antenna array also has connecting cables that need to enter the astral cabin, and there are no other auxiliary facilities on the air flotation platform except the air foot, it avoids the need to expand the hanger Risks such as cable hooking caused by the zero-gravity method provide important equipment guarantees for the installation and deployment of phased array antennas.

5) The present invention incorporates the comprehensive flatness of the waveguide front that the biplane antenna needs to achieve into the evaluation variable, and is also suitable for the star installation of the large phased array antenna with two wings.

Description of drawings

Fig. 1 (a) is the flow chart of the accurate installation method of single-wing large-scale phased array antenna according to the embodiment of the present invention

Fig. 1 (b) is the flow chart of the precise installation method of the biplane large-scale phased array antenna according to the embodiment of the present invention;

Fig. 2 is a diagram showing the positional relationship between stars and antennas according to an embodiment of the present invention;

Fig. 3 is a schematic diagram of the sticking position of the array target point according to the embodiment of the present invention;

Fig. 4 (a) is a diagram of the relationship between the intersection line L of the two installation surfaces and the normal vectors of the two installation surfaces according to the embodiment of the present invention;

Fig. 4 (b) is the position relationship diagram of the star installation facing the common vertical plane M projection of the embodiment of the present invention;

Fig. 4 (c) is the projected position relationship diagram of two mounting surfaces on the common vertical plane M of the embodiment of the present invention;

Fig. 4(d) is a schematic diagram for calculating the distance from the antenna installation point to the corresponding coordinate axis according to the embodiment of the present invention.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Taking the installation process of a large-scale phased array antenna of a certain satellite system as an example, it is known that the coordinates required by the system corresponding to the center points of the three installation surfaces on the star are A(xa,ya,za), B(xb,yb,zb), C (xc, yc, zc), the comprehensive flatness R0 (unit: mm) and comprehensive pointing N0={cosα, cosβ, cosγ} required by the precise installation of the large-scale phased array antenna of the system, the expanded comprehensive flatness refers to The fitting flatness is obtained by scanning the target point of the antenna array by precise measurement equipment such as laser radar; the comprehensive pointing refers to the three-direction angle between the normal line of the fitting plane and the star coordinate system obtained by scanning the target point of the antenna array The composed vector N0={cosα, cosβ, cosγ}, which requires the antenna to meet the requirements of: α=0°±0.1°; β=90°±0.1°; γ=90°±0.1°.

Fig. 1 is the flow chart of the accurate installation method of the phased array antenna based on mathematical modeling of the present invention, wherein, Fig. 1 (a) is the flow chart of the precise installation method of the single-wing large-scale phased-array antenna, and Fig. Flowchart of precise installation method of control array antenna.

1. The specific steps of the precise installation method of the single-wing large phased array antenna are as follows:

Step 1, establish a star coordinate system, the coordinate origin O of the star coordinate system is the center point of the satellite-arrow separation surface (the center point of the lower end frame of the bearing tube), the X direction is the satellite flight direction, the Z direction is the direction to the ground, and the Y direction is The direction and the X0Z plane satisfy the right-hand law.

In order to accurately measure the coordinates, comprehensive flatness and comprehensive pointing of the installation point on the star and the antenna under the star coordinate system, it is necessary to install the star reference Precisely measure the cross cube mirror 4, the antenna frame finely measure the cross cube mirror 2, the antenna target point 8 and the public target ball point 7, and establish the conversion relationship between the laser radar coordinate system, the laser tracker coordinate system and the satellite coordinate system.

The establishment process of the coordinate transformation relationship is as follows:

(1) As shown in Figure 2, the large phased array antenna 1 is parked on the air flotation platform 5 through the air foot 6, and the zero gravity installation of the phased array antenna is realized through the air foot 6 and the air flotation platform 5.

(2) Install the stellar reference fine measurement cross cube mirror, the antenna frame fine measurement cross cube mirror, the antenna target point and the public target ball point.

a. Install the stellar reference fine measurement cross cube mirror at a position where precise measurement is convenient and where star deformation is not easy to occur, and is used to reflect the attitude of the star.

For example: the position near the lower end frame of the load-bearing tube as shown in No. 4 in Figure 2, the structure here is not easy to deform, and it will not be blocked by the installation of the antenna.

b. Install the antenna frame precise measurement cross cube mirror in a position where precise measurement is convenient and the antenna deformation is not easy to occur. The theodolite can be used to measure before and after the antenna is installed with a star, which is used to qualitatively reflect the pointing change of the antenna frame before and after the installation of the star. For the laser radar The precise measurement data play the role of auxiliary interpretation.

For example: the position at the lower end of the antenna frame as shown in number 2 in Figure 2 is a position where the antenna is not easily deformed and is not blocked by stars.

c. Paste the antenna target points evenly on the antenna array, the number is enough to reflect the flatness and comprehensive pointing accuracy of the antenna array.

For example: as shown in number 8 in attached drawing 3, in order to ensure the accuracy of the antenna target point reflecting the flatness of the antenna, the pasting density should not be less than 18 pieces/m ² .

d. Paste the public target ball points on the air bearing platform and the ground, and jointly obtain the three-dimensional point coordinates of the public target ball center point in the star coordinate system through theodolite, laser radar and laser tracker, and establish the laser radar coordinate system and laser tracker The conversion relationship between the coordinate system and the astral coordinate system.

For example: as shown in No. 7 in attached drawing 2, 3 public target ball points are pasted on the air bearing platform, and 2 public target ball points are pasted on the ground. In order to ensure the accuracy of coordinate system conversion, a lot of them should be pasted There are 4 public target ball points, and the 4 points cannot be located on the same plane.

(3) All precise measurement data in the present invention will be uniformly converted into data relative to the astral coordinate system. The specific coordinate transformation is realized through the following steps:

1) Set up 3 theodolites, measure the cube mirror (serial number 4 in the accompanying drawing 2) representing the star coordinate system on the satellite, and measure the target ball on the public target ball base, and obtain the public target ball center point in the star body 3D point coordinates in the coordinate system;

2) Set up and fix the laser radar measurement system at a suitable position directly in front of the air bearing platform, so that the target points on all fronts can be within the measurement range of the laser radar, and use the target ball measurement function of the laser radar to measure the public target ball base On the target ball, obtain the three-dimensional point coordinates of the center point of the public target ball in the lidar coordinate system;

3) Set up and fix the laser tracker next to the laser radar, so that the star installation surface and the antenna installation surface are within the measurement range of the laser tracker, and use the target ball measurement function of the laser tracker to measure the target ball on the public target ball base, Obtain the three-dimensional point coordinates of the center point of the public target ball in the coordinate system of the laser tracker;

4) Through the conversion of the common target ball point, the conversion relationship between the laser radar coordinate system, the laser tracker coordinate system and the satellite coordinate system is established.

Step 2. Pre-installation star attitude fine-tuning:

Before the large-scale phased array antenna is installed, fine-tune the attitude of the star, turn the installation surface on the star to the docking position with the phased array antenna, and use the theodolite to fine-tune the attitude of the star to make the attitude of the star in three directions: pitch, yaw, and yaw The angular error with the X-axis, Y-axis, and Z-axis of the star coordinate system is less than 0.1°, and the height of the three installation points on the star (Y coordinate value) and the system required height (Y coordinate value) are required to be less than 0.1mm.

Step 3. Measurement of mounting surface accuracy:

Before installing the large-scale phased array antenna (without adding adjustment shims), the coordinate values A1(xa ₁ , ya ₁ ,za ₁ ), B1(xb ₁ ,yb ₁ ,zb ₁ ), C2(xc ₁ ,yc ₁ ,zc ₁ ) and the fitting plane pointing (N1) and the coordinates of the installation points corresponding to A2, B2 and C2 on the star A2(xa ₂ ,ya ₂ ,za ₂ ), B2(xb ₂ ,yb ₂ ,zb ₂ ), C2(xc ₂ ,yc ₂ ,zc ₂ ) and fitting plane pointing (N2) are used for accuracy measurement, and the public The target ball point is converted to the star coordinate system, and the angles between the two vectors and each coordinate axis of the star coordinate system are α1, β1, γ1; α2, β2, γ2 respectively.

The three installation points A1, B1, and C1 on the antenna and the corresponding A2, B2, and C2 on the star are actually the installation surfaces in the project. For large phased array antennas over 5 meters, the installation size of 10mm to 20mm The surface can be considered as the installation point, and each installation surface is processed by machine tool, and the flatness is below 0.1mm. Therefore, for the simplification of measurement and calculation, each installation surface is calculated by a The center point of the screw mounting hole is replaced, and the mounting surface of the antenna is required to be consistent with the selected mounting point on the star.

At this point, the theodolite can be used to measure the antenna frame to precisely measure the pointing data of the cross cube mirror and record it for comparison with the pointing data of the cube mirror after the antenna is equipped with stars.

Step 4. Calculation of adjusting gasket:

As shown in Figure 3, define the three installation points of the antenna as the actual position, and the corresponding installation point on the star as the target position. The coordinate value A1 of the installation point to be adjusted has been obtained in step 3 (xa ₁ , ya ₁ , za ₁ ), B1(xb ₁ ,yb ₁ ,zb ₁ ), C2(xc ₁ ,yc ₁ ,zc ₁ ) and the target location installation point coordinates A2(xa ₂ ,ya ₂ ,za ₂ ), B2(xb ₂ , yb ₂ , zb ₂ ), C2(xc ₂ , yc ₂ , zc ₂ ), use the plane geometry method to construct the projected triangle of the target position and the actual position on the common vertical plane, and solve the position of each installation surface by using trigonometric functions. The thickness of the adjusting gasket h _A , h _B , h _C , the specific calculation process is as follows:

(1) Assuming that point A2 is the lowest point on the star installation surface A2B2C2, translate the star installation surface A2B2C2 so that A2 and A1 coincide, and translate the normal vector N1 of the antenna installation surface and the normal vector N2 of the star installation surface At point A2, the intersection line between the antenna installation surface A1B1C1 and the star installation surface A2B2C2 is a straight line L passing through point A2 and perpendicular to N1 and N2, as shown in Figure 4(a); the normal vector N1 of the antenna installation surface and the star body The normal vector N2 of the installation surface constitutes a plane M, which is the common vertical plane of the antenna installation surface A1B1C1 and the star installation surface A2B2C2. Project the antenna installation surface and the star installation surface to its common vertical plane M, and the projection of the antenna installation points A1, B1, and C1 on the plane M obtains the projection points A1', B1', C1' and the projection points of the star installation points on the plane , translate the projection point of the star installation point on the plane to get A2', B2', C2', make the two closest installation points A2' and A1' coincide into one point, and eliminate the common A1 and A2, B1 and B2 And the public height difference between C1 and C2, finally get the projected triangle A1'C1'C2' shown in Figure 4(c).

(2) Assume that the installation point with the largest distance between the antenna installation surface and the star installation surface is C1, and the thickness of the adjustment gasket added to point C1 is: h _C = 0, no need to add gaskets, only the installation points A1, B1 on the antenna Raise it until it is parallel to the projection line of the astral target position.

(3), calculate the value α' of ∠C1'A1'C2' of the projection triangle, α'=α, α is the vector angle between the star installation plane pointing to N1 and the antenna installation plane pointing to N2.

According to the accuracy measurement results of the laser tracker, the vector relationship between N1 and N2 is used to establish a mathematical model, and the vector angle α between N1 and N2 is solved without adding shims.

Let the angle between two vectors N1={cosα1, cosβ1, cosγ1} and N2={cosα2, cosβ2, cosγ2} be α, use the formula for the angle between two vectors:

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span>$

That is, the vector angle α between the antenna installation surface pointing to N1 and the star installation surface N2 when no adjusting shim is installed can be obtained.

(4) According to the coordinate value of the star installation point, calculate the straight line vector A2B2, A2C2; Wherein, the A2B2 vector is The A2C2 vector is

(5) Calculate the included angles θ ₁ and θ ₂ between A2B2 and A2C2 and the common vertical plane M, obtained by the vector angle formula:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span>$

(6) As shown in the geometric relationship in Figure 4(b), define the projection lengths S ₁ and S ₂ of the installation point line vectors A2B2 and A2C2 on the common vertical plane M on the star installation surface, and calculate the projection triangle according to the following formula | A ₂ 'B ₂ '| and |A ₂ 'C ₂ '|:

|A ₂ 'B ₂ '|＝S ₁ ＝|A ₂ B ₂ |×sinθ ₁ , |A ₂ 'C ₂ '|＝S ₂ ＝|A ₂ C ₂ |×sinθ ₂ ;

(7) Calculate the thickness of the adjusting shim added at point A1 as: d ₁ ＝h _A ＝|A ₂ 'C ₂ '|×tgα'=S ₂ ×tgα', and the thickness of adding the adjusting shim at point B1 as: h _B ＝h _A −h ₁ =(|A ₂ 'C ₂ '|−|A ₂ 'B ₂ '|)×tgα'=(S ₂ −S ₁ )×tgα'.

Step 5. According to the calculation results obtained in step 4, add corresponding adjustment gaskets at the three installation points of the large phased array antenna to install the antenna on the star. At the same time, the theodolite can be used to measure the antenna frame to precisely measure the pointing data of the cross cube mirror and record it, which can be used to compare the data with the pointing of the cube mirror before the antenna is installed, and to judge the change trend of the antenna pointing after the star is installed. If the direction change trend of the cube mirror is consistent with the expected change trend, it can be determined that the installation plan for adjusting the shim is effective. If not, it is necessary to repeat steps 3 and 4.

Step 6. Use the laser radar to accurately measure the comprehensive pointing of the target point plane of the antenna array after the antenna is installed with the star to Nt0, solve the angle between the normal of the antenna array and the X-axis, Y-axis, and Z-axis of the star coordinate system, and determine the three included angles Whether the absolute values of the difference between the angles required by the system are all lower than the preset threshold, and if they are all lower, the antenna installation process is ended; otherwise, go to step (7).

Step 7. Adjust the shim addition scheme correction.

Since the calculation model is established under purely rigid ideal conditions, in the process of actual star installation and precise measurement, there will still be a small amount of deformation of the large phased array antenna and the attitude of the star. According to the precise measurement results Nt0 Analysis and judgment of the increase or decrease trend of the adjustment gasket, and appropriately reduce or increase the thickness of the adjustment gasket at the corresponding position.

When the difference between the angle between the normal of the antenna front and the corresponding coordinate axis and the angle required by the system is +Δ, and Δ is a positive number, reduce the thickness of the gasket at the corresponding installation point. When the normal of the antenna front and the corresponding coordinate axis The difference between the included angle and the included angle required by the system is -Δ, Δ is a positive number, increase the thickness of the gasket at the corresponding position.

As shown in Figure 4(d), according to the location characteristics of the antenna installation surface A1B1C1, B1C1 is located on the antenna front, and the vertical line is drawn from A1 to B1C1 to obtain the vertical foot D1, and D1 is used as the coordinate origin to establish the coordinates of the whole star An antenna coordinate system with three parallel directions, then A1D1 is the distance from point A1 to the X-axis on the antenna front, and B1D1 and C1D1 are the distances from points B1 and C1 to the Z-axis on the antenna front.

Increase and decrease the adjustment amount of gasket thickness as h _{adjustment amount} :

h _{adjustment amount} = tg (Δ) × L

In the formula, L is the distance from the installation point to the corresponding coordinate axis on the antenna coordinate system, unit: mm.

The corresponding installation point to be adjusted is determined according to the coordinate axis corresponding to the normal line of the antenna array. If the deviation in the X direction is Δ, the antenna installation point at A1 needs to be adjusted, and L is the distance from A1D1; if the deviation in the Z direction is Δ, it is necessary to adjust Adjust the antenna installation point at point B1 (or point C1), and L is the distance from B1D1 (or C1D1).

According to the characteristics of the installation point of the large phased array antenna, the antenna installation points at positions B1 and C1 can be equipped with adjusting gaskets on the X and Z surfaces of the antenna. Generally, if the angle between the normal line of the antenna array and the Y direction meets the requirements, then The antenna installation points at positions B1 and C1 do not need to be equipped with adjusting shims on the Z side, so the adjusting shims at the B1 and C1 positions mentioned in this article are all on the X side unless otherwise emphasized. If the deviation in the Y direction is Δ, it is necessary to adjust the installation point on the Z surface of the antenna at point B1 (or point C1), and L is the distance from B1D1 (or C1D1).

Example: If Nt0={cosαt 0, cosβt 0, cosγt 0} is precisely measured, where γt 0=90.15°, αt 0 and βt 0 meet the requirements within the deviation range of ±0.1°, which means that the normal line of the antenna front and the star X If the included angle in the axial direction is too large, the thickness of the adjusting gasket at point A should be appropriately reduced. The amount of reduction is based on:

h _{adjustment amount} = tg (Δ) × L

Among them: Δ is the angle deviation, in this example, it is 90.15°-90°=0.15°;

L is the distance from point A to the X-axis on the antenna array. In this example, the distance from point A to the array is 1200mm, so the thickness of the shim to be reduced at point A is:

h _{adjustment amount} = tg (0.15°) × 1200 = 3.1mm.

Step 8. Repeat steps 6 to 7 until the absolute values of the differences between the three included angles and the included angles required by the system are all lower than the preset thresholds. , then the monoplane antenna installation process ends.

2. The specific steps of the precise installation method of the biplane large phased array antenna are as follows:

(1), establish a star coordinate system, the coordinate origin O of the star coordinate system is the center point of the satellite-arrow separation plane, the positive direction of the X-axis is the flight direction of the satellite, the positive direction of the Z-axis is the direction to the ground, and the positive direction of the Y-axis is in line with X0Z The surface satisfies the right-hand law;

(2) Turn the installation surface on the star to the direction of docking with the phased array antenna in the positive direction of the X-axis, fine-tune the attitude of the star, and make the attitude of the star in the three directions of pitch, yaw, and yaw correspond to the X-axis and Y-axis of the star coordinate system , The angle error of the Z axis is less than 0.1, and the Y axis coordinate value of the three installation points on the star is less than 0.1mm from the theoretical requirement;

(3) Precisely measure the coordinate values A1(xa ₁ ,ya ₁ ,za ₁ ), B1(xb ₁ ,yb ₁ ,zb ₁ ) of the three installation points of the antenna in the astral coordinate system under the state of not adding the adjustment shim , C1(xc ₁ ,yc ₁ ,zc ₁ ) and its fitting plane pointing to N1(cosα1, cosβ1, cosγ1) and the coordinates of the corresponding installation point on the star A2(xa ₂ ,ya ₂ ,za ₂ ), B2(xb ₂ ,yb ₂ ,zb ₂ ), C2(xc ₂ ,yc ₂ ,zc ₂ ) and its fitting plane point to N2(cosα2, cosβ2, cosγ2);

(4), define the three installation points of the antenna as the actual position, and the corresponding installation point on the star as the target position, use the plane geometry method to construct the projection triangle of the target position and the actual position on its common vertical plane, and solve each The thickness of the adjustment gasket needs to be increased at the installation point;

(5) According to the calculation results obtained in step (4), add corresponding adjustment gaskets at the three installation points of the large-scale phased array antenna to install the X-axis positive direction phased array antenna on the star; at the same time, measure the antenna frame and accurately measure the cross The pointing data of the cube mirror is recorded and used for data comparison with the pointing of the cube mirror before the antenna is installed to judge the change trend of the pointing of the antenna after the star is installed;

(6) Precisely measure the comprehensive pointing of the antenna array target point plane after the antenna is installed with stars, solve the angles between the antenna array normal and the X-axis, Y-axis, and Z-axis of the star coordinate system, and judge that the three included angles meet the system requirements Whether the absolute value of the difference between the included angles is all lower than the preset threshold, all lower than, then end the antenna installation process, otherwise, go to step (7);

(7) When the difference between the angle between the normal of the antenna front and the corresponding coordinate axis and the angle required by the system is +Δ, and Δ is a positive number, reduce the thickness of the gasket at the corresponding installation point. When the normal of the antenna front and the corresponding The difference between the angle between the coordinate axis and the angle required by the system is -Δ, and Δ is a positive number, increase the thickness of the gasket at the corresponding position, and increase and decrease the adjustment amount of the gasket thickness as h _{adjustment amount} ;

h _{adjustment amount} = tg (Δ) × L

In the formula, L is the distance from the installation point to the corresponding coordinate axis on the antenna array, unit: mm.

(8) Repeat steps (6) to (7) until the absolute values of the differences between the angles between the normal of the antenna front and the X-axis, Y-axis, and Z-axis of the star coordinate system and the angles required by the system are all lower than the preset values. set threshold.

(9) Follow steps (2) to (8) to accurately measure and calculate the number of adjustment shims added to the three installation points of the large phased array antenna in the negative direction of the X-axis, and add corresponding adjustment shims to the -X side to install the antenna On the Astral-X side;

(10) Precisely measure the comprehensive pointing point Nt of the whole-wing antenna array target point plane and the comprehensive flatness (Rt) of the whole-wing antenna;

(11) Judging whether the comprehensive direction of the whole-wing antenna front plane Nt or the comprehensive flatness Rt of the whole-wing antenna is less than the deviation range required by the system, if any of them does not meet the requirements, follow the step (7) in the single-wing antenna star installation method ~ Step (8) Continue to adjust the height of the gasket until the two requirements are met at the same time, that is, the star installation work of the double-flank antenna is completed.

The antenna installation accuracy of the present invention is easy to guarantee, and the calculation and analysis of the mathematical model can make the star installation accuracy reach or approach the target value as quickly as possible within a limited number of commissioning times. The antenna can be installed and adjusted in place at one time, and its unfolded comprehensive flatness reaches 3mm, and its comprehensive pointing accuracy reaches 0.02°.

The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims (7)

1. A method for accurately installing a large-scale phased array antenna based on mathematical modeling, characterized in that it comprises the following steps: (1), establish a star coordinate system, the coordinate origin O of the star coordinate system is the center point of the satellite-arrow separation plane, the positive direction of the X-axis is the flight direction of the satellite, the positive direction of the Z-axis is the direction to the ground, and the positive direction of the Y-axis is in line with X0Z The plane satisfies the right-hand law; (2) Turn the installation surface on the star to the orientation of docking with the phased array antenna, and fine-tune the attitude of the star so that the attitude of the star in the three directions of pitch, yaw, and yaw is consistent with the X-axis, Y-axis, and Z-axis of the star coordinate system. The angle error is less than 0.1, and the deviation between the Y-axis coordinates of the three installation points on the star and the system requirements is less than 0.1mm; (3), construct the three installation points of the antenna and the projection triangles of the three installation points on the star on the common vertical plane of the star installation surface and the antenna installation surface, adopt the method of plane geometry, and solve the position of each installation point by analytic trigonometric function. The thickness of the adjusting gasket; (4) According to the calculation results obtained in step (3), add corresponding adjustment gaskets at the three installation points of the large phased array antenna to install the antenna on the star; (5) Measure the comprehensive pointing of the antenna front plane after the antenna is installed on the star Nt0, solve the angle between the normal line of the antenna front and the X-axis, Y-axis and Z-axis of the star coordinate system, and judge the three included angles and the system requirements Whether the absolute values of the difference between the angles reached are all lower than the preset threshold, and if they are all lower, then the antenna installation process is ended, otherwise, go to step (6); (6) When the difference between the normal line of the antenna front and the coordinate axis of the corresponding star coordinate system and the angle required by the system is +Δ, and Δ is a positive number, reduce the thickness of the gasket at the corresponding installation point, and the difference between the angle is -Δ, Δ is a positive number, increase the thickness of the gasket at the corresponding installation point; (7) Repeat steps (5) to (6) until the absolute values of the differences between the angles between the normal of the antenna front and the X-axis, Y-axis, and Z-axis of the star coordinate system and the angles required by the system are all lower than the preset values. set threshold. 2. A mathematical modeling-based precise installation method for large-scale phased array antennas according to claim 1, characterized in that the docking orientation of the phased array antennas is located in the flight direction of the satellite, that is, the positive direction of the X axis or the negative direction of the X axis direction. 3. A mathematical modeling-based precise installation method for large-scale phased array antennas according to claim 1, characterized in that when two phased array antennas are installed on a star, the antenna docking orientations are the positive direction of the X axis and the X axis respectively. In the negative direction of the axis, the following steps are included: First, according to the above steps (1) to (7), replace the docking orientation of the phased array antenna in step (2) with the positive direction of the X-axis and the negative direction of the X-axis, and set the two phased arrays in the positive and negative directions of the X-axis The array antenna is installed on the star; Then, measure the comprehensive pointing Nt of the whole-wing antenna front plane and the comprehensive flatness Rt of the whole-wing antenna; Finally, it is judged whether the comprehensive direction of the whole-wing antenna array plane Nt or the comprehensive flatness Rt of the whole-wing antenna is less than the deviation range required by the system. At the same time, the requirements are met, that is, the star installation work of the double-flank antenna is completed. 4. according to claim 1 or 3 described a kind of precise installation method of large-scale phased array antenna based on mathematical modeling, it is characterized in that described step (3) constructs three installation points of antenna and three installation points on the star body On the projected triangle of the common vertical plane of the star installation surface and the antenna installation surface, the detailed process of adjusting the thickness of the gasket that needs to be increased for each installation point position by using the method of plane geometry and analytical trigonometry is as follows: (3.1), measure the coordinate values A1(xa ₁ ,ya ₁ ,za ₁ ), B1(xb ₁ ,yb ₁ ,zb ₁ ) of the three installation points of the antenna in the star coordinate system without adding the adjustment shim C1(xc ₁ ,yc ₁ ,zc ₁ ) and its fitting plane point to N1(cosα1, cosβ1, cosγ1) and the coordinates of the corresponding installation point on the star A2(xa ₂ ,ya ₂ ,za ₂ ), B2(xb ₂ , yb ₂ , zb ₂ ), C2(xc ₂ , yc ₂ , zc ₂ ) and their fitting plane point to N2(cosα2, cosβ2, cosγ2); (3.2), the antenna installation surface and the star installation face are projected on the common vertical plane M, and the projection points A1, B1, C1 of the antenna installation points on the plane M are projected to obtain the projection points A1', B1', C1' and the star installation points at The projection point on the plane, translate the projection point of the star installation point on the plane to get A2', B2', C2', make the two closest installation points A2' and A1' coincide into one point, and eliminate A1 and A2, The public height difference between B1 and B2 and C1 and C2, and the projected triangle A1'C1'C2' is obtained; (3.3), define the installation point with the largest distance between the antenna installation surface as C1, add the thickness of the adjusting gasket at C1 point: h _C = 0, no need to add gasket; (3.4), calculate the value α' of ∠C1'A1'C2' of the projection triangle, α'=α, α is the vector angle between the star installation plane pointing to N1 and the antenna installation plane pointing to N2, and its calculation formula is: $\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ (3.5), according to the coordinate value of three installation points of star, calculate straight line vector A2B2, A2C2; Wherein, A2B2 vector is The A2C2 vector is (3.6), calculate the angles θ1 and θ2 between A2B2 and A2C2 and the common vertical plane M, obtained by the vector angle formula: ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ (3.7) Define the installation point straight line vector A2B2 on the star installation surface, the projection lengths S ₁ and S ₂ of A2C2 on the common vertical plane M, and calculate |A ₂ 'B ₂ '| and |A ₂ ' in the projection triangle according to the following formula C ₂ '|: |A ₂ 'B ₂ '|＝S ₁ ＝|A ₂ B ₂ |×sinθ ₁ , |A ₂ 'C ₂ '|＝S ₂ ＝|A ₂ C ₂ |×sinθ ₂ ; (3.8) Calculate the thickness of the adjusting shim added at point A1 as: d ₁ ＝h _A ＝|A ₂ 'C ₂ '|×tgα', and the thickness of adding the adjusting shim at point B1 as: h _B ＝h _A -h ₁ ＝( |A ₂ 'C ₂ '|-|A ₂ 'B ₂ '|)×tgα'. 5. A mathematical modeling-based precise installation method for large-scale phased array antennas according to claim 1 or 3, characterized in that the adjusted installation points in step (7) are determined by the following principles: when B1, C1 When it is installed at the installation point of the antenna front at the same time, when the absolute value of the difference between the angle between the normal line of the antenna front and the X-axis of the star coordinate system and the angle required by the system exceeds the preset threshold, adjust A1 When the absolute value of the difference between the angle between the normal of the antenna front and the Z-axis of the star coordinate system and the angle required by the system exceeds the preset threshold, adjust the antenna installation point at B1 or C1. 6. A mathematical modeling-based precise installation method for large-scale phased array antennas according to claim 1 or 3, characterized in that the increased or decreased gasket thickness adjustment h _adjustment in step (7) is: h _{adjustment amount} = tg (Δ) × L When the adjusted installation point is A1, L is the distance of A1D1, when the adjusted installation point is B1 or C1, L is the distance of B1D1 or C1D1; D1 is the vertical foot of A1 to B1C1. 7. A mathematical modeling-based precise installation method for a large-scale phased array antenna according to claim 1 or 3, characterized in that the large-scale phased-array antenna is parked on an air-floor platform (5) through an air foot (6) ), the zero-gravity installation of the phased array antenna is realized through the air foot (6) and the air flotation platform (5).