JPH10209747A - Method for determining antenna-reflecting mirror surface by optimal spherical approximating method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To prevent distortion from being generated by shortening the overall length of a connection structure for a reflecting surface and a support structure and hold a radio wave reflecting surface precisely and stably by designing the spherical shell, which supports the antenna of an artificial satellite so that a part as the maximum point of the difference between the approximate rotary parabolic surface and radio wave reflecting surface of the spherical shell in a Z-axial direction with respect to the earth direction is minimized. SOLUTION: A reflecting surface structure 5, which has a metallic film surface of a rotary parabolic surface and a support structure 7 which can be expanded, are connected by the connection structure 6. When the spherical shell of the support structure 7 is designed, the spherical surface is so determined that the sum of >=4 even numbers of the Z-directional difference between an expression Zp for finding the rotary parabolic surface of the reflection structure 5 and an expression ZS for finding the rotary parabolic surface of the spherical shell which are raised to a power is minimized, thereby minimizing the Z-axial maximum error between the reflecting surface 5 and the spherical shell 7. Thus, the overall length of the connection structure 6 can be made short for improving the precision of a cable network forming a metallic film surface and reduce the load placed on the support structure, thereby making the antenna lightweight.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a reflector antenna structure mounted on an artificial satellite, which comprises a reflecting surface structure, a support structure, and a connection structure for connecting the two.

[0002] For example, an antenna structure in which a reflecting surface structure is formed by a lightweight and flexible structure such as a metal film surface and supported by a deployable framework structure corresponds to this.

[0003]

2. Description of the Related Art In many cases, a reflector antenna structure mounted on an artificial satellite uses a method in which a reflecting surface 1 is formed using a CFRP honeycomb plate and the back surface thereof is reinforced using a frame structure 2 or a rib structure. (Figure 1).

When an attempt is made to make a large reflector antenna structure with such a structure, it is possible to store the antenna in a small area to some extent by moving a portion fixed to the satellite body (FIG. 2). , Diameter 10
It is practically difficult to house a reflector antenna structure having a size exceeding m in a rocket fairing having a diameter of about 5 m including the satellite body.

[0005] Therefore, in a satellite for mobile communication using a relatively low communication frequency, there has been proposed an idea that a reflecting surface structure is formed by using a metal film surface and is supported by using a deployable structure. (FIG. 3). In many cases, the reflector antenna structure mounted on a satellite has a paraboloid of revolution, but approximating the paraboloid of revolution for both the reflective surface structure and the support structure takes into account that the support structure expands Then it is difficult. Therefore, in many cases, the support structure constitutes a spherical surface approximating a paraboloid of revolution, and by adjusting the length of the connection structure 6 (FIG. 4) connecting the support structure 7 and the reflective surface structure 5, the support structure is formed. Absorbs the error of the paraboloid of revolution.

Therefore, it is necessary to derive a spherical surface that approximates the shape of the reflecting surface structure by a given paraboloid of revolution with as few errors as possible. An approximation sphere was derived such that the sum of the portions having a reflection surface structure of the square of the difference between the sphere and the paraboloid of revolution was minimized.

[0007]

When an approximate spherical surface is obtained by a method that minimizes the sum of the portion having a reflective surface structure of the square of the difference between the approximate spherical surface in the direction of radio wave reflection and the paraboloid of revolution, the approximate spherical surface is obtained. The difference in the paraboloid of revolution, that is, the length of the connection structure connecting the reflection surface structure and the support structure does not become shorter than a certain value. If the connection structure is not shortened, a force is applied to the connection structure by the tension of the reflection surface structure attached to the tip of the connection structure, and if the connection structure is bent, the accuracy of the reflection surface structure cannot be maintained.

An object of the present invention is to provide a method for further shortening the length of the connection structure for deriving the length of the connection structure by the above-described method, thereby preventing a force from being applied to the connection structure.

[0009]

The spherical surface is determined so as to minimize the sum of even powers of the difference between the approximate spherical surface in the direction of radio wave reflection and the paraboloid of revolution in the portion forming the reflecting surface structure. The overall length of the connection structure is shortened, and a force is prevented from being applied to the connection structure.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS As described in the description of the prior art, a spherical shell formed by a supporting structure of an antenna mounted on a satellite using a connecting structure and a deployable supporting structure with a metal film surface as a reflecting surface structure is described below. Designed in the way. At that time, the point where the difference in the Z-axis direction between the paraboloid of revolution having the reflecting surface structure and the spherical shell approximating the paraboloid of revolution was largest was minimized.

First, the equation of the paraboloid of revolution shown by the flow chart element 8 in FIG. 8 is derived. As shown in Fig. 5, the origin is the vertex of the paraboloid of revolution, the Z-axis is the direction in which the paraboloid of revolution is spreading, and the direction coincides with the direction in which the earth is viewed from the antenna. Let it be the Y axis.
Next, the portion used for the reflection surface structure is determined as follows. The distance from the origin of the paraboloid of revolution to the portion where the reflecting surface structure starts is Y-axis offset, YD, and the size of the reflecting surface structure portion in the Y-axis direction is D. And from the electrical characteristics, the formula Z _p of the paraboloid is expressed focal length of the paraboloid of revolution is at fm, as shown in the following equation.

[0012]

(Equation 1)

The position on the Z axis is O _z , and the position on the Y axis is O
_y, wherein Z _s spherical shell shown in the flow chart element 9 is represented by the radius r is as follows. At this time, since both the paraboloid of revolution and the spherical shell are axisymmetric with respect to the Z axis, no offset on the X axis is considered.

[0014]

(Equation 2)

The Z expressed by these equations (1) and (2)
The difference in the Z direction wherein _p and Z _s in order to minimize, firstly,
An equation was created so that the part where the difference in the Z direction is the largest becomes larger and the part where the difference in the Z direction becomes smaller becomes smaller.

Therefore, the value obtained by subtracting Z _p from Z _s is 2
The value was raised to the m-th power, and the portion forming the reflection surface structure was integrated. m to 10.
When a large number such as 0 is set, a portion where Z _s and Z _p are large can be made larger and a portion where Z _s and Z _p are small can be made smaller. As shown in FIG. 5, the portion of the paraboloid of revolution that is the integration range, which becomes the reflecting surface structure, is YD to YD in the Y-axis direction.
Up to + D, the diameter D in the X-axis direction when viewed from the Z-axis
This is the part of the circle. The equation shown in flowchart element 10 that integrates Z _s -Z _{p to} the power of 2m is as follows.

[0017]

(Equation 3)

The time when the value obtained by differentiating r, O _y , and O _{z in} equation (3) once becomes 0 is the time when the difference between Z _s and Z _{p in} the Z-axis direction becomes minimum. The equations are shown below.

[0019]

(Equation 4)

[0020]

(Equation 5)

[0021]

(Equation 6)

The values of r, O _y , and O _z when these equations (4), (5), and (6) are satisfied are represented by the flowchart element 11.
Is derived using the equation (7) of the Newton method shown in FIG. i
Is the number of iterations of the Newton method.

[0023]

(Equation 7)

When an approximate spherical surface is obtained by the conventional method of least squares, m in equations (3) to (6) becomes 1. When the Newton method converges as shown in flowchart elements 12 and 13, r, O _y , and O _z are obtained.

FIG. 6 shows the error in the Z-axis direction between the paraboloid of revolution and the spherical shell obtained by the least square method. D of the paraboloid of revolution is 1
5000mm, YD is 3000mm, fm is 10,000
mm. The solid lines and various dotted lines in FIG. 6 are differences (approximation errors) between the paraboloid of revolution in the Z-axis direction and the spherical shell, and indicate the position of a cross section parallel to the X-axis as a parameter. The positive maximum value at this time, the position of the paraboloid of revolution in the Z-axis direction is the Z of the spherical surface.
The maximum value when it is larger than the axial position is 241.51 mm
And the minimum value when the position of the paraboloid of revolution in the Z-axis direction is smaller than the position of the spherical surface in the Z-axis direction is -192.8.
6 mm. Since the spherical surface supports the paraboloid of revolution from the lower side in the Z-axis direction, the fact that there is a portion where the value of the Z-axis of the spherical surface is larger than that of the paraboloid of revolution means that the spherical surface has a negative maximum value. Must be lowered from the paraboloid of revolution in the Z-axis direction. Then, the value in the Z-axis direction of the approximate spherical surface and the paraboloid of revolution becomes a value obtained by adding the positive maximum value and the negative maximum value, and the height difference of the connection structure is 438.37 m.
m. In order to further reduce the height difference of the connection structure, it is more effective to use a method of reducing the maximum error in the Z-axis direction between the approximate spherical surface and the paraboloid of revolution than using the least squares method.

FIG. 7 shows the result of calculating the value of m proposed in the present invention with a larger value, and compares the result with the result of calculation using the least square method described above. When m is 10, D is 15000 mm, YD is 3000 mm, and fm is 10
000 mm, and the positive maximum value of the difference in the Z-axis direction at that time is 186.33 mm, and the negative maximum value is -176.1.
6 mm. That is, the height difference of the connection structure is 364.49.
mm. Compared to the difference in height of the connection structure of 438.37 mm when the least squares method is used, the height can be reduced by 73.88 mm.

When the connection structure becomes longer, a force is applied to the tip of the connection structure due to the tension of the reflection surface structure, and the connection position between the connection structure and the reflection surface structure is shifted from the prescribed position to the reflection surface structure side. For example, when the deviation is 5 mm, the position of the node point 14 attached to the reflecting surface structure is 1 at the maximum.
If the connection position is shifted by 10 mm, the position of the node point is shifted by 21.43 mm. As described above, even when the difference between the connection positions of the connection structure and the reflection surface structure is small, the node position is largely shifted. If the deviation is large, it becomes impossible even to adjust the tension of the reflecting surface structure to a desired tension. For this reason, it is necessary to prevent the deformation of the connection structure by making the connection structure as short as possible.

[0028]

When the paraboloid of revolution is approximated by a spherical shell, the method of minimizing the largest error in the Z-axis direction between the paraboloid of revolution and the spherical shell has a smaller error than the least squares method. The connection structure for connecting the reflector structure and the support structure can be made shorter.

To minimize the largest part of the error,
What is necessary is just to minimize the sum of the even powers of the error. The even value is preferably 4 or more. Even powers are smaller, smaller errors are larger, and larger errors are larger, so the sum of even powers is represented by the largest part of the error.

By shortening the connection structure, the accuracy of the cable network forming the metal film surface can be increased, the load on the support structure can be reduced, and the weight of the entire antenna mounted on the satellite can be reduced.

[Brief description of the drawings]

FIG. 1 shows a conventional reflector antenna structure.

FIG. 2 shows a deployed and stored state of a reflector antenna structure of a conventional antenna mounted on a satellite.

FIG. 3 shows an image diagram of a conventional satellite.

FIG. 4 is a connection diagram of a reflection surface structure, a support structure, and a connection structure.

FIG. 5 is an explanatory view of a portion having a paraboloidal reflection surface structure.

FIG. 6 is a graph of the error in the Z-axis direction between the paraboloid of revolution and the spherical shell according to the method of least squares.

FIG. 7 is a graph of the Z-axis error between the paraboloid of revolution and the spherical shell due to a larger even power.

FIG. 8 is a flowchart for implementing the method of the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 Conventional reflector antenna structure 2 Frame structure 3 Conventional satellite mounted antenna deployment state 4 Conventional satellite stored in rocket fairing 5 Reflective surface structure 6 Connection structure 7 Support structure 8 Flow chart element 9 Flow chart element 10 Flow chart element 11 Flow chart element 12 Flow chart element 13 Flow chart element 14 Node point

Claims (2)

[Claims] 1. A shape of a reflecting surface structure for reflecting a radio wave is given by a paraboloid of revolution, and discrete points supporting the reflecting surface structure are located on a spherical surface, and between the spherical surface and the paraboloid of revolution. A method of determining an antenna reflecting mirror surface by an optimal spherical approximation method, wherein a sum of even powers of the difference in the axial direction is determined, and the spherical surface is determined so as to minimize the sum. 2. The method according to claim 1, wherein the even number is greater than four.