阅读说明：本技术 一种基于磁梯度张量的航天器磁矩测试方法 (magnetic gradient tensor-based spacecraft magnetic moment testing method ) 是由 随阳轶 刘珂 程浩 王梓骁 张明维 王康 刘世斌 毕忠华 于 2019-09-16 设计创作，主要内容包括：本发明涉及一种基于磁梯度张量的航天器磁矩测试方法,解决了现有的近场分析法需建造专用零磁设备、测量方法复杂以及测试结果易受磁场等外部环境影响的技术问题。本发明基于磁梯度张量的航天器磁矩测试方法,对近场分析法进行改进,从近场分析法的理论基础出发,用磁梯度张量值替换近场方程组中的磁场值,在试验中将测量航天器及其部件的磁场值改为测量其磁梯度张量值。该方法受外干扰磁场的影响小,无需建造零磁设备,适用范围更广；无需复杂的误差补偿机制,更加灵活。(the invention relates to a magnetic moment testing method of a spacecraft based on magnetic gradient tensor, which solves the technical problems that the existing near field analysis method needs to build special zero magnetic equipment, the measuring method is complex, and the testing result is easily influenced by external environments such as a magnetic field and the like. The invention relates to a magnetic moment testing method of a spacecraft based on magnetic gradient tensor, which improves a near field analysis method, uses a magnetic gradient tensor value to replace a magnetic field value in a near field equation set from the theoretical basis of the near field analysis method, and changes the magnetic field value for measuring the spacecraft and components thereof into the magnetic gradient tensor value for measuring the spacecraft and components thereof in the test. The method is little influenced by an external interference magnetic field, zero-magnetic equipment does not need to be built, and the application range is wider; and a complex error compensation mechanism is not needed, and the method is more flexible.)

1. A magnetic moment test method of a spacecraft based on magnetic gradient tensor comprises the following steps:

A. Placing the spacecraft or a part thereof on a non-magnetic rotary table, and placing a magnetic gradient tensor instrument at the x' axis of the equatorial plane of the spacecraft or the part thereof and at the r position from the center of the spacecraft or the part thereof;

B. Setting the working state of the spacecraft or the component thereof;

C. The output of the magnetic gradient tensor instrument returns to zero;

D. Rotating the non-magnetic turntable at intervals of 10 degrees around the z' axis of the turntable by 360 degrees, and measuring B by the magnetic gradient tensor instrument at each angle_ij(r,Φ)；

E. Calculating the remanence magnetic moment value M of the x and y directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3)_{x remains},M_{y remains}magnetic moment value M of superposition of z-direction remanence magnetic moment value and magnetic induction moment_{z sense of remaining +}；

The Fourier series expansion coefficient calculation formula is as follows:

In the formula:

r is the distance between the magnetic gradient tensor instrument and the center of the spacecraft or the test piece, m;

k is the number of poles of the multipole of the spacecraft or part thereof. When k is 1, a dipole is represented;

Phi is the corresponding initial position, the angle rotated by the spacecraft or the test piece, (°);

B_ij(r, phi) is the magnetic field component B surrounding each point on the equatorial plane of the spacecraft measured by a magnetic gradient tensor instrument_iRate of change in j direction, i, j ═ x, y, z, nT;

a_2k-1,1magnetic dipole moment and multipole moment, A.m, of spacecraft along the X-axis direction of the turntable^2k(M_x’＝a_1,1)；

b_2k-1,1magnetic dipole for spacecraft along Y-axis direction of rotary tableMoment and multipole moment, A.m^2k(M_Y’＝b_1,1)；

a_2k-1,0magnetic dipole moment and multipole moment, A.m, of spacecraft along the Z-axis direction of the rotary table^2k(M_z’＝a_1,0)；

F. Rotating the spacecraft or the components thereof clockwise by 90 degrees around the y axis of the spacecraft to enable the z axis to be in a horizontal plane;

G. repeating the steps C-D;

H. Calculating the remanence moment value M of the y and z directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3)_{y remains},M_{z remains}Magnetic moment value M of superposition of x-direction remanence magnetic moment value and magnetic induction moment_{feeling of x remaining +}；

I. Rotating the spacecraft or the components thereof clockwise by 90 degrees around the z-axis of the spacecraft to enable the x-axis to be in a horizontal plane;

J. repeating the steps C-D;

K. Calculating the remanence magnetic moment value M of the x and z directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3)_{x remains},M_{z remains}Magnetic moment value M of superposition of residual magnetic moment value and magnetic induction moment in y direction_{feeling of y remaining +}；

And L, calculating the magnetic induction moment of the spacecraft or the component according to the formula (5):

2. A magnetic moment testing method for a spacecraft based on a magnetic gradient tensor according to claim 1, wherein: the remanent magnetic moments include stray magnetic moments, i.e., the remanent magnetic moments refer to remanent plus stray magnetic moments.

3. A magnetic moment testing method for a spacecraft based on a magnetic gradient tensor according to claim 1, wherein: and step A, the position where the r is placed meets the condition that the signal-to-noise ratio of the tensor instrument is more than 10 dB.

Technical Field

The invention belongs to the technical field of magnetic testing of spacecrafts, particularly relates to a magnetic moment testing method of a spacecraft, and particularly relates to a magnetic moment testing method of a spacecraft based on magnetic gradient tensor.

Background

A spacecraft operating in a magnetic field in a space environment is affected by aspects of the magnetic field in the space environment. On one hand, the on-orbit attitude of the spacecraft can be influenced by magnetic interference torque, and the interference torque is generated by interaction of residual magnetic moment existing in the spacecraft, magnetic moment generated by a current loop inside the spacecraft and a space environment magnetic field. On the other hand, for a spacecraft which has the task of detecting the magnetic field in the space environment, a high-sensitivity magnetic sensor is used. Based on this, the magnetic cleanliness of the spacecraft is strictly required to ensure that the data acquired by the magnetic sensor is not submerged in the magnetic interference of the spacecraft. Therefore, before the spacecraft is launched, the spacecraft must be subjected to magnetic testing to determine the residual magnetic moment, the stray magnetic moment and the induced magnetic moment of the spacecraft and parts thereof, the magnetic state of the spacecraft in orbit and the magnetic characteristics inside the spacecraft are estimated, a basis is provided for reasonable material selection and current wiring, and reliable guarantee is provided for magnetic compensation.

Currently, the most common method for testing the magnetic moment of a spacecraft is a near-field analysis method. In the near field analysis method, a spacecraft is placed on a nonmagnetic turntable in the center of a geomagnetic field or a zero magnetic coil system, a plurality of magnetic sensors fixed at intervals are placed at a certain distance from the spacecraft, the nonmagnetic turntable is rotated to measure the magnetic field values of the spacecraft at different angles, the magnetic field values are functions of the rotation angle, and mathematical inversion can be performed according to the angles and the distributed magnetic field values at the angles to obtain the magnetic moment values of the spacecraft.

The near field analysis may be performed in a zero magnetic device or in a geomagnetic field environment. In the zero magnetic field equipment with the earth magnetic field offset by the artificial magnetic field, the residual magnetic moment and the stray magnetic moment of the spacecraft can be obtained by applying the method, and the magnetic moment is not influenced. However, most of zero magnetic field devices belong to special devices, the development period is long, the device integration level is low, the requirement on space is high, and the movement and expansion are inconvenient. When the magnetic field is measured in the geomagnetic field, the magnetic moments obtained by the near field analysis method comprise residual magnetic moments, stray magnetic moments and magnetic induction moments, and the magnetic moment value which does not comprise the magnetic induction moments generated by the geomagnetism is obtained by adopting a side-arranged or inverted method. In addition, measurement in the geomagnetic field is affected by external disturbance magnetic fields such as fluctuation of the geomagnetic field and an industrial magnetic field. Currently, there are some researchers who propose to cancel the effect of the external disturbing magnetic field by using sensor differentiation (setting a measurement sensor and a reference sensor) or error compensation. However, the differencing method has a high requirement on the parallelism between the axes of the sensors, and increases the measurement error; the closed-loop control method needs to arrange a complex interference magnetic field monitoring sensor, and the influence on the test result when the fluctuation of external environments such as a geomagnetic field and the like is too large cannot be completely solved by using a compensation method, and the test can only be carried out in a time with relatively small external interference such as early morning and the like.

Disclosure of Invention

The invention aims to provide a magnetic moment testing method of a spacecraft based on magnetic gradient tensor aiming at the defects of the prior art, and solves the technical problems that the existing near field analysis method needs to build special zero magnetic equipment, the measuring method is complex, and the testing result is easily influenced by external environments such as a magnetic field and the like.

the purpose of the invention is realized by the following technical scheme:

A magnetic moment test method of a spacecraft based on magnetic gradient tensor comprises the following steps:

A. placing the spacecraft or a part thereof on a non-magnetic rotary table, and placing a magnetic gradient tensor instrument at the x' axis of the equatorial plane of the spacecraft or the part thereof and at the r position from the center of the spacecraft or the part thereof;

B. Setting the working state of the spacecraft or the component thereof;

C. The output of the magnetic gradient tensor instrument returns to zero;

D. Rotating the non-magnetic turntable at intervals of 10 degrees around the z' axis of the turntable by 360 degrees, and measuring B by the magnetic gradient tensor instrument at each angle_ij(r,Φ)；

E. Calculating the remanence magnetic moment value M of the x and y directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3)_{x remains},M_{y remains}Magnetic moment value M of superposition of z-direction remanence magnetic moment value and magnetic induction moment_{z sense of remaining +}；

the Fourier series expansion coefficient calculation formula is as follows:

In the formula:

r is the distance between the magnetic gradient tensor instrument and the center of the spacecraft or the test piece, m;

k is the number of poles of the multipole of the spacecraft or part thereof. When k is 1, a dipole is represented;

phi is the corresponding initial position, the angle rotated by the spacecraft or the test piece, (°);

B_ij(r, phi) is the magnetic field component B surrounding each point on the equatorial plane of the spacecraft measured by a magnetic gradient tensor instrument_iRate of change in j direction, i, j ═ x, y, z, nT;

a_2k-1,1Magnetic dipole moment and multipole moment, A.m, of spacecraft along the X-axis direction of the turntable^2k(M_x’＝a_1,1)；

b_2k-1,1Magnetic dipole moment and multipole moment, A.m, of spacecraft along Y-axis direction of rotary table^2k(M_Y’＝b_1,1)；

a_2k-1,0magnetic dipole moment and multipole moment, A.m, of spacecraft along the Z-axis direction of the rotary table^2k(M_z’＝a_1,0)；

F. rotating the spacecraft or the components thereof clockwise by 90 degrees around the y axis of the spacecraft to enable the z axis to be in a horizontal plane;

G. Repeating the steps C-D;

H. calculating the remanence moment value M of the y and z directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3)_{y remains},M_{z remains}Magnetic moment value M of superposition of x-direction remanence magnetic moment value and magnetic induction moment_{Feeling of x remaining +}；

I. rotating the spacecraft or the components thereof clockwise by 90 degrees around the z-axis of the spacecraft to enable the x-axis to be in a horizontal plane;

J. Repeating the steps C-D;

K. Calculating the remanence magnetic moment value M of the x and z directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3)_{x remains},M_{z remains}Magnetic moment value M of superposition of residual magnetic moment value and magnetic induction moment in y direction_{feeling of y remaining +}；

And L, calculating the magnetic induction moment of the spacecraft or the component according to the formula (5):

Further, the remanent magnetic moments include stray magnetic moments, i.e., the remanent magnetic moments are all referred to as remanent plus stray magnetic moments.

Further, step A, the r is placed at a position which satisfies that the signal-to-noise ratio of the tensor instrument is more than 10 dB.

Compared with the prior art, the invention has the beneficial effects that:

The invention relates to a magnetic moment testing method of a spacecraft based on magnetic gradient tensor, which improves a near field analysis method, uses a magnetic gradient tensor value to replace a magnetic field value in a near field equation set from the theoretical basis of the near field analysis method, and changes the magnetic field value for measuring the spacecraft and components thereof into the magnetic gradient tensor value for measuring the spacecraft and components thereof in the test. The method is little influenced by an external interference magnetic field, zero-magnetic equipment does not need to be built, and the application range is wider; and a complex error compensation mechanism is not needed, and the method is more flexible.

Drawings

FIG. 1 is a schematic view of a spacecraft and magnetic gradient tensor arrangement;

FIG. 2 is a flow chart of steps of a magnetic moment testing method for a spacecraft based on magnetic gradient tensor.

In the figure, 1, a magnetic gradient tensor instrument 2, a three-axis non-magnetic turntable 3, a spacecraft or a part thereof.

Detailed Description

the invention is further illustrated by the following examples:

The spacecraft magnetic moment testing method based on the magnetic gradient tensor specifically comprises the following steps:

A. the spacecraft or the part thereof is placed on a non-magnetic rotary table, a magnetic gradient tensor instrument is placed on an x' axis of the equatorial plane rotary table of the spacecraft or the part at a position r away from the center of the spacecraft or the part, wherein the position r is placed at a position which satisfies that the signal-to-noise ratio of the tensor instrument is more than 10dB (so as to ensure that the relative error of a calculation result is less than 5 percent), and the schematic diagram is shown in an attached figure 1. r is the distance between the magnetic gradient tensor instrument and the center of the spacecraft or the test piece, x ', y ', z ' are three rotating shafts of the non-magnetic rotary table, and x, y and z are coordinate axes of the spacecraft;

B. Setting the working state of the spacecraft or the component thereof;

C. The output of the magnetic gradient tensor instrument returns to zero;

D. rotating the non-magnetic turntable at intervals of 10 degrees around the z' axis of the turntable by 360 degrees, and measuring B by the magnetic gradient tensor instrument at each angle_ij(r,Φ)

E. Programming with a computer according to equations (1a) - (1c), (2a) - (2c), and(3) calculating to obtain the value M of the remanent magnetic moment (including stray magnetic moment) of the x and y directions of the spacecraft_{x remains},M_{y remains}and a magnetic moment value M in which a z-direction residual magnetic moment (including a stray magnetic moment) is superimposed with a magnetic induction moment_{z sense of remaining +}；

F. Rotating the spacecraft or the components thereof clockwise by 90 degrees around the y axis of the spacecraft to enable the z axis to be in a horizontal plane;

G. repeating the steps C-D;

H. calculating the residual magnetic moment (including stray magnetic moment) value M of the y and z directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3) by using computer programming_{y remains},M_{z remains}And the value M of the magnetic moment which is the superposition of the x-direction remanent magnetic moment (including the stray magnetic moment) and the magnetic induction moment_{feeling of x remaining +}；

I. rotating the spacecraft or the components thereof clockwise by 90 degrees around the z-axis of the spacecraft to enable the x-axis to be in a horizontal plane;

J. Repeating the steps C-D;

K. calculating the residual magnetic moment (including stray magnetic moment) value M of the x and z directions of the spacecraft according to the formulas (1a) - (1c), (2a) - (2c) and (3) by using computer programming_{x remains},M_{z remains}and the value M of the magnetic moment in which the y-direction remanent moment (including the stray moment) is superimposed with the magnetic induction moment_{feeling of y remaining +}；

and L, calculating the magnetic moment of the spacecraft or the component according to the formula (5).

the derivation processes of the formulas (1) to (3) are as follows:

The magnetic flux density generated by the magnetic source is expanded by a vector spherical harmonic as follows:

The form of the written component in the spherical coordinate system is:

The expression of the magnetic gradient tensor in the spherical coordinate system is:

namely, it is

according to a conversion formula between coordinate unit vectors of a rectangular coordinate system and a spherical coordinate system:

getAnd phi is 0, and the magnetic gradient tensor expression is converted to a rectangular coordinate system: b is₁₁＝B_rr,B₁₂＝B_rφ,B₁₃＝-B_rθ,B₂₂＝B_φφ,B₂₃＝-B_φθ,B₃₃＝B_θθ(ii) a Foulier transformation is carried out on the magnetic gradient tensor, and each fundamental component is as follows:

Corresponding to the multipole coefficient equals:

While

The above equation set can be simplified as:

in the formula:

r is the distance between the magnetic gradient tensor instrument and the center of the spacecraft (or the test piece), m;

k is the number of poles of the multipole of the spacecraft (or component thereof). When k is 1, a dipole is represented;

phi is the corresponding initial position, the angle rotated by the spacecraft (or the test piece) (°);

B_ij(r, phi) is the magnetic field component B surrounding each point on the equatorial plane of the spacecraft measured by a magnetic gradient tensor instrument_irate of change in j direction, i, j ═ x, y, z, nT;

a_2k-1,1magnetic dipole moment and multipole moment, A.m, of spacecraft along the X-axis direction of the turntable^2k(M_x’＝a_1,1)；

b_2k-1,1Magnetic dipole moment and multipole moment, A.m, of spacecraft along Y-axis direction of rotary table^2k(M_Y’＝b_1,1)；

a_2k-1,0magnetic dipole moment and multipole moment, A.m, of spacecraft along the Z-axis direction of the rotary table^2k(M_z’＝a_1,0)；