CN101762284B - Determining method of single-frame control moment gyro dynamic unbalance disturbance moment - Google Patents

Abstract

The present invention relates to a determining method of positive cone-shaped single-frame control moment gyro group motion unbalance disturbance moment; a rotor coordinate system, a frame coordinate system and a gyro base coordinate system are built, the gyro rotor disturbance moment in the rotor coordinate system determines the disturbance moment of the gyro rotor in the star coordinate system by continuous coordinate conversion; the determining method fills up the technology blank, attitude disturbance analysis and flutter analysis to quick moonlet are carried out possibly by utilizing disturbance moment continuously, so as to provide basis for judging satellite imagery quality and improving image quality in earlier stage; the determining method can adjust the disturbance moment of the moment gyro by adjusting the installation mode of the gyro and the processing precision of the gyro, so as to achieve the purpose of improving the image quality finally; in the method, the disturbance moment generated by the rotor dynamic unbalance is determined from the point of the disturbance moment generated by the dynamic unbalance of a fixed shaft rotating part by combining the two-freedom-degree rotation of the single-frame control moment gyro rotor through continuous coordinate conversion, the method is simple and easy.

Description

Definite method of the uneven disturbance torque of a kind of positive taper single frame control-moment gyro group motion

Technical field

The present invention relates to a kind of definite method of control-moment gyro unbalance dynamic disturbance torque, particularly the disturbance torque of single frame frame control moment gyro dynamic unbalance generation is determined method, belong to the satellite dynamics technical field, can be used for attitude of satellite interference, flutter analysis.

Background technology

People such as Yin Qiuyan 2007 in " disturbance restraining method research in the counteraction flyback " literary composition from the counteraction flyback movement characteristic, labor the wheel sound is uneven disturbs, set up corresponding mathematics model, adopted corresponding inhibition method and carried out simulation calculation according to the effect characteristics of disturbing.The disturbance torque that produces for the reaction wheel unbalance dynamic determines that research is more at present, and is also comparatively ripe, but less for the research of control-moment gyro disturbance torque.

Development along with quick moonlet, control-moment gyro becomes the preferred configuration of attitude control actuator so that bigger angular momentum ability can be provided, yet the small imbalance that the control-moment gyro rotor quality distributes equally can be in rotary course produces direction and size all in time and the disturbance that changes causes vibratory response, attitude disturbance response and the flutter response of satellite to satellite.At present, also do not have a kind of special method of determining the unbalance dynamic disturbance torque of control-moment gyro, cannot carry out attitude disturbance analysis, flutter analysis etc. to the quick moonlet that adopts control-moment gyro, test the resolution of satellite and whether adhere to specification thereby also just can't pass judgment on the moonlet image quality according to the flutter analysis result.

The present invention is directed to present technological gap, a kind of definite method of disturbance torque of single frame control-moment gyro unbalance dynamic generation has been proposed first, the disturbance torque that utilizes the present invention to determine, can carry out attitude disturbance analysis, flutter analysis to quick moonlet, thereby pass judgment on the satellite imagery quality, the resolution of test satellite can also finally make the resolution of satellite reach designing requirement by the disturbance torque of adjusting control-moment gyro.

The disturbance torque that relevant controlling moment gyro unbalance dynamic at present causes determines that method do not see disclosed pertinent literature report as yet.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of definite method of disturbance torque of single frame control-moment gyro unbalance dynamic generation is provided, fill up the prior art blank, the inventive method provides the input foundation for satellite flutter analysis and flutter to the impact analysis and the final satellite imagery quality of improving of satellite imagery quality.

Technical solution of the present invention is: a kind of definite method of single-frame control moment gyro dynamic unbalance disturbance moment, realize by following steps:

The first step is utilized the rotor quality characteristic test method, obtains the amount J of the principal axis of inertia relative rotation axi line inclined degree of each gyrorotor of tolerance control-moment gyro group _Xz, J _Yz

Second step obtained the dynamic unbalance value and the starting phase angle of gyrorotor according to formula group (1),

$\left\{\begin{array}{c}{I}_0=\sqrt{{J_{\mathrm{xz}}}^2+{J_{\mathrm{yz}}}^2}\\ \cos \mathrm{\φ}=-J_{\mathrm{yz}}/I_0\\ \sin \mathrm{\φ}=J_{\mathrm{xz}}/I_0\end{array}\right.---\left(1\right)$

Wherein, I ₀Be the dynamic unbalance value of gyrorotor, φ is the starting phase angle of gyrorotor dynamic unbalance;

The 3rd step, satellite control system topworks measure portion record each gyrorotor of control-moment gyro group relatively the corner of self framework be angle of rotor γ _iThe corner of relative gyro pedestal with framework is framework corner ζ _i, and the angular velocity that rotates around turning axle of rotor

I=1,2...N, N are total numbers of control-moment gyro;

In the 4th step, utilized for second step obtained I ₀Go on foot the angular velocity that obtains with φ and the 3rd

Obtain gyrorotor at rotor coordinate system ox according to formula (2) _my _mz _mMiddle disturbance torque,

T wherein _DmFor gyrorotor at rotor coordinate system ox _my _mz _mThe disturbance torque of following generation,

Be rotor coordinate system ox _my _mz _mX _mTo, y _mTo unit vector;

In the 5th step, utilize the 3rd to go on foot the angle of rotor γ that obtains _iWith framework corner ζ _i, obtaining frame coordinates according to formula (3), (4) is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix A _RsiWith rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix A _Mri,

$A_{\mathrm{rsi}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\ζ}}_i& \sin {\mathrm{\ζ}}_i\\ 0& -\sin {\mathrm{\ζ}}_i& \cos {\mathrm{\ζ}}_i\end{array}\right]---\left(3\right)$

$A_{\mathrm{mri}}=\left[\begin{array}{ccc}\cos {\mathrm{\γ}}_i& \sin {\mathrm{\γ}}_i& 0\\ -\sin {\mathrm{\γ}}_i& \cos {\mathrm{\γ}}_i& 0\\ 0& 0& 1\end{array}\right]---\left(4\right)$

A _RsiThe frame coordinates that is i gyro is the transition matrix of relative gyro base coordinate system, A _MriIt is the transition matrix of the relative frame coordinates of the rotor coordinate system system of i gyro;

In the 6th step, obtain each gyro base coordinate system ox of positive taper control-moment gyro group by formula (5) _sy _sz _sTo celestial body coordinate system o _bx _by _bz _bTransition matrix, each gyro gimbal axle and satellite celestial body coordinate system o _bx _by _bz _bZ _bAxle coplane, and and z _bThe angle of axle is β, and gimbal axis is at satellite celestial body coordinate plane x _by _bProjection and x _bThe axle clamp angle is α _i,

$M_{\mathrm{sbi}}=\left[\begin{array}{ccc}\sin \mathrm{\β}\cos {\mathrm{\α}}_i& \sin \mathrm{\β}\sin {\mathrm{\α}}_i& \cos \mathrm{\β}\\ -\mathrm{cps\β}\cos {\mathrm{\α}}_i& -\cos \mathrm{\β}\sin {\mathrm{\α}}_i& \sin \mathrm{\β}\\ \sin {\mathrm{\α}}_i& -\cos {\mathrm{\α}}_i& 0\end{array}\right]---\left(5\right)$

Wherein, M _SbiBe the transition matrix of i gyro base coordinate system to the celestial body coordinate system;

In the 7th step, utilize the transition matrix A that obtains in the 5th step _Rsi, A _MriWith the 6th transition matrix M that obtains of step _Sbi, formula (2) through three coordinate conversion, is transformed into satellite celestial body coordinate system from the rotor coordinate system, obtain the disturbance torque T that every i gyrorotor unbalance dynamic produces in satellite celestial body coordinate system _Di,

$T_{\mathrm{di}}={M_{\mathrm{sbi}}}^T\·A_{\mathrm{rsi}}^T\·A_{\mathrm{mri}}^T\·T_{\mathrm{dm}};$

In the 8th step, obtain the disturbance torque T that single frame control-moment gyro group produces in satellite celestial body coordinate system according to formula (6) _d,

$T_d=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{T}_{\mathrm{di}}$

Design concept of the present invention:

1, sets up the coordinate system of using in the analysis

Definition rotor coordinate system ox _my _mz _m, be the rotor body coordinate system, be connected with rotor;

Definition frame coordinate system ox _ry _rz _r, coordinate axis along gimbal axis, axis of torque and rotor angular momentum axle, is connected with framework respectively, initial time ox _ry _rz _rAnd ox _my _mz _mOverlap;

Definition gyro base coordinate system ox _sy _sz _s, when frame corners was zero, it and frame coordinates were ox _ry _rz _rOverlap.Arrange according to the configuration of gyro group and the direction of each gyro gimbal axle, can determine the installation matrix M of each gyro pedestal.Each coordinate system as shown in Figure 1.

2, the conversion between each coordinate system

The corner of the relative framework of control-moment gyro rotor is designated as γ, and the corner of the relative gyro pedestal of framework is designated as ζ.The gyro base coordinate system can be obtained by twice rotation to the conversion of rotor coordinate system, promptly earlier around x _rAxle turns over ζ, again around z _mAxle turns over γ.

Frame coordinates is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix be

Rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix be

For the single frame control-moment gyro group of taper configuration, a certain axon of the gimbal axis of every gyro and celestial body (for example z axle) coplane, with this axle clamp angle β, gimbal axis is at celestial body coordinate plane x _by _bProjection and x _bAxle clamp angle α, the angular momentum of frame corners zero-bit is parallel to x _by _bThe plane can determine that each gyro base coordinate system gets transition matrix to the celestial body coordinate system, and promptly the installation matrix of gyro pedestal is

3, determine disturbance torque that the rotor unbalance dynamic produces according to d'Alembert principle under the rotor coordinate system, the moment of inertia that during rotation of dead axle rotatable parts rotation axis is produced is:

Particularly when constant speed is rotated

$U_d=\stackrel{\→}{k}\×(J_{\mathrm{xz}}\stackrel{\→}{i}+J_{\mathrm{yz}}\stackrel{\→}{j})$

Wherein Be the angular velocity that rotatable parts rotate around dead axle, U _dBe unbalance dynamic, do not overlap by rotor principal axis of inertia and rotation and cause J _Xz, J _YzBe the amount of the principal axis of inertia relative rotation axi line inclined degree of tolerance rotor, obtain by the rotor quality characteristic test.

For the single frame control-moment gyro, its rotor is done uniform rotation around the axis of angular momentum, so the disturbance torque T of rotor unbalance dynamic generation _DmAt rotor coordinate system o _mx _my _mz _mIn be

Order

, I ₀Be unbalance dynamic size tolerance, then following formula can be expressed as

4, determine the disturbance torque that the rotor unbalance dynamic produces under the celestial body coordinate system

Disturbance torque expression formula according to the rotor unbalance dynamic produces under the rotor coordinate system is transformed into it under celestial body coordinate system by continuous coordinate transform, finally determines the disturbance torque that the rotor unbalance dynamic produces under the celestial body coordinate system.

At celestial body o _bx _by _bz _bIn the coordinate system, T _dFor

$T_d={M_{\mathrm{sb}}}^T\·A_{\mathrm{rs}}^T\·A_{\mathrm{mr}}^T\·T_{\mathrm{dm}}$

With each transition matrix substitution above, must the rotor unbalance dynamic be to the disturbance torque that satellite body produces

The present invention compared with prior art beneficial effect is:

(1) the present invention proposes definite method of the disturbance torque of single frame control-moment gyro rotor unbalance dynamic generation first, filled up technological gap, make the later use disturbance torque to quick moonlet carry out the attitude disturbance analysis, flutter analysis becomes possibility, thereby for passing judgment on the satellite imagery quality, improve picture quality, foundation in earlier stage is provided;

(2) machining precision of mounting means that definite method of the present invention can also be by regulating gyro and gyro is adjusted the disturbance torque of control-moment gyro, finally reaches the purpose that improves picture quality;

(3) the present invention is set out by the disturbance torque that the unbalance dynamic of dead axle rotatable parts produces, and in conjunction with the two-freedom rotation of single frame control-moment gyro rotor, by continuous coordinate conversion, determines the disturbance torque that its rotor unbalance dynamic produces, and method is simple.

Description of drawings

Fig. 1 is a single frame control-moment gyro coordinate system synoptic diagram of the present invention;

Fig. 2 is the positive five face cone shape single frame control-moment gyro group configuration synoptic diagram of the present invention.

Embodiment

Be configured as example with five face cone shape single frame gyro groups and specify performing step of the present invention.

One, the gimbal axis of each gyro in the gyro group and satellite celestial body coordinate system o _bx _by _bz _bZ _bAxle coplane, and and z _bThe angle of axle is β, and gimbal axis is at satellite celestial body coordinate plane x _by _bProjection and x _bAxle clamp angle α _i, i=1,2 ... 5, each gyro base coordinate system ox then _sy _sz _sTo celestial body coordinate system o _bx _by _bz _bTransition matrix M _SbiFor

As shown in Figure 2, five face cone shape single frame gyro groups, the gimbal axis of each gyro in the gyro group is at satellite celestial body coordinate plane x _by _bProjection and x _bThe axle clamp angle is respectively α ₁=90 °, α ₂=π-18 °, α ₃=-(π-54 °), α ₄=-54 °, α ₅=18 °, can get the installation matrix of five gyro pedestals in the substitution formula (5).

Two, utilize the rotor quality characteristic test method, obtain the amount J of the principal axis of inertia relative rotation axi line inclined degree of each gyrorotor of tolerance _Xz, J _Yz

Three, obtain the dynamic unbalance value and the starting phase angle of gyrorotor according to formula group (1),

Wherein, I ₀Be the dynamic unbalance value of gyrorotor, φ is the starting phase angle of gyrorotor dynamic unbalance.

Four, satellite control system topworks measure portion record each gyrorotor relatively the corner of self framework be angle of rotor γ _iThe corner of relative gyro pedestal with framework is framework corner ζ _i, and the angular velocity that rotates around turning axle of rotor

Five, obtain each gyrorotor at rotor coordinate system ox according to formula (2) _my _mz _mMiddle disturbance torque,

T wherein _DmFor gyrorotor at rotor coordinate system ox _my _mz _mThe disturbance torque of following generation,

Be rotor coordinate system ox _my _mz _mx _mTo, y _mTo unit vector.

Six, obtaining frame coordinates according to formula (3), (4) is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix A _RsiWith rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix A _Mri

A _RsiThe frame coordinates that is i gyro is the transition matrix of relative gyro base coordinate system, A _MriIt is the transition matrix of the relative frame coordinates of the rotor coordinate system system of i gyro.

Seven, utilize the transition matrix M of formula (5) _SbiAnd the transition matrix A of formula (3), (4) _Rsi, A _Mri, formula (2) through three coordinate conversion, is transformed into satellite celestial body coordinate system from the rotor coordinate system, obtain the disturbance torque T of i gyrorotor in satellite celestial body coordinate system _Di,

$T_{\mathrm{di}}={M_{\mathrm{sbi}}}^T\·A_{\mathrm{rsi}}^T\·A_{\mathrm{mri}}^T\·T_{\mathrm{dm}}.$

Eight, obtain the disturbance torque T of gyro group in satellite celestial body coordinate system according to formula (6) _d,

For the single frame moment gyro group of five face cone shape configurations, ignore the starting phase angle φ of rotor dynamic unbalance _i, can get its rotor unbalance dynamic and be total disturbance torque that celestial body produces

In the formula, ζ _i(i=1,2 ..., 5) and be respectively the corner of five frameworks; γ is the corner of rotor, and five control-moment gyro angle of rotor are identical, is provided by satellite control system topworks measure portion.

So far, determined the uneven total disturbance torque that produces of positive five face cone shape single frame control-moment gyro group motions, for the satellite flutter is determined also and then carry out evaluation of imaging quality the anticipated import foundation is provided.

Above-mentioned definite total disturbance torque substitution based on the flexible spacecraft dynamic modeling method, in conjunction with the stiffness characteristics of moonlet parts, is mainly considered the flexibility of the sun wing, the moonlet flexible spacecraft trembling vibration mechanical equation of foundation

In, utilize the derivation algorithm of ordinary differential equation initial-value problem to resolve, obtain the attitude response of satellite under the effect of flutter disturbance torque, the attitude response of satellite under the effect of flutter disturbance torque deducted utilize the controlled attitude part of attitude of satellite control rule, obtain the flutter response that satellite causes under the effect of flutter disturbance torque, and then carry out satellite flutter response the influence of image quality is passed judgment on.

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (1)

1. definite method of the uneven disturbance torque of positive taper single frame control-moment gyro group motion is characterized in that realizing by following steps:

The first step is utilized the rotor quality characteristic test method, obtains the amount J of the principal axis of inertia relative rotation axi line inclined degree of described each gyrorotor of gyro group of tolerance _Xz, J _Yz

Second step obtained the dynamic unbalance value and the starting phase angle of gyrorotor according to formula group (1),

$\left\{\begin{array}{c}{I}_0=\sqrt{{J_{\mathrm{xz}}}^2+{J_{\mathrm{yz}}}^2}\\ \cos \mathrm{\φ}=-J_{\mathrm{yz}}/I_0\\ \sin \mathrm{\φ}=J_{\mathrm{xz}}/I_0\end{array}\right.---\left(1\right)$

Wherein, I ₀Be the dynamic unbalance value of gyrorotor, φ is the starting phase angle of gyrorotor dynamic unbalance;

The 3rd step, satellite control system topworks measure portion record each gyrorotor of described gyro group relatively the corner of self framework be angle of rotor γ _iThe corner of relative gyro pedestal with framework is framework corner ζ _i, and the angular velocity that rotates around turning axle of rotor

I=1,2...N, N are total numbers of the gyro in the described gyro group;

In the 4th step, utilized for second step obtained I ₀Go on foot the angular velocity that obtains with φ and the 3rd

Obtain gyrorotor at rotor coordinate system ox according to formula (2) _my _mz _mMiddle disturbance torque,

T wherein _DmFor gyrorotor at rotor coordinate system ox _my _mz _mThe disturbance torque of following generation,

Be rotor coordinate system ox _my _mz _mX _mTo, y _mTo unit vector;

In the 5th step, utilize the 3rd to go on foot the angle of rotor γ that obtains _iWith framework corner ζ _i, obtaining frame coordinates according to formula (3), (4) is ox _ry _rz _rRelative gyro base coordinate system ox _sy _sz _sTransition matrix A _RsiWith rotor coordinate system ox _my _mz _mFrame coordinates is ox relatively _ry _rz _rTransition matrix A _Mri,

$A_{\mathrm{rsi}}=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos {\mathrm{\ζ}}_i& \sin {\mathrm{\ζ}}_i\\ 0& -\sin {\mathrm{\ζ}}_i& \cos {\mathrm{\ζ}}_i\end{array}\right]---\left(3\right)$

$A_{\mathrm{mri}}=\left[\begin{array}{ccc}\cos {\mathrm{\γ}}_i& \sin {\mathrm{\γ}}_i& 0\\ -\sin {\mathrm{\γ}}_i& \cos {\mathrm{\γ}}_i& 0\\ 0& 0& 1\end{array}\right]---\left(4\right)$

A _RsiThe frame coordinates that is i gyro is the transition matrix of relative gyro base coordinate system, A _MriIt is the transition matrix of the relative frame coordinates of the rotor coordinate system system of i gyro;

In the 6th step, obtain each gyro base coordinate system ox of described gyro group by formula (5) _sy _sz _sTo satellite celestial body coordinate system o _bx _by _bz _bTransition matrix, each gyro gimbal axle and satellite celestial body coordinate system o _bx _by _bz _bZ _bAxle coplane, and and z _bThe angle of axle is β, and gimbal axis is at satellite celestial body coordinate plane x _by _bProjection and x _bThe axle clamp angle is α _i,

$M_{\mathrm{sbi}}=\left[\begin{array}{ccc}\sin \mathrm{\β}\cos {\mathrm{\α}}_i& \sin \mathrm{\β}\sin {\mathrm{\α}}_i& \cos \mathrm{\β}\\ -\cos \mathrm{\β}\cos {\mathrm{\α}}_i& -\cos \mathrm{\β}\sin {\mathrm{\α}}_i& \sin \mathrm{\β}\\ \sin {\mathrm{\α}}_i& -\cos {\mathrm{\α}}_i& 0\end{array}\right]---\left(5\right)$

Wherein, M _SbiBe the transition matrix of i gyro base coordinate system to satellite celestial body coordinate system;

In the 7th step, utilize the transition matrix A that obtains in the 5th step _Rsi, A _MriWith the 6th transition matrix M that obtains of step _Sbi, formula (2) through three coordinate conversion, is transformed into satellite celestial body coordinate system from the rotor coordinate system, obtain the disturbance torque T that every i gyrorotor unbalance dynamic produces in satellite celestial body coordinate system _Di,

$T_{\mathrm{di}}={M_{\mathrm{sbi}}}^T\·A_{\mathrm{rsi}}^T\·A_{\mathrm{mri}}^T\·T_{\mathrm{dm}};$

In the 8th step, obtain the disturbance torque T that described gyro group produces in satellite celestial body coordinate system according to formula (6) _d,

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