CN106586034A - Self-compensating method for dynamic and still unbalancing disturbance moment of satellite rotating part - Google Patents

Abstract

The invention discloses a self-compensating method for a dynamic and still unbalancing disturbance moment of a satellite rotating part. The dynamic and still unbalancing disturbance moment produced by quick rotating of the rotating part on a satellite can influence the stability of the satellite and reduce the control precision of the satellite. A traditional method for eliminating a dynamic and still unbalancing disturbance moment of a rotating part comprises the steps that the rotating part is subjected to dynamic balancing, and then, active control over dynamic and still unbalancing disturbance is conducted through a satellite attitude control system. The traditional method has limitation to application of rotating parts which are large in inertia, high in rotating speed and irregular in shape. According to the self-compensating method for the dynamic and still unbalancing disturbance moment of the satellite rotating part, two small bias momentum wheels are arranged on the rotating part of the satellite, and the rotating speed of the two bias momentum wheels is set according to the on-orbit calibration result of dynamic and still unbalancing disturbance so that the dynamic and still unbalancing disturbance moment produced during rotating of the rotating part can be eliminated. The self-compensating method is simple, obvious in effect and low in cost, and engineer achieving can be facilitated.

Description

Satellite rotary part Wheel static and dynamic imbalance torque method of self compensation

Technical field

The invention belongs to technical field of spacecraft attitude control, is related to a kind of satellite with rotary part and eliminates rotary part The method of Wheel static and dynamic imbalance torque.

Background technology

With the continuous expansion of Modern Satellite application, load on star, particularly detection application class load, to rotating machine The demand of structure is increasing, and the rotary part on star is more and more, and the inertia of rotary part requires increasing, rotation speed requirements It is more and more faster.

On star rotary part rotate when can be formed rotary shaft axial direction disturbance torque and interference angular momentum, can by Stabilizer is configured on satellite health, is offset by way of synchronous backward rotates.But the barycenter deviation of rotary part and matter Amount skewness, can produce in the surfaces of revolution when rotary part quickly rotates Wheel static and dynamic imbalance (static unbalance disturb and Unbalance dynamic is disturbed).

As shown in Fig. 1 (a) and Fig. 1 (b), rotary part is around rotary shaft z ' z " axle rotation, angular velocity of rotation is ω₀。O_cFor whole Star barycenter, with O_cRotary part frame of reference O is set up for origin_cXYZ, O_cZ axis and rotary shaft z ' z " parallel, O_cX-axis with O_cZ In the vertical plane of axle, the zero-bit direction of rotary part, O are pointed to_cY-axis meets the right-hand rule, coordinate system O with other two axles_cXYZ Do not rotate with rotary part.

Ideally, rotary part Mass Distribution is uniform, and barycenter (O in Fig. 1 in rotary shaft_xPoint), will not produce Raw static unbalance interference and unbalance dynamic are disturbed.

The barycenter of actual rotary part deviates O_xPoint, but and O_xPoint is equivalent to apart from O in the same surfaces of revolution_xPoint r_s It is m that place has a quality_sMass, shown in such as Fig. 1 (a).When rotary part rotates, m_sProduce centripetal force F_s, effect with Whole star barycenter O_c, produce static unbalance disturbance torque T_s, its size is：

T_s=F_s·r_sc=m_sω²r_s·r_sc

T_sIn O_cIn XY faces, direction is rotated and mechanical periodicity with rotary part, when rotary part is in zero-bit state, T_sWith O_cThe angle of X is defined as α₀。

Rotary part is uneven along rotation direction of principal axis Mass Distribution simultaneously, is equivalent to apart from O_xTwo rotations up and down at point h Turn in face, relative to O_x(with rotary shaft apart from r at point symmetry position_d) respectively there is a quality for m_dMass, such as Fig. 1 (b) It is shown.When rotary part rotates, a pair of centrifugal force F that two masses are produced_dForm unbalance dynamic disturbance torque T_d, its size For：

T_d=F_d2h=m_dω²r_d·2h

T_dIn O_cIn XY faces, direction is rotated and mechanical periodicity with rotary part, when rotary part is in zero-bit state, Unbalance dynamic disturbance torque T_dWith angle be defined as β₀。

Wheel static and dynamic imbalance torque T is formed after static unbalance disturbance torque and the superposition of unbalance dynamic disturbance torque_sd.According to T_sAnd T_dCharacteristic understand, T_sdSize be defined as A, work as T_sWith T_dWhen direction is consistent, A takes maximum for (m_sr_sr_sc+2m_dr_dh) ω²；T_sdIt is similarly in O_cIn XY faces, direction is rotated and mechanical periodicity with rotary part, when rotary part is in zero-bit state, T_sdWith O_cThe angle of X is defined as γ₀(-180°≤γ₀≤180°)。

For the interference, traditional way is to enter action balance trim to rotary part, and the barycenter for reducing rotary part is inclined Difference and couple-unbalance, reduce the interference of static unbalance and unbalance dynamic from source, while passing through Satellite Attitude Control System pair again Wheel static and dynamic imbalance carries out active control.It is less for size, the rotary part of regular shape, due to Wheel static and dynamic imbalance Amplitude it is less, said method has certain effect.But big for inertia, rotating speed is fast, rotary part in irregular shape, structure The difficulty of trim is very big, still can remain very big Wheel static and dynamic imbalance after trim in the surfaces of revolution, if passing through satellite completely Posture control system carries out active suppression, very high for the configuration and control performance requirement of posture control system.

For the limitation of the method for breaking traditions, Wheel static and dynamic imbalance when solving the problems, such as that rotary part is rotated on star, carry High satellite control performance, needs a kind of new Research Thinking and solution.

The content of the invention

The technical problem to be solved is：A kind of satellite rotary part Wheel static and dynamic imbalance compensation skill is provided Art, eliminates the interference to satellite when rotary part is rotated on star, improves the control accuracy of satellite.

To solve the problem, the present invention provides satellite rotary part Wheel static and dynamic imbalance torque method of self compensation, bag Include：

Step one, in rotary part or at least two bias momentum wheels of surface configuration, the rotating shaft of the bias momentum wheel Perpendicular to the rotating shaft of rotary part, and mutually angle is not equal to 0 ° or 180 °；

Step 2, acquisition Wheel static and dynamic imbalance torque；

Step 3, the rotating speed that bias momentum wheel is configured according to Wheel static and dynamic imbalance torque, realize Wheel static and dynamic imbalance The in-orbit self compensation of torque.

Further, the first bias momentum wheel and the second bias momentum wheel are configured in the step one, first biasing is dynamic The maximum angular momentum index H of amount wheel_1max, the second bias momentum wheel maximum angular momentum index H_2maxMeet following condition：

H_1max≥A_max/|ω₀|,H_2max≥A_max/|ω₀|

In above formula, ω₀Represent the rotary speed of rotary part, A_maxFor Wheel static and dynamic imbalance torque T_sdMaximum, root It is calculated according to the barycenter deviation and Inertia Characteristics measured value of rotary part.

Further, the step 2 carries out on-orbit calibration to Wheel static and dynamic imbalance torque using the in-orbit angular velocity of satellite, Or Wheel static and dynamic imbalance torque is obtained according to the ground test result of Wheel static and dynamic imbalance torque.

Further, the method that Wheel static and dynamic imbalance torque carries out on-orbit calibration is included using satellite in-orbit angular velocity：

Step 2.1, guarantee satellite attitude stabilization, rotary part is with initial speed ω₀Rotation, inflight measurement Satellite Angle speed Degree, Wheel static and dynamic imbalance torque T_sd0Size A₀For：

I_iIt is satellite to ω_i0The rotary inertia of corresponding reference axis, ω_i0For satellite angular velocity with rotary part rotary shaft The vertical axial component of a certain benchmark, ω_i0,p-pFor ω_i0The peak value of sinusoidal variations.

The step 2 also includes：

Step 2.2, rotary part are kept with initial speed ω₀Rotation, the first bias momentum wheel constant revolution, sound are uneven Weighing apparatus disturbance torque T_sd0With the angle theta of the first momenttum wheel rotary shaft_{h1_sd}Absolute value be：

Wherein, A₁=| ω₀|×|h₁₀| the size of the first control moment produced for the first bias momentum wheel, h₁₀For first Biasing angular momentum；A₂For the first control moment T₁₀With Wheel static and dynamic imbalance torque T_sd0Resultant moment T_{sd_10}Size；

Step 2.3, rotary part are kept with initial speed ω₀Rotation, the first bias momentum wheel are stopped the rotation, the second biasing Momenttum wheel uniform rotation；Wheel static and dynamic imbalance torque T_sd0With the angle theta of the rotary shaft of the second momenttum wheel_{h2_sd}Absolute value be：

A₃For the second control moment T₂₀Size, A₄For the second control moment T₂₀With Wheel static and dynamic imbalance torque resultant moment T_sd0Resultant moment T is formed after superposition_{sd_20}Size；

Step 2.4, Wheel static and dynamic imbalance torque resultant moment T_sd0Direction be：

Further, in step 2, the direction of Wheel static and dynamic imbalance torque is by T_sd0With the angle of 1 rotary shaft of momenttum wheel Absolute value | θ_{h1_sd}| and T_sd0With the absolute value of the angle of 2 rotary shaft of momenttum wheel | θ_{h2_sd}| it is determined that：

Further, in step 3, the rotating speed r of the first bias momentum wheel₁With the rotating speed r of the second bias momentum wheel₂Respectively：

In formula, I₁And I₂Respectively the first bias momentum wheel and the second bias momentum wheel are for the rotary inertia of its rotary shaft； h₁For the angular momentum and h of the first bias momentum wheel₂For the angular momentum of the second bias momentum wheel

Beneficial effects of the present invention include：

By configuring bias momentum wheel, and bias momentum wheel is configured according to Wheel static and dynamic imbalance torque, effectively can be offset The Wheel static and dynamic imbalance torque that rotary part is produced when rotating, improves the gesture stability performance of satellite.

Further, Wheel static and dynamic imbalance compensation method proposed by the present invention adopts in-orbit self-compensating mode, rotating part Part need not enter action balance trim work on ground, simplify satellite and develop flow process；Wheel static and dynamic imbalance proposed by the present invention Method of self compensation is only capable of achieving by installing two small-sized bias momentum wheels, and method is simply effective, and cost of implementation is low, is easy to work Cheng Shixian.

Technical scheme proposed by the present invention has already been through ground simulation checking, and the result shows, by the present invention into Fruit eliminates the Wheel static and dynamic imbalance of rotary part, so as to improve the control performance of posture control system.

Description of the drawings

Fig. 1 (a) disturbs schematic diagram for satellite rotary part static unbalance；Fig. 1 (b) is dry for the unbalance dynamic of satellite rotary part Disturb schematic diagram；

Fig. 2 illustrates for rotary part Wheel static and dynamic imbalance torque method of self compensation principle provided in an embodiment of the present invention Figure.

Specific embodiment

With reference to the accompanying drawings and examples spirit and substance of the present invention are described further.

To eliminate the Wheel static and dynamic imbalance torque that rotary part rotation is produced, rotary part provided in an embodiment of the present invention The principle of Wheel static and dynamic imbalance torque method of self compensation is as shown in Figure 2.

Rotary part Wheel static and dynamic imbalance torque method of self compensation provided in an embodiment of the present invention includes：

Step one, inside rotary part 10 or the first bias momentum wheel 11 and the second bias momentum wheel 22 are installed in surface, In other embodiments of the invention, it would however also be possible to employ multiple bias momentum wheels, principle is similar to.The first bias momentum wheel 11 Rotary shaft and the rotary shaft of the second bias momentum wheel 22 be each perpendicular to the rotary shaft of rotary part 10, and two bias momentum wheels Rotary shaft angle is not zero, as shown in Figure 2 (in Fig. 2, for ease of illustrating, coordinate system is moved on rotary part).In Fig. 2, the The rotary shaft and O of one bias momentum wheel_cThe angle of Z is 90 °, with O_cThe angle of X is φ, the rotary shaft and O of bias momentum wheel 2_cZ Angle be 90 °, with O_cThe angle of X is that ψ, φ and ψ meet following condition：

(1)0≤φ≤360°,0≤ψ≤360°；

(2)φ≠ψ；

Condition (1) shows, as long as ensureing the rotary shaft of the rotary shaft perpendicular to rotary part of two bias momentum wheels, while full On the premise of sufficient condition (2), the installation site of two bias momentum wheels just can be arbitrarily chosen according to the structure of rotary part.

Meet condition (2) and can ensure that the rotary shaft of two bias momentum wheels is not parallel, such that it is able to pass through to adjust two biasings The biasing angular momentum h of momenttum wheel₁And h₂, produce the synthesis biasing angular momentum h of any direction in the rotary part surfaces of revolution_c, be up to To optimal synthetic effect ,=90 ° of | φ-ψ | are typically taken, therefore, the present embodiment is illustrated by taking ψ-φ=90 ° as an example.

The maximum angular momentum index H of the first bias momentum wheel_1maxWith the maximum angular momentum index H of the second bias momentum wheel_2max Meet following condition：

H_1max≥A_max/|ω₀|,H_2max≥A_max/|ω₀|

In above formula, A_maxFor Wheel static and dynamic imbalance torque T_sdMaximum, can be according to the barycenter deviation of rotary part and used Flow characteristic measured value is calculated.

H_1maxAnd H_2maxMeet above-mentioned condition, it is ensured that synthesis angular momentum h in any direction_cIt is sufficiently large, with rotation Part is with angular velocity omega₀During rotation, the coupling torque T of generation_cWheel static and dynamic imbalance torque T can be offset_sd.Consider abundant Amount, H_1maxAnd H_2maxA is taken typically_max/|ω₀| 2～3 times.

Step 2, carrying out on-orbit calibration according to the in-orbit angular velocity of satellite to Wheel static and dynamic imbalance, to obtain sound uneven dry Disturb torque；Or Wheel static and dynamic imbalance torque is obtained according to the ground test result of Wheel static and dynamic imbalance torque.According to dynamic It has been those skilled in the art that the ground test result of static unbalance disturbance torque obtains the method for Wheel static and dynamic imbalance torque It is known, on-orbit calibration is carried out according to the in-orbit angular velocity of satellite to Wheel static and dynamic imbalance in this elaboration and obtains sound imbalance Disturbance torque, the method for obtaining the size and Orientation of Wheel static and dynamic imbalance torque.Concrete calibration process implements as follows：

Step 2.1, ensure satellite attitude stabilization on the premise of, rotary part is with certain initial speed ω₀Rotation, treats rotating speed After stable and satellite three-axis attitude stabilization, Satellite Attitude Control System stops implementing control, makes satellite in Wheel static and dynamic imbalance torque The lower free movement of effect, the persistent period is 2～3 swing circle T₀(T₀=2 π/ω₀)。

Under Wheel static and dynamic imbalance moment loading, satellite angular velocity is in sinusoidal variations, and the cycle is T₀, according to Satellite Angle speed The inflight measurement data of degree, can go out ω with inverse₀Wheel static and dynamic imbalance torque T under rotating speed_sd0Size A₀, computing formula is such as Under：

In formula, ω₀For the initial rotational angular velocity of rotary part.

ω_i0O is typically taken (in a certain reference axis vertical with rotary part rotary shaft for satellite angular velocity_cX-axis or O_cY-axis) The component in direction, can obtain according to the position calculation of Satellite Angle velocity measurement and the reference axis, ω_i0,p-pFor ω_i0It is sinusoidal The peak-to-peak value of change.

I_iIt is satellite to ω_i0The rotary inertia of corresponding reference axis, can be according to satellite Inertia Characteristics measured value and the benchmark The position calculation of axle is obtained.

Step 2.2, on the basis of step 2.1, open the first bias momentum wheel, keep certain constant rotational speed, it is inclined first Put biasing angular momentum h is formed on momenttum wheel rotation direction of principal axis₁₀, the biasing angular momentum h₁₀With rotary part angular velocity omega₀Effect shape Into control moment T₁₀。

Control moment T₁₀Size be A₁, computing formula is as follows：

A₁=| ω₀|×|h₁₀|

T₁₀Direction in the surfaces of revolution of rotary part, with the direction of rotation of rotary part and the first biasing angular momentum h₁₀ Direction meet the right-hand rule, the control moment T of the generation of the first bias momentum wheel₁₀With Wheel static and dynamic imbalance torque T_sd0It is folded Plus after formed resultant moment T_{sd_10}, with step 2.1 in measure A₀Same principle, can obtain T_{sd_10}Amplitude A₂。

According to T₁₀, T_sdAnd T_{sd_10}Amplitude, using the cosine law, Wheel static and dynamic imbalance torque T is obtained_sd0With first The angle theta of bias momentum wheel rotary shaft_{h1_sd}Absolute value, computing formula is as follows：

Step 2.3, on the basis of step 2.2, close the one the first bias momentum wheels, start the second bias momentum wheel, Certain constant rotational speed is kept, biasing angular momentum h is formed₂₀, the biasing angular momentum h₂₀With rotary part angular velocity omega₀Effect forms control Torque T₂₀, control moment T₂₀Size be A₃。

Equally, T₂₀Direction in the surfaces of revolution of rotary part, with the direction of rotation of rotary part and biasing angular momentum h₂₀ Direction meet the right-hand rule, the control moment T that the second bias momentum wheel is produced₂₀With Wheel static and dynamic imbalance torque resultant moment T_sd0Resultant moment T is formed after superposition_{sd_20}, with step 2.1 in measure A₀Same principle, is obtained T_{sd_20}Amplitude A₄。

According to T₂₀, T_sdAnd T_{sd_20}Amplitude, using the cosine law, Wheel static and dynamic imbalance torque T is obtained_sd0With momentum Take turns the angle theta of 2 rotary shafts_{h2_sd}Absolute value, computing formula is as follows：

Sub-step four, according to T_sd0With the absolute value of the angle of 1 rotary shaft of momenttum wheel, and T_sd0With 2 rotary shaft of momenttum wheel The absolute value of angle, determines the direction of Wheel static and dynamic imbalance torque, and method is as follows：

Thus, the on-orbit calibration of satellite Wheel static and dynamic imbalance torque is completed, Wheel static and dynamic imbalance torque is obtained Size and Orientation.

Step 3, according to the Wheel static and dynamic imbalance torque on-orbit calibration result obtained described in step 2, or according to Two bias momentum wheel speeds are configured by the ground test result of Wheel static and dynamic imbalance torque, are realized that sound is uneven and are closed The in-orbit self compensation of torque.

Step 3.1, according to determine Wheel static and dynamic imbalance torque, the angular momentum h to two bias momentum wheels₁And h₂Carry out Arrange, method to set up is as follows：

In formula, ω₀For the working speed of rotary part, A₀For the big of the Wheel static and dynamic imbalance torque demarcated in step 2 It is little, θ_{h1_sd}The direction of the Wheel static and dynamic imbalance torque to determine in step 2.

Step 3.1, according to step 3.1, the rotating speed r to bias momentum wheel₁And r₂It is configured, realizes that sound is uneven dry Disturb the in-orbit self compensation of torque：

In formula, I₁And I₂Respectively the first bias momentum wheel and the second bias momentum wheel are used for the rotation of its rotary shaft Amount.

Example

This example is directed to concrete model satellite, describes the specific embodiment of the embodiment of the present invention.

The version of satellite includes rotary part, and during satellite operation on orbit, rotary part working speed is 20rpm, i.e., Rotational angular velocity is ω₀=2 π/3rad/s.Trim is carried out to rotary part using dynamic balancing machine.

According to the technology of the present invention, as follows, the Wheel static and dynamic imbalance torque of self compensation satellite rotary part.

Step one, the first bias momentum wheel and the second bias momentum wheel, two bias momentum wheels are installed on rotary part surface Rotary shaft be each perpendicular to the rotary shaft of rotary part, the rotary shaft and O of the first bias momentum wheel_cThe angle of X is φ=0 °, the The rotary shaft and O of two bias momentum wheels_cThe angle of X is ψ=90 °.

The configuration of two bias momentum wheels is identical, rotates the rotary inertia on direction of principal axis along which and is：

I₁=I₂=0.0007kgm²

Maximum (top) speed is：

r_1max=r_2max=4000rmp

Corresponding two bias momentums wheel maximum angular momentum index is：

H_1max=H_2max≈0.29Nms

Step 2, on-orbit calibration is carried out according to the in-orbit angular velocity of satellite to Wheel static and dynamic imbalance, obtained at the zero-bit moment Wheel static and dynamic imbalance torque size and Orientation.Concrete calibration process implements as follows：

Step 2.1, ensure satellite attitude stabilization on the premise of, rotary part is with initial speed ω₀=2 π/3rad/s rotations Turn, after stabilization of speed and after satellite three-axis attitude stabilization, Satellite Attitude Control System stops implementing control, makes satellite uneven in sound The lower free movement of disturbance torque effect, continues the 9s times.

In the presence of Wheel static and dynamic imbalance torque, satellite angular velocity is in sinusoidal variations, and the cycle is 3s, is selected in the cycle At a certain moment, according to the inflight measurement data of satellite angular velocity, rotational speed omega can be gone out with inverse₀Under, Wheel static and dynamic imbalance torque T_sd0Size A₀：

A₀=0.3Nm

Step 2.2, on the basis of sub-step one, open momenttum wheel 1, keep constant rotational speed 2000rpm, first biasing The angular velocity omega of biasing angular momentum, the biasing angular momentum and rotary part is formed on momenttum wheel rotation direction of principal axis₀Effect forms control Torque T processed₁₀, control moment T₁₀Size be A₁, control moment T₁₀With Wheel static and dynamic imbalance torque T_sd0Superposition formation is made a concerted effort Square T_{sd_10}, repeat sub-step one, obtain T_{sd_10}Size A₂。

Using the cosine law, the angle of Wheel static and dynamic imbalance torque and the first bias momentum wheel rotary shaft can be obtained θ_{h1_sd}Absolute value：

|θ_{h1_sd}|=π/6rad

Step 2.3, on the basis of sub-step two, close the first bias momentum wheel, start the second bias momentum wheel, keep Constant rotational speed 2000rpm, forms biasing angular momentum, the biasing angular momentum and rotation on the second bias momentum wheel rotation direction of principal axis The angular velocity omega of part₀Effect forms control moment T₂₀, control moment T₂₀Size and A₁It is equal, control moment T₂₀With sound not Balance disturbance torque T_sd0Superposition forms resultant moment T_{sd_20}, repeat step 2.1 obtains T_{sd_20}Size A₄。

Using the cosine law, the angle of Wheel static and dynamic imbalance torque and the second bias momentum wheel rotary shaft can be obtained θ_{h2_sd}Absolute value：

|θ_{h2_sd}|=2 π/3rad.

Step 2.4, according to the result of step 2.2 and step 2.3, in the cycle, synchronization determines Wheel static and dynamic imbalance power The direction of square：

θ_{h1_sd}=-π/6rad

Step 3, according to the Wheel static and dynamic imbalance torque on-orbit calibration result at the moment obtained described in step 2, The rotating speed of two bias momentum wheels is configured.

Step 3.1, the angular momentum h first to two bias momentum wheels₁And h₂It is configured：

Step 3.2, according to the angular momentum of two bias momentum wheel of gained, the rotating speed r to two bias momentum wheels₁And r₂Set Put：

The wherein positive negative indication bias momentum wheel of rotating speed is rotated and reverse.

With reference to satellite Wheel static and dynamic imbalance torque on-orbit calibration result, the first bias momentum wheel at remaining moment and second The rotating speed configuration of bias momentum wheel can also be obtained in this way.

Here description of the invention and application are illustrative, are not wishing to limit the scope of the invention to above-described embodiment In.The deformation and change of embodiments disclosed herein is possible, real for those skilled in the art The replacement and equivalent various parts for applying example is known.It should be appreciated by the person skilled in the art that without departing from the present invention Spirit or essential characteristics in the case of, the present invention can in other forms, structure, arrangement, ratio, and with other components, Material and part are realizing.In the case of without departing from scope and spirit of the present invention, embodiments disclosed herein can be entered Other deformations of row and change.

Claims (7)

1. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation, it is characterised in that include：

Step one, in rotary part or at least two bias momentum wheels of surface configuration, the rotating shaft of the bias momentum wheel is vertical In the rotating shaft of rotary part, and mutually angle is not equal to 0 ° or 180 °；

Step 2, acquisition Wheel static and dynamic imbalance torque；

Step 3, the rotating speed that bias momentum wheel is configured according to Wheel static and dynamic imbalance torque, realize Wheel static and dynamic imbalance torque In-orbit self compensation.

2. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation according to claim 1, it is characterised in that：

The first bias momentum wheel and the second bias momentum wheel, the maximum angular of the first bias momentum wheel are configured in the step one Momentum index H_1max, the maximum angular momentum index H of the second bias momentum wheel_2maxMeet following condition：

H_1max≥A_max/|ω₀|,H_2max≥A_max/|ω₀|

In above formula, ω₀Represent the rotary speed of rotary part, A_maxFor Wheel static and dynamic imbalance torque T_sdMaximum, according to rotation The barycenter deviation and Inertia Characteristics measured value of rotation member is calculated.

3. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation according to claim 1, it is characterised in that The step 2 carries out on-orbit calibration using the in-orbit angular velocity of satellite to Wheel static and dynamic imbalance torque, or uneven according to sound The ground test result of weighing apparatus disturbance torque obtains Wheel static and dynamic imbalance torque.

4. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation according to claim 3, it is characterised in that： The method that Wheel static and dynamic imbalance torque carries out on-orbit calibration is included using satellite in-orbit angular velocity：

Step 2.1, guarantee satellite attitude stabilization, rotary part is with initial speed ω₀Rotation, inflight measurement satellite angular velocity, sound Uneven disturbance torque T_sd0Size A₀For：

$A_0=\frac{I_i\left|{\mathrm{\ω}}_0\right|}{2}\×{\mathrm{\ω}}_{i0,p-p};$

I_iIt is satellite to ω_i0The rotary inertia of corresponding reference axis, ω_i0It is satellite angular velocity vertical with rotary part rotary shaft The axial component of a certain benchmark, ω_i0,p-pFor ω_i0The peak value of sinusoidal variations.

5. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation according to claim 4, it is characterised in that： The step 2 also includes：

Step 2.2, rotary part are kept with initial speed ω₀Rotation, the first bias momentum wheel constant revolution, sound are uneven dry Disturb torque T_sd0With the angle theta of the first momenttum wheel rotary shaft_{h1_sd}Absolute value be：

$\left|{\mathrm{\θ}}_{h1\_sd}\right|=180-acos\left(\frac{{A_0}^2+{A_1}^2-{A_2}^2}{2A_0{A}_1}\right);$

Wherein, A₁=| ω₀|×|h₁₀| the size of the first control moment produced for the first bias momentum wheel, h₁₀For the first biasing Angular momentum；A₂For the first control moment T₁₀With Wheel static and dynamic imbalance torque T_sd0Resultant moment T_{sd_10}Size；

Step 2.3, rotary part are kept with initial speed ω₀Rotation, the first bias momentum wheel are stopped the rotation, the second bias momentum Wheel uniform rotation；Wheel static and dynamic imbalance torque T_sd0With the angle theta of the rotary shaft of the second momenttum wheel_{h2_sd}Absolute value be：

$\left|{\mathrm{\θ}}_{h2\_sd}\right|=180-a\cos \left(\frac{{A_0}^2+{A_3}^2-{A_4}^2}{2A_0{A}_3}\right);$

A₃For the second control moment T₂₀Size, A₄For the second control moment T₂₀With Wheel static and dynamic imbalance torque resultant moment T_sd0 Resultant moment T is formed after superposition_{sd_20}Size；

Step 2.4, Wheel static and dynamic imbalance torque resultant moment T_sd0Direction be：

6. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation according to claim 5, it is characterised in that：

In step 2, the direction of Wheel static and dynamic imbalance torque is by T_sd0With the absolute value of the angle of 1 rotary shaft of momenttum wheel | θ_{h1_sd}| And T_sd0With the absolute value of the angle of 2 rotary shaft of momenttum wheel | θ_{h2_sd}| it is determined that：

7. satellite rotary part Wheel static and dynamic imbalance torque method of self compensation according to claim 5, it is characterised in that：

In step 3, the rotating speed r of the first bias momentum wheel₁With the rotating speed r of the second bias momentum wheel₂Respectively：

$\left\{\begin{array}{c}{r}_1=\frac{30h_1}{{\mathrm{\πI}}_1}\\ r_2=\frac{30h_2}{{\mathrm{\πI}}_2}\end{array}\right.$

In formula, I₁And I₂Respectively the first bias momentum wheel and the second bias momentum wheel are for the rotary inertia of its rotary shaft；h₁For The angular momentum and h of the first bias momentum wheel₂For the angular momentum of the second bias momentum wheel

$\left\{\begin{array}{c}{h}_1=-\frac{A_{0}cos\left({\mathrm{\θ}}_{h1\_sd}\right)}{{\mathrm{\ω}}_0}\\ h_2=-\frac{A_0\sin \left({\mathrm{\θ}}_{h1\_sd}\right)}{{\mathrm{\ω}}_0}\end{array}\right..$