CN109063237A - A kind of system mode calculation method being suitble to more attachment flexible spacecrafts - Google Patents
A kind of system mode calculation method being suitble to more attachment flexible spacecrafts Download PDFInfo
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- CN109063237A CN109063237A CN201810631111.0A CN201810631111A CN109063237A CN 109063237 A CN109063237 A CN 109063237A CN 201810631111 A CN201810631111 A CN 201810631111A CN 109063237 A CN109063237 A CN 109063237A
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- 238000004364 calculation method Methods 0.000 title claims abstract description 16
- 238000013461 design Methods 0.000 claims abstract description 11
- 238000009434 installation Methods 0.000 claims description 14
- 238000012360 testing method Methods 0.000 claims description 5
- 238000013016 damping Methods 0.000 claims description 4
- 239000000463 material Substances 0.000 claims description 3
- 238000004458 analytical method Methods 0.000 abstract description 7
- 230000008878 coupling Effects 0.000 abstract description 7
- 238000010168 coupling process Methods 0.000 abstract description 7
- 238000005859 coupling reaction Methods 0.000 abstract description 7
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- 230000006872 improvement Effects 0.000 description 3
- 230000007246 mechanism Effects 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 238000007796 conventional method Methods 0.000 description 1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
Abstract
The present invention provides a kind of system mode calculation methods for being suitble to more attachment flexible spacecrafts, include the following steps: step A: according to overall tasks demand, determining entire spacecraft total arrangement and centerbody mass property；Step B: the model of spacecraft centerbody is established；Step C: the finite element model of flexible accessory is established；Step D: design and assembly flexible accessory model and spacecraft central body model are pressed；Step E: the system mode of spacecraft is calculated based on the spacecraft Flexible Model about Ecology after combination.The present invention can be calculated using spacecraft centerbody as flexible characteristic, and can meet the dynamic analysis demand of high-precision satellite in view of the coupling between multiple flexible accessories, the in-orbit state of flight of closer satellite.
Description
Technical field
The present invention is based on the finite element models of spacecraft and flexible accessory, for the system suitable for more flexible accessory spacecrafts
Modal calculation method.
Background technique
Different according to the task of spacecraft payload with the development of modern spacecraft technology, spacecraft needs foot
Enough pointing accuracies and stability, and guarantee long-life and high reliability.In the spacecraft that China emitted in recent years, have
Different degrees of flexible accessory coupled resonance has occurred in more spacecrafts in orbit, gradually causes spacecraft totality and appearance
The great attention of rail control system designer.In the design of modern high-precision spacecraft Attitude and orbit control system, task analysis, scheme opinion
The links such as card, l-G simulation test, ground test and on-orbit fault analysis require to calculate the coefficient of coup of flexible accessory and consolidate
There is frequency.
Model analysis be divided into Constrained mode (Constrained Mode) and system mode (Unconstrained Mode,
Also known as Unconstrained mode) two kinds, Constrained mode describes Rigid Base and fixes, flexible accessory undamped-free vibration
Journey embodies inherent characteristic of the flexible accessory under restrained condition, can carry out Constrained mode verification experimental verification on ground；System mode is retouched
What is stated is that Rigid Base is not fixed, flexible accessory undamped-free vibration process, and embodiment is entire spacecraft dynamics system
System characteristics of mode, closer to the in-orbit practical flight situation of spacecraft, but ground is not easy to carry out system mode experimental enviroment.It is flexible attached
Part vibration with spacecraft on other disturbance components interference analysis work answer emphasis consider system mode, it is all close to system mode simultaneously
And the scheme that the direction of motion has the disturbance of coupled relation that should all design isolation or be staggered, to guarantee entire spacecraft dynamics environment
Stability.
By investigation, it is mainly at present Rigid-flexible Coupling Dynamics method about the calculation method of system mode, i.e., carries out first
Flexible spacecraft dynamic analysis modeling extracts the Constrained mode of flexible accessory as a result, last secondly by conventional method
The calculation method of system mode is completed in conjunction with entire spacecraft dynamics model.But there are 2 aspects for Rigid-flexible Coupling Dynamics method
Hypothesis: 1. have ignored the flexible characteristic of spacecraft centerbody in Flexible spacecraft dynamic modeling, and real satellite centerbody
It can deform, the installation site of flexible body is also that can change, for needing to consider the high-precision satellite of micro-vibration, no
It can ignore；2. having carried out mode truncation according to depression of order criterion when the Constrained mode of flexible accessory calculates, this makes multiple flexibilities attached
Coupling between part is weakened.For high-precision satellite, the mistake of the depression of orders criterion cut away portion such as current completeness criterion
Difference cannot be ignored.
For the flexible spacecraft of more attachmentes, the calculation amount of Rigid-flexible Coupling Dynamics method is significantly increased.Consider simultaneously
To needing the result to Rigid-flexible Coupling Dynamics method to check, therefore more attachment flexible spacecrafts are directed to, the invention proposes
The flexible multibody dynamics calculation method of system mode.
Summary of the invention
For the demand that more attachment flexible spacecraft system modes calculate, the invention proposes one kind to be suitble to more attachmentes flexible
The system mode calculation method of spacecraft, includes the following steps:
Step A: according to overall tasks demand, entire spacecraft total arrangement and centerbody mass property are determined；
Step B: the model of spacecraft centerbody is established；
Step C: the finite element model of flexible accessory is established；
Step D: design and assembly flexible accessory model and spacecraft central body model are pressed；The position designed according to satellite configuration
It sets and flexible accessory model is mounted on spacecraft ontology model, form the overall model of flexible spacecraft；
Step E: the system mode of spacecraft is calculated based on the spacecraft Flexible Model about Ecology after combination.
Preferably, in the step A, the installation of the mass property, centroid position and flexible accessory of spacecraft centerbody
Position needs to provide valid data, the data be measured result, or and measured result deviation be not more than 5%.
Preferably, in the step B, spacecraft centerbody is in modeling, mass property in model, centroid position and soft
Property attachment installation site setting need with offer valid data it is consistent.
Preferably, in the step C, when the modeling of the finite element model of flexible accessory, material parameter in model, damping,
Configuration is consistent with flexible accessory time of day, it is ensured that the Constrained mode and flexible accessory Constrained mode test data one of flexible accessory
It causes.
Preferably, in the step D, multiple flexible accessories can be mounted on spacecraft centerbody simultaneously, is installed
Position and design input are consistent.
It preferably,, can be in-orbit according to spacecraft when being calculated based on spacecraft Flexible Model about Ecology in the step E
Working condition, the setting flexible accessory angular relationship different from spacecraft centerbody is (for example, sun battle array is located at different drivings
Angle), the changing rule of the system mode of spacecraft under various working is calculated.
The model of ontology both can simplify into the rigid body containing mass property in the present invention, can also with true spacecraft sheet
The consistent finite element model of body flexible characteristic；Spacecraft ontology model can install multiple flexible accessory models simultaneously.
The present invention can be calculated using spacecraft centerbody as flexible characteristic, and can in view of multiple flexible accessories it
Between coupling, closer to satellite in-orbit state of flight, meet the dynamic analysis demand of high-precision satellite.
Detailed description of the invention
Upon reading the detailed description of non-limiting embodiments with reference to the following drawings, other feature of the invention,
Objects and advantages will become more apparent upon:
Fig. 1 is the spacecraft central body model schematic diagram in the embodiment of the present invention；
Fig. 2 is the finite element model of the flexible accessory in the embodiment of the present invention；
In figure: 1- spacecraft centerbody centroid position；2- spacecraft+x wing sun battle array installation site；3- spacecraft-x the wing is too
Positive battle array installation site.
Specific embodiment
The present invention is described in detail for satellite below with reference to certain carrying double-vane solar battery array.Following embodiment
It will be helpful to those skilled in the art and further understand the present invention, but the invention is not limited in any way.It should be understood that
It is that those skilled in the art, without departing from the inventive concept of the premise, several improvement can also be made.
These are all within the scope of protection of the present invention.
The embodiment of the invention provides a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts, including it is as follows
Step:
1) according to overall tasks demand, the total arrangement and mass property of entire spacecraft are determined
The input condition of the calculating of Space Vehicle System frequency specifically includes that 1. coordinate system defines (attachment local coordinate system)；
2. the quality of spacecraft centerbody, centroid position, rotary inertia；3. the installation point position of flexible accessory, the definition of corner polarity.
In order to ensure the Space Vehicle System mode being calculated is consistent with in-orbit measured result, in combing input condition
When, optimum state is that production in kind is completed in spacecraft, and all input conditions have measured data；If there is no measured data,
It then requires the overall configuration of spacecraft to design to complete, single machine installation site and Xing Shang cable net layout are end-state, are based on this
Design point obtains required calculating input, and the calculated result of all input conditions and the deviation of measured result are not more than 5%.
2) model of spacecraft centerbody is established
The model of spacecraft centerbody generally can simplify as rigid model, this is because centerbody is in design by structure
The constraint of intensity, structure fundamental frequency are generally at least 10Hz magnitude, much larger than fundamental frequency (the 0.1Hz magnitude or more of flexible accessory
It is low), as shown in Figure 1, this is the simplification rigid model an of satellite body, the outer dimension of the cuboid is in no specific requirement
Under the premise of be arranged to the largest enveloping of satellite body.
It is created and is corresponded on spacecraft centerbody according to the installation site of spacecraft centerbody centroid position and flexible accessory
Coordinate points, can remember the entitled cm of center of mass point；Mass property is assigned to spacecraft central body model, specific value is according to calculating
Input setting, the reference point of rotary inertia need to be set as cm.
3) finite element model of flexible accessory is established
When the finite element model modeling of flexible accessory, material parameter, damping, configuration and flexible accessory time of day in model
Unanimously, the mass property (quality, center of gravity, inertia) of flexible accessory finite element model should be with practical equal, flexible accessory (such as sun
Battle array etc.) if there is driving mechanism, need to reflect the characteristic (quality, rigidity, damping etc.) of driving mechanism part in a model, it is desirable that
First three the order frequency deviation for Constrained mode and flexible accessory the Constrained mode test that the finite element model of flexible accessory is calculated
No more than 5%.
The finite element model for the flexible accessory used in step 4) is the model that installation point is free state, when be somebody's turn to do from
When being fixed by the installation point of the finite element model of state, the modal parameter for the flexible accessory being calculated should be with the pact of the attachment
Beam modal parameter is completely the same.
4) design and assembly flexible accessory model and spacecraft central body model are pressed
When assembling flexible accessory model and spacecraft central body model, the installation point for needing to be arranged flexible accessory is connected in
In installation site on spacecraft central body model.The phase between flexible accessory and spacecraft centerbody is needed to pay attention in assembling
To position relation, it is ensured that flexible accessory installs polarity and design input is consistent.
When containing multiple flexible accessories in Spacecraft guidance and control, it should which multiple flexible accessories are mounted on spacecraft center simultaneously
On body, installation site and angle definition should be identical as input, so that it is guaranteed that the subsequent spacecraft system being calculated based on this model
Mode of uniting and the in-orbit state consistency of spacecraft.
5) system mode of spacecraft is calculated based on the spacecraft Flexible Model about Ecology after combination
When being calculated based on spacecraft Flexible Model about Ecology, when flexible accessory is different from the relative angular relationship of spacecraft centerbody
When, the parameters such as inertia, mass center of spacecraft change, so that the Space Vehicle System frequency being calculated has difference.
When the inertia accounting of flexible accessory is larger, and in-orbit and spacecraft centerbody relative position can change, then need to calculate
Flexible accessory is from the system mode under spacecraft centerbody different angle relationship (for example, sun battle array is located at different driving angles
Degree), to obtain the changing rule of Space Vehicle System mode.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the principle of the present invention, it can also make several improvements and retouch, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (6)
1. a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts, characterized by the following steps:
Step A: according to overall tasks demand, entire spacecraft total arrangement and centerbody mass property are determined；
Step B: the model of spacecraft centerbody is established；
Step C: the finite element model of flexible accessory is established；
Step D: design and assembly flexible accessory model and spacecraft central body model are pressed；
Step E: the system mode of spacecraft is calculated based on the spacecraft Flexible Model about Ecology after combination.
2. a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts as described in claim 1, it is characterised in that:
In the step A, the installation site of the mass property of spacecraft centerbody, centroid position and flexible accessory needs to provide effective
Data, the data be measured result, or and measured result deviation be not more than 5%.
3. a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts as described in claim 1, it is characterised in that:
In the step B, spacecraft centerbody is in modeling, the installation position of mass property in model, centroid position and flexible accessory
The setting set needs consistent with the valid data provided.
4. a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts as described in claim 1, it is characterised in that:
In the step C, when the finite element model of flexible accessory models, material parameter, damping, configuration and flexible accessory are true in model
Real state consistency, it is ensured that the Constrained mode of flexible accessory is consistent with flexible accessory Constrained mode test data.
5. a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts as described in claim 1, it is characterised in that:
In the step D, multiple flexible accessories can be mounted on spacecraft centerbody simultaneously, installation site and design input one
It causes.
6. a kind of system mode calculation method for being suitble to more attachment flexible spacecrafts as described in claim 1, it is characterised in that:
In the step E, when being calculated based on spacecraft Flexible Model about Ecology, working condition that can be in-orbit according to spacecraft is arranged soft
The property attachment angular relationship different from spacecraft centerbody, is calculated the variation of the system mode of spacecraft under various working
Rule.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109612666A (en) * | 2019-01-09 | 2019-04-12 | 上海卫星工程研究所 | The in-orbit relative displacement method and system of satellite flexible appendage is recognized using gyro data |
| CN111123702A (en) * | 2019-12-05 | 2020-05-08 | 上海航天控制技术研究所 | Large flexible spacecraft dispersion coordination robust control method based on consistency theory |
| CN112131764A (en) * | 2020-08-24 | 2020-12-25 | 航天科工空间工程发展有限公司 | Device and method for calculating satellite flexible coupling coefficient and calculating equipment |
Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101286281A (en) * | 2008-06-03 | 2008-10-15 | 清华大学 | Rigid-elastic liquid coupled spacecraft physical simulation experiment system |
| CN102073280A (en) * | 2011-01-13 | 2011-05-25 | 北京科技大学 | Fuzzy singular perturbation modeling and attitude control method for complex flexible spacecraft |
| CN104483835A (en) * | 2014-11-06 | 2015-04-01 | 中国运载火箭技术研究院 | T-S fuzzy model-based flexible spacecraft multi-objective integrated control method |
| CN105631167A (en) * | 2016-03-03 | 2016-06-01 | 北京空间飞行器总体设计部 | Aircraft thermally-induced vibration dynamics response evaluation method |
| CN105955332A (en) * | 2016-06-02 | 2016-09-21 | 北京航空航天大学 | Constraint gyro flexible body actuating mechanism optimizing configuration method |
| CN106295196A (en) * | 2016-08-12 | 2017-01-04 | 上海卫星工程研究所 | A kind of modal calculation method in-orbit with rotational flexibility sun battle array satellite |
| CN107089348A (en) * | 2017-04-01 | 2017-08-25 | 中国空间技术研究院 | On-orbit fault game method based on many flexible accessory satellite dynamics optimized Control Modes |
| US9776741B1 (en) * | 2016-06-02 | 2017-10-03 | Beihang University | Method for refined attitude control based on output feedback for flexible spacecraft |
| CN107885911A (en) * | 2017-10-24 | 2018-04-06 | 航天东方红卫星有限公司 | A kind of satellite random vibration test thrust appraisal procedure |
| CN107941441A (en) * | 2017-11-14 | 2018-04-20 | 北京卫星环境工程研究所 | Determine the method that the in-orbit border of simulation influences the in-orbit dynamics of spacecraft |
-
2018
- 2018-06-19 CN CN201810631111.0A patent/CN109063237A/en active Pending
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101286281A (en) * | 2008-06-03 | 2008-10-15 | 清华大学 | Rigid-elastic liquid coupled spacecraft physical simulation experiment system |
| CN102073280A (en) * | 2011-01-13 | 2011-05-25 | 北京科技大学 | Fuzzy singular perturbation modeling and attitude control method for complex flexible spacecraft |
| CN104483835A (en) * | 2014-11-06 | 2015-04-01 | 中国运载火箭技术研究院 | T-S fuzzy model-based flexible spacecraft multi-objective integrated control method |
| CN105631167A (en) * | 2016-03-03 | 2016-06-01 | 北京空间飞行器总体设计部 | Aircraft thermally-induced vibration dynamics response evaluation method |
| CN105955332A (en) * | 2016-06-02 | 2016-09-21 | 北京航空航天大学 | Constraint gyro flexible body actuating mechanism optimizing configuration method |
| US9776741B1 (en) * | 2016-06-02 | 2017-10-03 | Beihang University | Method for refined attitude control based on output feedback for flexible spacecraft |
| CN106295196A (en) * | 2016-08-12 | 2017-01-04 | 上海卫星工程研究所 | A kind of modal calculation method in-orbit with rotational flexibility sun battle array satellite |
| CN107089348A (en) * | 2017-04-01 | 2017-08-25 | 中国空间技术研究院 | On-orbit fault game method based on many flexible accessory satellite dynamics optimized Control Modes |
| CN107885911A (en) * | 2017-10-24 | 2018-04-06 | 航天东方红卫星有限公司 | A kind of satellite random vibration test thrust appraisal procedure |
| CN107941441A (en) * | 2017-11-14 | 2018-04-20 | 北京卫星环境工程研究所 | Determine the method that the in-orbit border of simulation influences the in-orbit dynamics of spacecraft |
Non-Patent Citations (3)
| Title |
|---|
| MARCO SABATINI, PAOLO GASBARRI, RICCARDO MONTI, GIOVANNI BATTIST: ""Vibration control of a flexible space manipulator during on orbit operations"", 《ACTA ASTRONAUTICA》 * |
| 柴洪友，高峰编著: "《航天器结构与机构》" * |
| 郭其威，吴松，刘芳，唐国安: ""航天器柔性附件对整器固有振动特性影响因素及规律分析"", 《振动与冲击》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109612666A (en) * | 2019-01-09 | 2019-04-12 | 上海卫星工程研究所 | The in-orbit relative displacement method and system of satellite flexible appendage is recognized using gyro data |
| CN109612666B (en) * | 2019-01-09 | 2020-07-14 | 上海卫星工程研究所 | Method and system for identifying on-orbit relative displacement of satellite flexible accessory by utilizing gyroscope data |
| CN111123702A (en) * | 2019-12-05 | 2020-05-08 | 上海航天控制技术研究所 | Large flexible spacecraft dispersion coordination robust control method based on consistency theory |
| CN111123702B (en) * | 2019-12-05 | 2022-06-24 | 上海航天控制技术研究所 | Large flexible spacecraft dispersion coordination robust control method based on consistency theory |
| CN112131764A (en) * | 2020-08-24 | 2020-12-25 | 航天科工空间工程发展有限公司 | Device and method for calculating satellite flexible coupling coefficient and calculating equipment |
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Application publication date: 20181221 |