Effect of Structure Flexibility on Attitude Dynamics of Modernizated Microsatellite

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Research Objectives and TasksResearch Objectives and Tasks MicroMicro satellite Configurationsatellite Configuration Reference framesReference frames Mathematical Models of Mathematical Models of flexible space flexible space

structuresstructures Major Findings and ResultsMajor Findings and Results Recommendations for Future ResearchRecommendations for Future Research

OverviewOverview

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The major objective ofThe major objective of this research this research is to study is to study the effect of structure flexibility on attitude the effect of structure flexibility on attitude behavior (Euler angles and angular velocities ) behavior (Euler angles and angular velocities ) of micro satellites and the degree of such effectof micro satellites and the degree of such effect

Research Objectives and TasksResearch Objectives and Tasks

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The research objectives and tasks of this The research objectives and tasks of this study are asstudy are as followsfollows :: Develop mathematical modelsDevelop mathematical models of flexible space of flexible space

structuresstructures Determine the Determine the attitude accuracy attitude accuracy

Research Objectives and TasksResearch Objectives and Tasks

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The construction of micro satellite can consist of main The construction of micro satellite can consist of main partsparts:: base plate, mounting plate, walls, blocks and the base plate, mounting plate, walls, blocks and the payloads.payloads.

Each part and subpart of this construction will be replaced Each part and subpart of this construction will be replaced by the equivalent solid mass and moment of inertia with by the equivalent solid mass and moment of inertia with respect to the real construction.respect to the real construction.

Micro Satellite ConfigurationMicro Satellite Configuration

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Micro Satellite ConfigurationMicro Satellite Configuration

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Micro Satellite ConfigurationMicro Satellite Configuration

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Reference FramesReference Frames

Inertial coordinate system Inertial coordinate system (ICS)(ICS)

Orbital coordinate system Orbital coordinate system (OCS)(OCS)

Design coordinate system Design coordinate system (DCS)(DCS)

Body axes system (BAS)Body axes system (BAS)

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Mathematical Models of FMathematical Models of Flexible lexible SSpace pace SStructurestructures

A mathematical model of the satellite takes into A mathematical model of the satellite takes into account flexible body components (solar panels, account flexible body components (solar panels, antennas, booms etc…); antennas, booms etc…);

This kind of modelling consists of two parts one This kind of modelling consists of two parts one related to rigid body motion and the other to related to rigid body motion and the other to flexible body motion.flexible body motion.

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Mathematical Models Of FMathematical Models Of Flexible lexible SSpace pace SStructurestructures

Two kind of software will be used Two kind of software will be used ANSYSANSYS and and MATLABMATLAB;;

ANSYSANSYS software will be used to calculate the modal software will be used to calculate the modal analysis (natural frequencies and mode shapes) ;analysis (natural frequencies and mode shapes) ;

MATLABMATLAB software will be used to integrate the system software will be used to integrate the system of equations .of equations .

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Mathematical Models Of FMathematical Models Of Flexible lexible SSpace pace SStructurestructures

Finite Element ModelFinite Element Model :

SHELL 99SOLID 92

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Mathematical Models Of FMathematical Models Of Flexible lexible SSpace pace SStructurestructures

The dynamic equations of motion around center of mass taken The dynamic equations of motion around center of mass taken into account the elastic oscillations of a housing of satellite and into account the elastic oscillations of a housing of satellite and solar panels can be written in the following form :solar panels can be written in the following form :

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The calculation of flexible modes elements (The calculation of flexible modes elements (GGααi)i) are usually are usually determined by the following way in BAS :determined by the following way in BAS :

ρb : : is a radius vector that connects satellite COM to any arbitrary point is a radius vector that connects satellite COM to any arbitrary point

of the satelliteof the satellite construction;construction;

Uαi :: is a vector is a vector to to describe the mode shape.describe the mode shape.

Mathematical Models Of FMathematical Models Of Flexible lexible SSpace pace SStructurestructures

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Mathematical Models Of FMathematical Models Of Flexible lexible SSpace pace SStructurestructures

Lines of micro satellite used for representing flexible elements.Lines of micro satellite used for representing flexible elements.

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Mathematical Models Of FMathematical Models Of Flexible lexible SSpace pace SStructurestructures

The satellite kinematics equations will be in the The satellite kinematics equations will be in the following form following form ::

ωωbo : : is the satellite body angular velocity with respect to the OCS;is the satellite body angular velocity with respect to the OCS;

, , ,, : : are EULER angles pitch, roll and yaw respectively.are EULER angles pitch, roll and yaw respectively.

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Finding and Major ResultsFinding and Major Results

Average values for frequencies (Average values for frequencies (ffii) for the first six tones ) for the first six tones groups are equal to: 14; 26.7; 65.5; 86.9; 90.2; 113 Hz groups are equal to: 14; 26.7; 65.5; 86.9; 90.2; 113 Hz respectivelyrespectively;;

It is noted that the first five tones groups is related to the It is noted that the first five tones groups is related to the solar panels of the satellite and at the group tone number solar panels of the satellite and at the group tone number six is for the housing.six is for the housing.

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Finding and Major ResultsFinding and Major Results

Micro satellite solar panels 2nd tones groups.Micro satellite solar panels 2nd tones groups.

26.85

HZ

27.02

HZ

26.99

HZ

27.03

Hz

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Finding and Major ResultsFinding and Major Results

113.36

HZ

Micro satellite housing 1st tone. Micro satellite housing 1st tone.

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Finding and Major ResultsFinding and Major Results

The simulations of satellite dynamics (Euler angles and angular velocities) is carried out using MATLAB software on the following two cases :

On the satellite as aOn the satellite as a RIGID BODYRIGID BODY On the satellite as aOn the satellite as a FLEXIBLE BODYFLEXIBLE BODY (taking (taking

into account vibration modes of the satellite)into account vibration modes of the satellite)

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On both the above situations the On both the above situations the gravitational gravitational momentmoment is the only external moment is the only external moment

Result of simulation are shown in the following Result of simulation are shown in the following figuresfigures.. From this results it is noted that their is From this results it is noted that their is unobserved differentunobserved different between rigid and flexible between rigid and flexible body simulationsbody simulations

Finding and Major ResultsFinding and Major Results

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Finding and Major ResultsFinding and Major Results

Simulation of attitude dynamics (angular velocities) with and without flexible Simulation of attitude dynamics (angular velocities) with and without flexible momentsmoments

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Simulation of attitude dynamics (Euler angles ) with and without flexible momentsSimulation of attitude dynamics (Euler angles ) with and without flexible moments

Finding and Major ResultsFinding and Major Results

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Finding and Major ResultsFinding and Major Results

Error of attitude dynamics (Euler angles and angular velocities) due to flexible Error of attitude dynamics (Euler angles and angular velocities) due to flexible moment in 20 secmoment in 20 sec

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Recommendations for designers and engineers concerning the satellite structure flexibility necessities within the framework of the following : Resolution requirements of the payload Satellite attitude accuracy requirements Satellite structural layout diagram

Recommendations For Future ResearchRecommendations For Future Research