ON THE STATIC AND DYNAMIC ANALYSIS OF A SMALLSATELLITE (MESBAH)

M. Sedighi, B. MohammadiMechanical Engineering Department, IROST, Tehran, IRAN

(E-mail : sedighi@irost.com)

ABSTRACT

The static and dynamic structural behavior of a micro-satellite has been studied using Finite ElementMethod. At first, the micro-satellite has been modeled parametrically using ANSYS code and afterseveral computations and initial satisfaction for static loads with an acceptable safety factor, the geometryparameters initially freezed for dynamic analysis. Then, based on the data provided by ARIANE-5launcher, the criteria for safe vibration range are extracted. The natural frequencies of the satellite havebeen derived by changing the most effective geometry parameters like tray thickness and stringer height.By using these results, the optimum shape of the satellite has been designed.

1. INTRODUCTION

MESBAH, a tele-communication small satellite for store and forward data service to be deployed in apolar sun synchronous LEO orbit of 893 km altitude is being design and manufactured at IROST.MESBAH has a LEO orbit with tip mass and gravity boom for attitude control. Its structure is made ofmodular trays in cubic shape (50x50x50 cm).

One of the important issues rises on the structural analysis of a satellite is the behavior of structureunder the dynamic loads during launching period. If the natural frequencies of the structure and theapplied load frequency be in the same range, resonance phenomenon happens which could cause thesevere damages on the structure and the components. There are some important tasks that should beimplemented in dynamic design of satellite structure. These tasks are: 1) The nature of the applieddynamic loads, 2) Recognition of frequency range, and 3) Obtaining the initial natural frequency.

In general the sources of applied load on the structure can be divided into four types:• Static or quasi-static external loads: These loads are related to the accelerations forces applied

on the structure and component during launching the satellite into the supposed orbit.• Static or quasi-static internal loads: Some of these types of loads could be compression

forces in driver, pre-stresses in mechanical components and thermo-elastic stresses.• Dynamic external loads: Some of these types of loads could be Engine trust, sonic forces,

forces caused by air turbulence effect on the launcher (Gust), Impulse thrust for orbitaladjustment, and loads caused by transportation from manufacturing site to launching site.

• Dynamic internal loads: Forces cause by internal motion for satellite attitude control likemomentum wheel, magnetic torquer or any other type of electric servo-motors.

On the bases of above four types of forces it can be decided that the first two types are for staticanalysis and the next two types are for dynamic analysis.

2. LAUNCHING LOADS AND FREQUENCY REQUIRMENTS

The launcher for MESBAH has been initially assumed to be ARIANE 5, and based on the frequencyrange and the range of dynamic excitations loads, the following conditions (table 1&2) have beenassumed [1].

Table 1- Static loadsLongitudinal Lateral

Acceleration (g=9.8 m/s2)/Static only 7g 1.5gAcceleration (g=9.8 m/s2)/Static + Dynamic 11 g 6 g

Table 2: Dynamic loads (Sinusoidal loads)Frequency range Qualification level Acceptance level

Longitudinal 4-6 / 6-100 17.3 mm/ 3.75 g 13.9 mm/ 3 gLateral 2-100 2.5 g 2 g

3. PARAMETRIC DESIGN

The aim of parametric modeling of MESBAH is to use optimization facilities provided in ANSYS FEsoftware [2] and also using APDL (ANSYS Parametric Design Language). At first stage, based onsimilar structures like SUNSAT, SAPPHIRE, BLUESAT, and KOMPSAT2 [3,4,5] a modular structurecontaining 10 frames has been considered as the primary type of construction. A schematic view ofMESBAH has been shown in Fig.-1. Five trays (machined from 2024-T3 Aluminum slabs)accommodate different modules (table-3).

At first step of parametric design, since the internal dimensions of satellite were not decided, framethickness, tray thickness, column dimension, height of supporting stringers, and the thickness ofsupporting stringers have assumed as variable parameters in a geometry file written in APDL.

Fig.-1:. MESBAH trays and components.

Table 3: Weight budgets for different traysTray No. Name Weight (Kg)1 Control 102 Telemetry and Tele command 63 Data handling system 2.54 Communication 35 Battery & power systems + solar panels 7+5

4. STATIC ANALYSIS

In the static analysis, the component masshas been applied on the trays, and the endsurface of bottom tray column have used asfixed points for boundary conditions(launcher attachment). After several run, theoptimum value for the discussed geometricparameters have been finalized with a safetyfactor equal 5 for the maximum stress. Thehighest stress value is observed in powersupply tray (fig.-2). The structure optimumweight has been calculated equal to 9.64 kg[6] with:

Frame thickness = 1 mmTray thickness = 1 mmColumn dimension = 30x 30 mm Fig.-2: Von mises stress in power supply trayHeight of supporting stringers =20 mmThickness of supporting stringers= 1 mm

5. DYNAMIC ANALYSIS

Methodology for dynamic design approach: In general there are four methods four analysis anddynamic control of satellite which are: 1) Using passive or active damping; In this method we could usematerials with high damping coefficient or in active case, actuators are used. 2) Controlling anddecreasing dynamic response of structure in sensitive sections; in this method, actuators are used inspecified sections, which are very sensitive to vibration and displacement. For instance, in the satellitethat camera location is very important, the method is applied for reducing the vibration at that specifiedregion. 3) Frequency separation; this method is one of the most common approaches used for vibrationcontrol. In this method the designer try to shift the natural frequency of the structure to a safe range farfrom the excitation loads frequency. 4) Controlling the applied load function; In this method we try tocontrol the applied load to not happen in the same frequency as the system first natural frequency appears.

By considering MESBAH characteristics and four suggested above methods, it could be released thatthe best-fitted method is third method. The first method needs viso-elastic or vibration damping systemthat increases the cost and weight of the satellite. The second approach is not applicable due to lack ofsensitive section in MESBAH base on its mission (like camera). In the forth approach, since we do nothave any control over the loads caused by launcher, as user we have to take into account the launcherspecification as design constrains. So as the unique solution, the designer has to change the geometricalparameters. Actually this can decrease the system response to excitations loads and prevents fromresonance phenomenon.

To avoid dynamic coupling between the low frequency vehicle and satellite modes, based on theLauncher loads and frequency requirements discussed earlier, the satellite should be designed with astructural stiffness which ensures that:

- The first natural frequency of the satellite in the longitudinal axis is > 100 HZ - The first natural frequency of the satellite in the lateral axes are > 50 HZModal Analysis by Finite Element Method: Based on the FE model for preliminary design stage

that has been used for static analysis a series of modal analyses have been conducted by using ANSYSFE code. The tray thickness and stringer height have used as two important parameters for obtaining thefirst five natural frequencies of structure. As a critical point the third tray results have been presented intable-4 and table-5.

Table-4: The first five natural Frequencies (Stringer height as constant parameter: h=60 mm)Natural frequency in longitudinal direction (Hz) Natural frequency in lateral direction (Hz)Trays

Thickness 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th

2 mm 41.5 49.3 72.9 100.2 100.4 41.8 49 69.3 71 101.8

4 mm 50.8 58.4 74.19 74.8 105.5 50.8 52.9 74.19 75 103

6 mm 52.7 63.3 74.8 75 106 51.5 53 74.8 75 104

10 mm 53.5 75.1 102 106.1 136.4 53.6 53.7 75 75.1 106.1

Table-5: The first five natural Frequencies (Tray thickness as constant parameter: t=6 mm)Natural frequency in longitudinal direction (Hz) Natural frequency in lateral direction (Hz)Stringer

height 1st 2nd 3rd 4th 5th 1st 2nd 3rd 4th 5th

0 mm 39.9 43.4 64.3 64.4 75.8 19.4 46.1 51.7 64.1 70.4

20 mm 51.3 74.4 74.8 101.6 105.8 52.3 52.9 74.4 78.7 105.8

40 mm 52.3 74.7 74.9 102 105.9 52.4 53.2 74.7 75.6 105.9

60 mm 52.7 74 74.8 102.5 106 50.8 52 74.1 76 105

As we can see in the above table, in spite ofincreasing the stringer height, and tray & stringerthickness, the dynamic design criteria has notbeen satisfied. Also it can be observed that at thepresence of stringer we have quiet considerableeffect on shifting of the first natural frequency tohigher values. By using an array of stringers (with 4 x 4 divisions) below all of tray surfaces(fig.-3), it can be seen that a Fig-3: Supported tray (4x4 array)

quiet significant shift appears for the first natural frequency. For the array stringer height andthickness equal 20 mm and 4mm respectively; the first four natural frequencies in longitudinal directionare: 255, 350, 470, 620 Hz and the first four natural frequencies in lateral direction are: 200, 280,400, 490 Hz.

6. RESULTS AND DISCUSSION

In the static analysis, a safety factor higher than 5 has been obtained (tray thickness=1, stringer height=20), but the first natural frequency is quiet below the launcher requirements and dynamic designcondition. Table-4 presents that increasing trays and stringer thickness have a very minor effect onshifting the first natural frequency to higher values. Increasing the stringer height has initial considerableeffect on the frequencies, but the stringer height higher than 20 mm has very small effect. So it could beconcluded that stringer height should be fixed at 20 mm (see table-5). In addition, it can be observedthat at the absence of stringers, the first natural frequency dropped dramatically. So the trays can bedivided into smaller sections with more stringers attached to tray bottom surface (fig.-3, an array of 4x4cells). This can help us to use mass more efficiently. This fact can be seen clearly in the results. Thegeometry with 4x4 cells trays has the first natural frequency higher than requirements. So a shorterstringers height or even tapered stringers can decrease the weight and keep the initial frequencies still atsafe side.

7. CONCLUSION

The tasks which are obtaining natural frequencies, recognition of frequency range, and the nature of theapplied dynamic loads have been explained. These tasks are necessary for avoiding resonance phenomenonin the structure. Then, based on ARIANE-5 launcher, launching loads and frequency requirements has beenshown. Parametric design approach was used to model geometry to minimize the design loops foroptimization. The static analysis results shows that a high value of safety factor has been considered, but itwas proved that for small satellite, dynamic design consideration have the main rule on the structurecapability under applied load.

REFERENCE

1. ARIANESPACE, “ARIANE-5 Structure For Auxiliary Payload, Users Manual”, ARIANE SpaceAgency (1997)

2. ANSYS Analysis Manual, Finite Element Software, ANSYS Inc. Houston, Pa (1996).3. T. F. Botha and D. M. Weber, “Development of a reliable tele command system for micro satellite

applications” AIAA Computing in Aerospace 9 Conference, San Diego, CA, USA, 1993.4. A. C. Kitts and K. H. William "The Design and Construction of the Stanford Audio Phonic

Photographic Infrared Experiment (SAPPHIRE) Satellite", Proceedings of the 8th AnnualAIAA/USU, Conference on Small Satellites, Logan, Utah, Aug. 29 - Sept. 1, 1994.

5. J. Rhee , Z.C. Kim, and D. S. Hwang; “Preliminary configuration Design of KOMPSAT2Structure”, 5th Asia –Pacific Conference on Applications Cooperation in of space TechnologyApplications, 1999, Tehran , Iran, (1999)

6. M. Sedighi, A. Azadmanesh et. al., “Structural Design, MESBAH micro satellite (Int. rep. AR-CO-55)” 20-75 (2000)