Missions of Small Satellite with Deployable Membrane Using Spiral Folding Lines

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1 Missions of Small Satellite with Deployable Membrane Using Spiral Folding Lines Tomoyuki MIYASHITA ), Nobuhisa KATSUMATA ), Hiroshi YAMAKAWA ), Michihiro NATORI ) ) Department of Modern Mechanical Engineering, Waseda University, Tokyo, Japan ) Department of Aeronautics and Astronautics, The Muroran Institute of Technology, Hokkaido, Japan ) The Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan (Received st Dec, 06) In microgravity conditions, the structures where the components with low stiffness are installed could maintain its initial shape. By deploying the membrane in space, it is possible to arrange the structural elements in wide area. Attention has been focused on the availability of satellites in low orbit due to its missions related with the distance to earth. We have developed WASEDA-SAT as U size satellite, by reducing the development costs using consumer products, to grasp the behavior of the film surface in low orbit. In this paper, we report all of the functions and the verification results of the satellite on ground and on orbit if the launch is finished and the operation is stared normally. Assuming the disturbance in low orbit, the spiral folding procedure is newly invented and applied to fold the curved surface into cylindrical shape. In flight model, the surface is implemented as a parabolic surface with the focal length as 80cm. A polyimide film coated one side with silver is used. The paint on the other side for facilitating image projected onto the polyimide surface is coated, for measuring the film surface shape by photographing images projected an image projected from the satellite body. On the other hand, takes into account the number of functionality. The focal length is the same as extension distance, although prospects improved reception gain of the satellite body, in an anechoic chamber, gain enhancement was not confirmed by the problems of deployment accuracy. The silver-deposited surface, are arranged thin-film solar cell to indicate the characteristics of the folding helix corresponding to film thickness variation. In addition, the satellite body, has been to place the LCD panel on one side, to confirm the effect of radiant heat controlled by the current situation, which has been confirmed in the ground experiment. Key Words: Small Satellite, Expansion of Membrane, Radiation Control Nomenclature N the number of vertexes of polygon at the center R distance from the center to Folding Line A angle between x axis and Folding Line A angle between a tangent of Folding Line A and a straight line from the center fold interval vector for vertical direction to a straight S line from the center fold interval vector for vertical direction to a tangent b of Folding Line A r radius of folded shape t* distance of a gap of folded membrane l height of parabolic surface from center slit angle a focal length of parabola u horizontal distance of the arc in parabola radiation shape factor m mass property of finite element of membrane c damping property of finite element of membrane k stiffness property of finite element of membrane a facial length of parabolic membrane F d C d drag force density of atmosphere at altitude 00 km drag coefficient. Introduction The launch by piggy bag style becomes popular and many launch opportunities are offered to us. The downsizing of the satellite has progressed. Here, the parts used in satellite become smaller and equip higher performance and sometimes selected from consumer products with a confirmation of adaptability for space environment. Then the environment of launch opportunities and profit of functions are greatly improved. In Japan, launch pod from U to U for several rockets and so on are developed and mechanical interface between rocket and satellite is offered. In this situation, nano-satellite can be frequently used for experiments of fundamental and aggressive missions due to many launch opportunities. In this paper, we will explain about missions of WASEDA-SAT with several missions. In these missions, an extension of dynamic hingeless mast and deployment of the parabolic membrane folded by spiral folding lines and measurement its shape on orbit. Unfortunately, the schedule of launch was not adapted for this paper and we could not obtain data until now. WASEDA-SAT is launched on 9 th Dec. as a transfer to ISS and scheduled to be launched from ISS. From the experiment on ground and simulation, mechanical properties of deployment of parabolic membrane was confirmed.

2 . Missions of WASEDA-SAT The missions of the satellite are shown in table. Our satellite use amatuor radio band 40MHz as uplink and 40MHz as downlink. I the satellite station, a dipole antenna is provided as downlink, a monopole as uplink shown in figure. This situation is normal situation then we will describe missions from No.. Figure shows (a) the assembly drawing and (b) inside view without outer panels. Table Mission of WASEDA-SAT No description Establish a radio counication Extension of dynamic hingeless mast Expansion of the structure with the folded membrane Investigation of the shape of the membrane Confirmation of the temperature control effect of 4 LCD Investigation of the deformation of the unfolded 5 membrane 6 De-orbit system using the membrane as drag chute in figure. This membrane is folded into cylinder shape to adopt storage are arranged in the satellite. To fold the membrane, the folding line was calculated considering following features. () Thickness of membrane () Thickness of pasted parts on membrane () Large area without folding lines To satisfy requirements () and (), the spiral folding method is applied. The folding lines are calculated by following equations considering thickness effect. Rd tan () dr Compatibility condition between neighbor folding lines. ds db tand S Scos db sin dr cos () () Compatibility condition of Area before and after folding: rdr t kr NR tan dr S cos Compatibility condition of Length before and after folding: (4) Ssin t r kr NR tan S (5) Folding lines S are derived by following equations considering thickness distribution of membrane and installed object on membrane with D shape decided by (R) that means a slit position for plane. It is not easy to obtain curved membrane. Then, we suppose to make from plane. (a) Assembly drawing Figure Definition of variables (b) Inside view Figure Assembly drawing and inside view. Membrane Mission This satellite equips a parabolic membrane with diameter 700 and facial length 00. The illustration is shown Figure 4 shows the flight model of membrane.

3 The folded membrane is extended by hingeles mast shown in figure 5. Normal hingeless mast equips a control wire for extend and stored. Due to only extension and simplicity of mechanism, we just expand using an elasticity of longeron and batten. The material of longeron is Ni-Ti hyper elastic material. And the batten is polymide. It is not easy to connect batten and longeron. To connect them firmly, silicon tube covers the longerons and is used to put battens from both sides. The stored shape is shown in figure 4.. Membrane shape measurement on orbit This is an another main mission of this satellite. To measure the shape of the membrane. We used method then the projector and camera are on board as shown in figure a. For the sake of confirmation of the performance of the system, the below surface with parabolic curve and the striped pattern is projected and the result was captured by camera. Due to downlink performance (00 bps) and simple download procedure during one window, size of image compressed on orbit is about 500 k. The limit of downlink performance comes from the limitation of electric power used in transmitter. The upper limit of performance of transmitter is 9600 bps. Figure 5 Membrane shape measurement on ground. Temperature control effect of LCD The satellite is cubic shape and there are 6 planes on surface. On one of surfaces, the LCD panel was installed. This LCD panel is controlled only ON-OFF state. The state ON means that 5V voltage is inputted to the LCD panel and the surface of LCD panel has the radiation shape factor ON. The state OFF means that no voltage is inputted to the LCD panel and the surface has the radiation shape factor OFF. The difference between ON and OFF is shown in figure 6. The measurement of the radiation shape factor is done in the laboratory. On orbit, we will measure the temperature and confirm the effect of the difference. The difference is estimated as the difference of o C for 90 min from the thermal effect simulation considering the radiation input according to the measured shape factor and the other radiation shape factor according to solar array and aluminum surface..4 De-orbit system using the membrane as drag chute The de-orbit system is recoended to be implemented as the fundamental function of the satellite. In our satellite, the expanded membrane becomes the drag chute to decrease the speed of the satellite. We estimate about one month to reentry if the drag chute expands on orbit from 400 km high from the ground. Figure 7 Dynamic hingeless mast and deployed shape. Discussions From the result of experiment on ground and simulations, we will discuss some aspect of this satellite below... Dynamics of Membrane Expansion The membrane is assisted to expand by Ni-Ti wire installed along folding lines. Then, it is important to understand the mechanism of the expansion. We have already obtained the relation between applied force on edge and rate of deployment in figure 8. The results shows that planar membrane is easiest to deploy because largest rate of deployment is obtained against with same load. Dimension Table Dimensions of membranes Nn r 0 Height r end t* Planar Curved A Curved B a Figure 6 Absorption spectrum measured by U-400 Figure 8 Applied load vs deployment rate [7]

4 Curved B seems to have a property to be most difficult to deploy due to lowest rate of deployment. To confirm this situation, we performed a deployment analysis using a mass-spring system shown in figure 9 and calculated a length of several elements shown in figure 9 in membrane. We could obtain the result that average maximum strain during deployment of plane membrane is smaller than that of curved membrane. Then, the deformation on plane is necessary in the case of deployment of parabolic membrane. surface Table Incidence calculation Angle of sun light incidence X+ cos γ = sin θ sin σ cos α cos β cos σ cos α sin β + sin σ cos θ sin α X- cos γ = sin θ sin σ cos α cos β + cos σ cos α sin β sin σ cos θ sin α Y+ cos γ = cos θ cos α cos β + sin θ sin α Y- cos γ = cos θ cos α cos β sin θ sin α We confirmed that the thermal effect of LCD panel is not so large. Only 0.7 K will be different for 45 min. The power consumption of while state affected this result. This means that the radiation was reduced by LCD effect but generated heat was canceled this reduction. Then the difference is no large... Membrane as a de-orbit system Our developed membrane has a larger stiffness normal to membrane due to dimensional shape. At altitude 00 km, the drag force F is estimated as follows. F d = ρac dv (6) Figure 9 Finite Elements Model of Membrane and model Table length difference ration before and after deployment pos Planar Parabolic folded deployed ratio folded deployed ratio Avg Effect of LCD Panel on orbit To confirm the effect of LCD panel on orbit based on the result of material property. We perform the thermal analysis using FEM model shown in figure 0. Material shown gray area is AL7075-T6 and solar cells are located all sides except Y surface. On Y surface, LCD panel with measured radiation shape factor was defined. The orbit supposed to be same with ISS. We estimate drag force about 7.0 x 0-4 N. This force could be supported by the Ni-Ti actuator used for deployment. The lager membrane and longer actuator have smaller bending stiffness. We expect that our proposed parabolic membrane will contribute for the larger area of membrane..4. Membrane Shape Accuracy For the confirmation of the shape of membrane calculated by our proposed method. We arranged three membrane shown in table 4. In this table, parameter for spiral folding is shown and we made folded shape for each membrane and measured the folded radius and deployed using Ni-Ti wire. We measure the radius of deployed membrane and the results were shown in table 5. Table 4 Arranged membrane for experiments No. Matrial Nn Paper t 9μm Polyimid film t 5μm Polyimid film t 7.5μm Core radius Height of Folding Radius Facial Table 5 Measured diameter for folded and deployed shape Figure 0 Satellite structure for thermal analysis No. Folded Shape Deployed Shape Ni-Ti Diameter Error Diameter Expand Measured Ideal % Measured Ideal % None Exist None Exist None Exist

5 We confirmed that the spiral folding lines worked well because error in folded shape is enough small except No. (wire exists). It is clear that this result comes from the effect of wire. The expand rate becomes better according to become thinner film and in the case of existence of wire. We confirmed the friction between side wall in storage area of satellite and selected the No. wire exist case as a membrane of flight model. 4. Conclusion We have proposed the small satellite WASEDA-SAT that equips small membrane for de-orbit function. The shape of membrane is parabolic so as to show an effectiveness of our proposed folding lines. On this parabolic membrane, soft solar cells are pasted so as to confirm the ability of consideration of thickness effect. LCD panel is installed on one side to control the radiation. The followings are conclusions. () The accuracy of diameter of folded shape by proposed folding lines are under 5.0 % error in the case of no actuator allocation case and under 4 % in the case of actuator allocation case. () The accuracy of diameter of deployed shape is largely improved by wire allocation on membrane. () The plane stiffness affect the deployment rate under same loading condition. (4) LCD panel can control radiation. In our case, we confirmed the 0.7 K for one circulation on orbit. Acknowledgments We express our gratitude to members of Light Weight Space Structure Research Group in Waseda University. This work was supported by JSPS KAKENHI Grant Number 6K4507. References ) S.D. Guest, S. Pellegrino, Inextensional Wrapping of Flat Membranes, First International Conference on Structural Morphology, Sept. 99, pp ) T. Nojima, Modeling of Facilely Deployable Folding/Wrapping Method of Circular Flat Membranes by using Origami (Foldings in Radial Direction and Wrapping by Archimedean Spiral Design), Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.67, No.65, 00, pp ) M.C. Natori, H. Watanabe, N. Kishimoto, and K. Higuchi, Folding Patterns of Deployable Membrane Space Structures Considering Their Thickness Effects, 8th International Conference on Adaptive Structures and Technologies,ICAST ) T. Nojima, Modeling of Folding Patterns in Flat Membranes and Cylinders by Origami, Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.45, No., 00, pp ) K. Samura, N. Kokawa, T. Miyashita, Victor Parque, M.C. Natori, Comparison of Mechanical Properties between Planar and Curved Surface with Spiral Folding Patterns 0 th ISTS, 05. 6) S.D. Guest, S. Pellegrino, A NEW CONCEPT FOR SOLID SURFACE DEPLOYABLE ANTENNAS, Transactions of the Acta Astronautica, vol.8, No., 996, pp.0-. 7) T.Miyashita, H.Yamakawa, N.Katsumata, M.Natori.: Expantion and Measurement of Spiral Folded Membrane by Small Satellite, AIAA, SciTech 07 (accepted). 8) Chishiki, Y., Mori, O., Sawada, H., and Shirasawa, Y., Shape Estimation of Membrane of IKAROS by Shape from Shading Method of Images Taken with Separation Camera, the 8th International Symposium on Space Technology and Science, Vol 60, No. 4, 0, pp ) S. Roose, Y.Stockman, P.Rochus, T.Kuhn, M.Lang, H.Baier, S.Langlois,G. Casaros, Optical methodsfornon-contactmeasurementsofmembranes, Acta Astronautica65(009)7 9 0) Mark Schenk, Andrew D. Viquerat, Keith A. Seffen, and Simon D. Guest, Review of Inflatable Booms for Deployable Space Structures:Packing and Rigidization, JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 5, No., May June 04 5