Available online at www.sciencedirect.com Available online at www.sciencedirect.com Energy Procedia 00 (2011) Energy Procedia 14000–000 (2012) 1967 – 1972 Energy Procedia www.elsevier.com/locate/procedia Conference Title An Overview of Dynamics Modeling of Inflatable Solar Array Delin Cuia,b,, Shaoze Yana*, Xiaosong Guob, Fulei Chua a The State Key Laboratory of Tribology, Department of Precision Instruments and Mechanology, Tsinghua University Haidian District, Beijing 100084 P.R China b Xi’an Research Institute of High Technology, Xi’an, Shanxi Province 710025 P.R China Abstract The inflatable solar array (ISA) is a new kind of solar array It has many advantages over the traditional ones, because it can be packaged into small volumes during launch, then sent into a pre-selected orbit, and finally deployed by its inflatable booms This paper gives a brief overview of development of inflatable space structure dynamics during the last two decades, and covers the highlights of the work that has been done during this time interval Some of the dynamic model of space inflatable booms and current development efforts are introduced, and future outlook for this promising structures technology is indicated Keywords: Inflatable solar array; spacecraft; dynamics; deployable structure Introduction In order to meet the requirements of energy supply in deep space exploration and reduce the launching costs, the inflatable solar array (ISA) technology is developed The inflatable deployment structure has many advantages over the traditional ones, because it can be packaged into small volumes during launch, then sent into a pre-selected orbit, and deployed by its inflatable booms Finally, the booms are hardened when the ISA is in full deployment and forms space structures [1] Therefore, knowledge of all states of inflation is essential for subsequent assessment of conditions of stability and controllability of the deployment process [2] Two companies, ILC Dover [3] and L’Garde [4], have early researched the inflatable solar array Both of the companies have been devoted to the related programs since 1990 and obtained fruitful achievements For instance, L’Garde developed a new type of inflatable solar array in the Inflatable Torus Solar Array Technology program [5] shown in Fig.1(a); ILC[3] successfully developed Mars Rover Inflatable Solar Array and Teledesic Inflatable Solar Array, shown in Fig.1(b) and Fig.1(c) respectively Many scholars * Shaoze Yan Tel.: 8610-18911300976; fax: +8610-62796046 E-mail address: yansz@tsinghua.edu.cn 1876-6102 © 2011 Published by Elsevier Ltd Selection and/or peer-review under responsibility of the organizing committee of 2nd International Conference on Advances in Energy Engineering (ICAEE) doi:10.1016/j.egypro.2011.12.887 1968 Delin name Cui et/al.\ / Energy Procedia 14 (2012) 1967 – 1972 Author Energy Procedia 00 (2011) 000–000 have performed to study design and dynamics of inflatable structures [1] However, it has been widely noticed that the dynamic characteristics of the supporting tubes determine mainly the performance of solar array, because the deployment of inflatable solar array is remarkably influenced by the inflation of the tubes This is an important reason why researchers focus more on the deployment dynamic characteristics of inflatable structures nowadays than the other performances of this kind of solar array (a)ITSAT Solar Array (b)Mars Rover Solar Array (c)Teledesic Solar Array Fig Application Examples of Inflatable Solar Arrays The inflatable solar arrays can be classified into Z-folded, rolled and some other types according to the different folding patterns of the supporting tubes The first two types are frequently used nowadays and deeply studied, so the related research developments of deployment dynamics for these two structures will be introduced in this paper Theoretical Models of Inflatable Structures Many scholars have pointed out that the practical and precise dynamic models of inflatable structures are extremely important in the space exploration [6] Several models suitable to different structures are presented as follows 2.1 Dynamic Model of Rolled Boom Fay and Steel [6] studied the deployment dynamics of the rolled tubes for the first time, and Smith introduced a dynamic model of the rolled boom [7] The basic equation of motion for the deployment of an inflated strut rigidly mounted at the base and initially wrapped around a hub from tip to base is[6,7] d ⎧ dα ⎫ (1) ⎨ I ⎡⎣ s (α ) ⎤⎦ ⎬ = p ⎡⎣ s (α ) ⎤⎦ πR r ⎡⎣ s (α ) ⎤⎦ dt ⎩ dt ⎭ where I is the moment of inertia about the lower edge of the unrolling portion of the strut, s is the arc length along the midline of the portion of the strut wrapped around the hub, α is the rigid body rotation of the roll, p is the internal pressure, R is the radius of the tube cross section when inflated, and r is the distance from the hub centre to the bottom of the rolled strut The assumed geometry of the deploying rolled strut is shown in Figure Fig.2 Geometry of the Deploying Rolled Strut [7] 1969 DelinAuthor Cui etname al.\ / /Energy – 1972 EnergyProcedia Procedia1400(2012) (2011)1967 000–000 The moment of inertia of the unrolling tube is given by I ( s ) = I ( s ) − I1 ( s ) + r ( s ) ρ 2πRhs (2) where I is the moment of inertia of the unrolling tube about the center of the hub and is given by ⎛h⎞ = I ( s ) ρ 2πRh ⎜ ⎟ ⎡⎣G (θ + θ ) − G (θ ) ⎤⎦ ⎝π ⎠ where ρ is the tube material density, h is the thickness of the tube material, and { (3) } 12 12 (4) + ϕ ) (ϕ + 2ϕ ) − log ⎢⎡ϕ + (1 + ϕ ) ⎥⎤ ( ⎣ ⎦ The I1 term in Eq (2) is caused by the fact that the centre of rotation of the unrolling strut is not the centre of mass and is defined by G (ϕ = ) θ +θ 12 ⎛h⎞ I1 ( s) ρ 4πRh ⎜ ⎟ (θ + θ ) ∫ ϕ cos (ϕ − θ ) (1 + ϕ ) dϕ (5) = θ0 π ⎝ ⎠ The wrapped arc length and wrap angle are related by [7] h (6) s (= θ) ⎡ F (θ + θ ) − F (θ ) ⎦⎤ π⎣ where 12 12 F (= ϕ) ϕ (1 + ϕ ) + log ⎡⎢ϕ + (1 + ϕ ) ⎤⎥ (7) ⎣ ⎦ Steele and Fay [6] applied above method to analyze dynamics behavior of the rolled boom, and research results shows that the reduction in pressure is greater, the average velocity is less, and the time required for the tube to unroll is longer Smith performed experimental studies to find out that the inertia of deployment gas caused a shock to the system when it struck the end of the tube at the conclusion of the unrolling process [7] This shock is directly related to the magnitude of the final unrolling velocity { } 2.2 Dynamic Model of Z-Folded Tube Several models have been applied in the dynamic studies of Z-folded tubes, including nonlinear hinge model [7,9,10], conservation model of energy and momentum[8,13], fluid-structure interaction model[14] and control volume model[11,12] The proper assignment of rotational spring stiffness to each hinge in the application of nonlinear hinge model only depends on the experimental results [7] And the conservation model of energy and momentum is only suitable for the case in which the injected gas flow is relatively slow [13] Besides, the fluid-structure interaction model is in its infancy, further work is still needed [8] Therefore, control volume model, which is used by many scholars, is introduced in this section In the control volume model, the continuum of enclosed volume is discretized in its stowed state into a set of connected smaller enclosures or finite volumes, or compartments [11], as shown in Figure Fig.3 Discretization of Inflatable Enclosure Into Connected Finite Volumes [11] Consider an ideal gas flowing between two finite volumes i and j , across orifice Aij Depending on the ratio of pressures downstream and upstream from the orifice, the gas flow may be subsonic or sonic For 1970 Delin name Cui et/al.\ / Energy Procedia 14 (2012) 1967 – 1972 Author Energy Procedia 00 (2011) 000–000 sub sonic flow, the rate of flow d mij of mass of gas across the orifice can be approximated by a onedimensional quasi-steady flow, expressed by [11] γ −1 γ −1 ⎧ ⎡ ⎤⎫2 d mij ⎪⎛ ⎞ ⎛ 2γ ⎞ ⎛ p0 ⎞ γ ⎢⎛ pu ⎞ γ ⎥⎪ (8) = kAij pd ⎨⎜ ⎟ × ⎢⎜ ⎟ − 1⎥ ⎬ ⎟⎜ ⎟⎜ − γ dt GT p p ⎠⎝ ⎠⎝ d ⎠ d ⎠ ⎝ ⎪⎝ ⎪ ⎢⎣ ⎥⎦ ⎭ ⎩ where p0 , pu and pd are the initial pressure, upstream pressure, respectively, and downstream pressure, γ is the specific heat ratio, G is the gas constant, T is the gas temperature, and k is the orifice coefficient Similarly, when the flow is sonic, it can be approximated in one dimension by [11] γ +1 γ +1 ⎧ ⎫ d mij ⎪⎛ ⎞ ⎛ 2γ ⎞ γ −1 ⎛ pu ⎞ γ ⎪ = kAij pd ⎨⎜ × (9) ⎬ ⎜ ⎟ ⎟ ⎟⎜ dt ⎝ pd ⎠ ⎪ ⎪⎝ GT ⎠ ⎝ γ + ⎠ ⎩ ⎭ Wang [12] neglected the inertia of the inflation gas, assumed all variables are known at time t − Δt In their research paper, equation of motion of the inflatable structure has the form [12] (10) [ M ]{D} + [C ]{D } + [ K ]{D} = {R e } where [ M ] , [C ] and [ K ] are the global mass, damping, and stiffness matrices computed with respect to } are displacement, velocity and acceleration vectors with the current configuration, { D} , { D } and { D respect to the current configuration at time t , { R e } is the external load vector 2.3 Simulation Analysis Simulation is of great importance for analyzing and forecasting the ISA deployment dynamics Software LS-DYNA3D is applied by Salama [11], Wang [12], Wei [1] and some other researchers to analyze dynamic behaviour of inflation deployment process, and Salama’s simulation results [11] show that the LSDYNA is much more suitable for inflation analysis than software ADAMS However, the deployment mechanism of the inflatable structures cannot be revealed completely only by finite element simulation [8] Experimental Methods of Inflatable Structures Three experimental methods, space-based experimentation, zero-gravity flight experimentation and Earth-based experimentation, have been adopted in analyzing dynamic characteristic of inflatable structures 3.1 Space-Based Experimentation The mechanical performances of ISA or inflatable structures can be fully and profoundly understood by space-based experiments NASA [15] successfully carried out the deployment of an inflatable antenna structure on May 20, 1996 This experiment clearly demonstrated the robustness of the inflatable space structures, and more important, it validated the potential of this new technology However, space-based experimentation is not an option for every new design for the expense of launching a test payload just to evaluate a design cannot be justified [16] DelinAuthor Cui etname al.\ / /Energy – 1972 EnergyProcedia Procedia1400(2012) (2011)1967 000–000 3.2 Zero-Gravity Flight Experimentation This kind of experimentation is carried out on a specially modified plane Reference [17] applied this method in a NASA-modified KC-135, which flied in a series of parabolic trajectories, causing 25-to-30second periods of alternating zero-g and two-g conditions Campbell [18] also conducted the experiment of inflating the scale-model solar concentrators aboard NASA’s KC-135 in 2002, and their results enabled better understanding of controlled deployment for design A defect of this experimentation has to be mentioned that the test space is usually small, so the size of test articles is limited [16] 3.3 Earth-Based Experimentation The environmental condition experienced on earth, which includes gravity and atmospheric pressure, has a dramatic effect of the deployment behaviour [16] Therefore, the air track shown in Figure is introduced into the experiments to simulate a type of microgravity environment [16] [19] Fig.4 Earth-Based Experiment Schematic [16] Clem and Welch conducted the experiments on an air table to predict the characteristics of the inflating beam deployment Xiao [20] and Liu [21] also applied this method to analyze the deployment velocity of the rolled booms at different times Although the earth-based experimentation can solve the problem to some extent, it only provides limited insight into the performance of the inflatable structures[16] Conclusions This paper mainly summarizes deployment dynamics of inflatable solar array This paper gives a brief overview of the development of dynamics of inflatable space structures during the last three decades, and covers the highlights of the work that has been done during this time interval This includes some of the dynamic characteristics of space inflatable booms, current development efforts, and future outlook for this promising structures technology The inflatable solar array technology has improved a lot during these years, the research achievements are fruitful However, there are many dynamics problems of the inflatable solar array to be solved, for instance, Modelling dynamic model of inflatable solar array system are intensely built in details, and the earth-based experimental equipments, which are much closer to the outer space environment, should be developed in the future Acknowledgements This work was supported by the National Science Foundation of China under Contract No 50875149, High Technology Project under Contract No 2009AA04Z401 1971 1972 Delin name Cui et/ al.\ / Energy Procedia 14 (2012) 1967 – 1972 Author Energy Procedia 00 (2011) 000–000 Reference [1] Jianzheng Wei Numerical Simulation for Deployment Dynamics of Lightweight Inflatable Solar Array 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2011: AIAA-2011-1969 [2] Salama M., Kuo C.P., and Lou, M Simulation of Deployment Dynamics of Inflatable Structures Proceedings of the 40th AIAA Structure, Structural Dynamics, and Materials Conference Washington, DC 1999: AIAA-1999-1521 [3] Cadogan D.P., Lin J.K Inflatable Solar Array Technology 37th AIAA Aerospace Sciences Meeting and Exhibit 1999 [4] Costa Cassapakis, Mitch Thomas Inflatable Structures Technology Development Overview AIAA 1995 Space Programs and Technologies Conference, Huntsville, AL 1995: AIAA-1995-3738 [5] David Lichodziejewski, Gordon Veal Inflatable Rigidizable Solar Array for Small Satellites 44th 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