Inflatable Reflector Research Articles

Predictive model for micrometeoroid damage to gossamer structures

A typical inflatable reflector for space application consists of two thin membranes with a parabolic shape. It is critical to understand the interaction of the inflatable and the micrometeoroid environment to which it is exposed. This interaction leads to a series of penetrations of the inflatable membrane on the entrance and exit of the impacting particle, creating a pathway for gas to escape. To increase the fidelity of the of the estimated damage that will be incurred, we examine the literature for descriptions of micrometeoroid fragmentation and present a theoretical formulation for the damage caused by an impacting particle to the entrance and exit membranes. This theory is compared with an initial set of hyper-velocity tests for micrometeoroid-sized particles on thin film membranes. We use the results of these tests to produce a predictive model. This model is applied to estimate the damage rate near the 1 AU location and output predictions for the effectiveness of a micrometeoroid shield to reduce the damage on the lenticular and effectively optimize its lifetime. Finally, we apply the kinetic theory of gasses to develop expressions for the expenditure of gas over a specified mission lifetime due to penetrations. Although we examine the specific case of an inflated lenticular protected by extra membrane layers, our predictive model can be applied to any gossamer structure composed of polyimide membranes.

Surface Measurement of a Large Inflatable Reflector in Cryogenic Vacuum

The metrology of membrane structures, especially inflatable, curved, optical surfaces, remains challenging. Internal pressure, mechanical membrane properties, and circumferential boundary conditions imbue highly dynamic slopes to the final optic surface. Here, we present our method and experimental results for measuring a 1 m inflatable reflector’s shape response to dynamic perturbations in a thermal vacuum chamber. Our method uses phase-measuring deflectometry to track shape change in response to pressure change, thermal gradient, and controlled puncture. We use an initial measurement as a virtual null reference, allowing us to compare 500 mm of measurable aperture of the concave f/2, 1-meter diameter inflatable optic. We built a custom deflectometer that attaches to the TVAC window to make full use of its clear aperture, with kinematic references behind the test article for calibration. Our method produces 500 × 500 pixel resolution 3D surface maps with a repeatability of 150 nm RMS within a cryogenic vacuum environment (T = 140 K, P = 0.11 Pa).

Design of a rapid transit to Mars mission using laser-thermal propulsion

The application of directed energy to spacecraft mission design is explored using rapid transit to Mars as the design objective. An Earth-based laser array of unprecedented size (10 m diameter) and power (100 MW) is assumed to be enabled by ongoing developments in photonic laser technology. A phased-array laser of this size and incorporating atmospheric compensation would be able to deliver laser power to spacecraft in cislunar space, where the incident laser is focused into a hydrogen heating chamber via an inflatable reflector. The hydrogen propellant is then exhausted through a nozzle to realize specific impulses of 3000 s. The architecture is shown to be immediately reusable via a burn-back maneuver to return the propulsion unit while still within range of the Earth-based laser. The ability to tolerate much greater laser fluxes enables realizing the combination of high thrust and high specific impulse, making this approach favorable in comparison to laser-electric propulsion and occupying a parameter space similar to gas-core nuclear thermal rockets (without the requisite reactor). The heating chamber and its associated regenerative cooling and propellant handling systems are crucial elements of the design that receive special attention in this study. The astrodynamics and the extreme aerocapture maneuver required at Mars arrival after a 45-day transit are also analyzed in detail. The application of laser-thermal propulsion as an enabling technology for other rapid transit missions in the solar system and beyond is discussed.

Large Spaceborne Deployable Antennas (LSDAs) —A Comprehensive Summary

This paper provides a survey of research activities of Large spaceborne deployable antennas (LSDAs) in the past, present and future. Firstly, three main kinds of spaceborne antennas, such as solid reflector, inflatable reflector and mesh reflector, are issued by showing the strengths and weaknesses. Secondly, a detailed research situation of LSDAs with mesh is discussed, for majority of the in-orbit large diameter and high frequency antennas are made in this type of structures. Thirdly, new conception of antenna is proposed as it does have both advantages of large aperture (high gain) and high precision (high frequency). Fourthly, the design theory and approach of LSDAs are concerned. It includes thermal-electromechanical multidisciplinary optimization, shaped beam design technique, performance testing technology and evaluation method, passive intermodulation of mesh, and application of new materials. Finally, the ultra large spaceborne deployable antennas of the next generation are presented, such as the deployable frame and inflatable reflector antennas, space-assembled ultra large antennas, smart array antennas and so on.

Inflation mechanics of a membrane reflector supported by an inflated toroidal rim

Abstract A stack of two identical flat circular membranes, bonded along the periphery can be inflated to form a reflector. To maintain the desired shape of the reflector surface, a supporting outer rim is required. An inflatable membrane reflector supported by an outer inflated toroidal rim structure is considered. Both the reflector and the toroidal rim are considered to be geometrically flat in the uninflated state. Initially, the circular membranes are pre-stretched and joined with the inner equator of the inflated torus, causing an inward radial force on the toroidal rim. The inflated shapes of the circular membranes (reflectors) under uniform pressure are obtained by an iterative solution scheme. The inflation problem is solved to determine the inflated shapes and the possible occurrence of wrinkling instability of the reflector or pull-in instability of the toroidal rim. The shape of the reflector is found to be close to a paraboloid whose focal length depends on the level of inflation and pre-stretch. Lower inflation pressure of the inflatable reflector is found to result in a better parabolic approximation of the reflecting surface.

Dynamic Testing of an Inflatable Wrap-rib Reflector Antenna

Dynamic testing of an inflatable wrap-rib reflector antenna with carbon fiber reinforced polymer (CFRP) supporting ribs was conducted. The inflatable reflector antenna was made of thin film, and the precision of off-set parabolic reflector was maintained by tension tailored CFRP ribs with a central hub and an outer inflatable torus. The effects of inner gas pressure and gravity on structural natural frequencies, modal shapes, and modal damping ratios were evaluated experimentally, inflatable wrap-rib reflector antenna with cup-up and cup down configurations with 10kPa and 20kPa inner inflation pressures were tested respectively. In ground vibration test based on experimental modal analysis, the whole antenna was fully deployed and hanged with a rope at central hub in lab environment. A series of impulse tests were conducted with high sensitive load cell to record input force, and several mini tri-axial accelerometers were instrumented on inflatable torus and supporting ribs to monitor the global vibration response, the excitation point was reinforced with a lightweight Alumina thin shell to minimize local deformation. Ground modal analysis results could be used as reference for predicting dynamic characteristics of inflatable wrap-rib reflector antenna on orbit.

Analytical Investigation of Dynamics of Inflatable Parabolic Membrane Reflector

An analytical method for computing the dynamic characteristics of a lenticular inflatable parabolic reflector supported by an inflatable torus is presented. The system is modeled by a combined structure consisting of two pressurized paraboloidal membranes with an elastic circular ring support. Equations of motion for the transverse free vibration of the pressurized paraboloidal membrane are derived first by using the nonlinear theory of shallow shells of revolution. Then, the analytic solutions for those equations of motion are formulated. Afterward, according to the force balance and the displacement continuity between the membranes and the circular ring, the displacements of the ring are calculated as boundary conditions of the paraboloidal membranes. As a result, the frequency equation and analytic mode shape functions of the inflatable reflector are obtained, and the influences of support stiffness on the dynamic characteristics of the reflector are analyzed. The validity of these analytical modal solutions is verified by finite-element simulations.

Mechanical study on initial profile solution for inflatable reflector made of orthotropic material

The woven fabric membrane materials are widely used in space and terrestrial inflatable reflectors. However the material׳s anisotropy makes the design analysis more complex. The deviation from the desired shape, so-called “W-profile error”, influences the precision of the membrane surface significantly. In this study, a model of an axisymmetric paraboloid surface using membrane theory is established for the purpose of facilitating the surface precision optimization. Analytical solutions for displacements of the reflector are derived. An iteration method of initial reflector profile solution is stated and a finite element (FE) software employed in the solution is presented. A case study is illustrated to make a comparison between numerical and theoretical analyses. Finally, the conclusions are drawn that the analytical method and the FE iterative method for initial profile solution are feasible and efficient.

Large deployable antennas

It is an honour and a great pleasure for us to present this special issue of the CEAS Space Journal devoted to the development of large deployable antennas and related technologies. Large deployable antennas for space applications have been under development worldwide for several decades, driven by both mission performance enhancement goals as well as mission enabling goals. Developments in ESA started already in the 80s with a 5-m metal-mesh reflector built by MBB/ERNO in Germany, continued later with a 10-m inflatable reflector built by Contraves in Switzerland and more recently a 12-m antenna built by Thales Alenia Space in Italy. However, for various reasons all these developments did not result in a final available European antenna reflector product. As a matter of fact, today there is no European antenna reflector product larger than 4 m aperture available, forcing European spacecraft developers to procure large reflectors from non-European sources. Three years ago, an ESA Working Group on large reflector antennas was set up with the mandate to define recommendations on how to proceed with new large reflector developments in Europe. Several spacecraft missions in need of antenna reflectors were identified, including well-established telecommunication markets such as fixed and broadcasting satellite services, mobile interactive/broadcast services, broadband services, but also new applications such as air traffic management and emergency communications. These missions cover the frequency spectrum up to Ka-band. Synergies with Earth Observation, Navigation and Scientific deep space missions were also identified. One of the main conclusions of the Working Group was that near-term effort should be devoted to the development of technologies for reflectors with scalability and/or modularity features to cover sizes above 4 m and up to 25 m for frequency bands ranging from P to Ka. It was understood that many of the technologies were in fact available or within reach, and the missing task of coordination and industrial implementation was considered achievable. In October 2012, the first Large Deployable Antenna Workshop took place at ESA/ESTEC, The Netherlands, with a significant participation from European industry and research organisations. During this workshop, several recent technology developments for large antenna reflectors were presented and discussed together with a new reflector deployment demonstration. The workshop addressed as well developments for inflight reconfigurability of space antennas using reflector reshaping that is finally becoming technically feasible after many years of trials. Reflect-arrays and lenses were also addressed, as well as radio frequency testing, especially relevant due to the challenges ahead of us for the development of test facilities required for large apertures. This special issue of the CEAS Space Journal is intended to present the key technologies addressed in this workshop. A second edition of the workshop is under preparation for 2014 with the objective to report on the major developments performed over the last 2 years. T. K. Henriksen (&) Structures and Mechanisms Division, ESA/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, ZH, The Netherlands e-mail: Torben.Henriksen@esa.int

Deformation Measurement of an Inflatable Reflector Using Digital Image Correlation

Inflatable antenna is a potential technique for large space deployable antenna and knowing its reflector’s deformation behavior is quite important for its accuracy improvement. A 1.5m-diameter inflatable reflector’s deformations at different internal pressures are studied using digital image correlation(DIC) in the paper. Because of the symmetry of the reflector, only two representative gores on the reflector are chosen to study. During the digital image correlation measurement, some article random dot patterns are drawn on the reflector’s surface. The 2D and 3D displacement maps of the reflector at different internal pressures are gained by DIC measurement and the cross-section of one gore of the reflector according to the internal pressure are analyzed from the measurement results.

Influence Parameter Analysis and Wrinkling Control of Space Membrane Structures

This paper aims to find the effective wrinkling control strategy for space membrane structures, including square solar sails and inflatable reflectors. The wrinkles in a square solar sail were first predicted using a nonlinear finite element solution. Analysis of wrinkling influence parameters was then evaluated to determine the shape and wrinkling control schemes for the solar sail. The wrinkling criterion and characteristics were then determined by introducing the principal stress criterion and an elliptical assumption for the shape of the wrinkled region in inflatable reflector. We then evaluated the effects of the parameters on the wrinkling characteristics. These results were used to determine an effective wrinkling control strategy. The wrinkling control for the solar sail effectively improved the membrane stiffness and controlled the initial prestress in the membrane, while simultaneously reducing the structural scale. For the inflatable reflector, controlling edge tension using a tape as a tension-compliant border was an effective wrinkling elimination scheme, and this was verified by the numerical results in the end. The conclusions of this paper are useful when applied to wrinkling and shape control of space membrane structures.

A Point Matching Method for Stereovision Measurement

Many vision tasks such as 3D measurement, scene reconstruction, object recognition, etc., rely on feature correspondence among images. This paper presents a point matching method for 3D surface measurement. The procedure of the method is as follows: (1) rectification for stereo image pairs; (2) computation of epipolar lines; (3) sequential matching in vertical direction; (4) sequential matching in horizontal direction. The fourth step is performed to deal with the ambiguity in dense areas where points have closer vertical coordinates. In the fourth step a threshold limit of vertical coordinate difference is designed to determine those points potential to cause ambiguity. This method was applied to the 3D surface measurement for an inflatable parabolic reflector with validity of point matching up to 100%. Experiment results show that this method is feasible in application of sparse point matching for continuous surface measurements.

Finite element analysis of wrinkling membrane structures with large deformations

Membrane wrinkling problems are formulated using the geometrically nonlinear finite element method with convected coordinates. A membrane structure which is initially in an under-constrained state cannot resist compressive stresses and experiences out-of-plane deformation to avoid occurrence of compressive stresses. When a membrane is in the state of wrinkling, it is crucial to determine the wrinkling direction and the corresponding stress state for an analysis of the wrinkled membrane. Tensile strain energy is defined to correctly and simply evaluate the wrinkling directions based on the assumption that wrinkles are aligned to maximize tensile strain energy. This approach requires neither extra parameter nor kinematic assumption to predict wrinkle orientation. A pseudo-dynamic method is also introduced to initiate Newton–Raphson solution procedures for the analysis of under-constrained membranes. Several benchmark problems are analyzed to demonstrate the effectiveness and accuracy of the proposed formulation, and a space inflatable reflector example is also presented.

Precision Analysis and Shape Adjustment of Inflatable Antenna

充气可展天线结构是以柔性薄膜材料制造的一种新型可展天线.对一类充气可展开天线系统进行结构设计,并相应地建立了充气结构的有限元分析模型.对充气反射面进行了精度分析,研究各参数对形面精度的影响,包括内压、膜材厚度、材料属性、天线焦距等;比较了3种实验姿态下重力对形面的影响,选择其中一种能够很好地模拟失重环境;针对特定的天线结构系统,提出了可行的形面调整新方法.分析和实验表明,调整方法能够有效提高形面精度.

Elastic Analysis of Circular Membrane and Its Application to an Inflatable Paraboloidal Reflector (Effect of Initial In-Plane Tension)

In this paper, we describe the generation of an inflatable reflector. The reflector is generated by applying pressure to a membrane surface. The in-plane force of the radius direction is also applied to the surrounding boundary of the membrane. The exact differential equations to describe the deformation of the membrane are introduced. The deformed shape of the membrane is obtained by numerical calculation. Furthermore, the deformed shape that was calculated is compared with a parabola shape. The standard deviation of shape is introduced to compare the shapes. Finally, the effect of the in-plane force in the radius direction to generating the inflatable reflector is discussed.

FULLY NONLINEAR MODELING AND ANALYSIS OF PRECISION MEMBRANES

International Journal of Computational Engineering ScienceVol. 04, No. 01, pp. 19-65 (2003) No AccessFULLY NONLINEAR MODELING AND ANALYSIS OF PRECISION MEMBRANESP. FRANK PAI and LEYLAND G. YOUNGP. FRANK PAIDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Search for more papers by this author and LEYLAND G. YOUNGDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Search for more papers by this author https://doi.org/10.1142/S1465876303000788Cited by:4 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractHigh precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODEs) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODEs, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.Keywords:Nonlinear membrane theorynumerically exact analysis References M. Salama , M. Lou and H. Fang , Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference ( 2000 ) . Google Scholar M. S. Smith , R. S. Schallenkamp and L. G. Seely , AIAA International Balloon Technology Conference . Google Scholar D. Gorinevsky , T. Hyde and C. Cabuz , Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference ( 2001 ) . Google Scholar V. Firt , Statics, Formfinding and Dynamics of Air-Supported Membrane Structures ( Martinus Nijhoff Publishers , Boston , 1983 ) . Google Scholar A. L. Palisoc, Inflatable Reflector Development Program, Task 3 Report, L'Garde Technical Report, LTR-94-AP-008, 1994 . Google Scholar S. V. Damle et al. , AIAA International Balloon Technology Conference . Google ScholarP. F. Pai, A. N. Palazotto and J. M. Greer Jr., Comput. Struct. 66, 823 (1998), DOI: 10.1016/S0045-7949(98)00004-2. Crossref, Google Scholar H. Furuya and Y. Kawasaki , Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference . Google Scholar G. Greschik , M. M. Mikulas and A. Palisoc , Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference ( 1998 ) . Google ScholarJ. Ruze, Proceedings of the IEEE 54, 633 (1966), DOI: 10.1109/PROC.1966.4784. Crossref, Google Scholar A. Palisoc et al. , Fifth SPIE Conference on Space Telescopes and Instruments . Google ScholarP. F. Pai and A. H. Nayfeh, Nonlinear Dynamics 6, 459 (1994). Crossref, Google ScholarP. F. Pai and A. N. Palazotto, J. Eng. Mech. 121, 568 (1995), DOI: 10.1061/(ASCE)0733-9399(1995)121:4(568). Crossref, Google ScholarP. F. Pai and A. H. Nayfeh, Nonlinear Dynamics 2, 445 (1991), DOI: 10.1007/BF00045438. Crossref, Google Scholar K. Washizu , Variational Methods in Elasticity & Plasticity , 3rd edn. ( Pergamon Press Inc , New York , 1982 ) . Google ScholarP. F. Pai and A. N. Palazotto, Int. J. Solids Struct. 32, 3047 (1995), DOI: 10.1016/0020-7683(94)00273-Y. Crossref, Google Scholar H. Golden , T. W. Strganac and R. A. Schapery , AIAA International Balloon Technology Conference ( 1997 ) . Google Scholar J. Stoer and R. Bulirsch , Introduction to Numerical Analysis ( Springer-Verlag , New York , 1980 ) . Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 4Analytical Investigation of Dynamics of Inflatable Parabolic Membrane ReflectorFushou Liu and Dongping Jin1 Jan 2015 | Journal of Spacecraft and Rockets, Vol. 52, No. 1A point collocation method for geometrically nonlinear membranesKyle F. Kolsti and Donald L. Kunz1 Jan 2013 | International Journal of Solids and Structures, Vol. 50, No. 2Numerical and experimental dynamic characteristics of thin-film membranesLeyland G. Young, Suresh Ramanathan, Jiazhu Hu and P. Frank Pai1 May 2005 | International Journal of Solids and Structures, Vol. 42, No. 9-10Modeling, Analysis and Testing of some Deployable/Inflatable StructuresPerngjin Pai and Leyland Young26 June 2012 Recommended Vol. 04, No. 01 Metrics History Received 26 August 2002 Accepted 4 November 2002 KeywordsNonlinear membrane theorynumerically exact analysisPDF download

Errata: “Tension Element to Reduce Loads in Rim Support of Inflatable Reflector” (April, 1994, Vol. 7, No. 2)

Errata: “Tension Element to Reduce Loads in Rim Support of Inflatable Reflector” (April, 1994, Vol. 7, No. 2)

Tension Element to Reduce Loads in Rim Support of Inflatable Reflector

A structural analysis is performed for the rim support of a pressurized off‐axis paraboloidal membrane that serves as a space‐based solar concentrator. The function of the elliptical rim support is to take up the tensile forces created by the stretched membrane. This paper extends earlier load and deformation analyses to include the effect of a tension element added along the major axis of the ellipse. Such an element, in the form of a string or cable, restrains the tendency for increased ovality of the rim support under load without seriously interfering with the packaging and deployment of the device, at negligible added mass. The internal forces and moments and the deformations resulting from the membrane‐applied loads have been calculated. The analysis has shown that a properly designed tension element can reduce the maximum bending moment by more than a factor of 2. The deformations are reduced by more than a factor of 20.

膜面の圧力及び重力による変形挙動

The reflecting surface of an inflatable reflector for space use consists of one or several inflatable elements (membrane elements), which are pressurized to generate an accurate reflecting surface. The surface of an inflatable element deforms as the pressure is applied. If the element is pressurized on the ground, gravity force also changes the deflection of the element. This means that the internal pressure and the gravity force influence the surface error of the element. This paper presents an analysis of the deflection and the surface accuracy of an inflatable element subjected to pressure and gravity loadings based on a flexible membrane strip model, the initial configuration of which is straight or a circle arc, with both ends immovably supported. The gravity is assumed to act in any direction in the plane which includes the membrane strip. The perturbation method is used to solve the membrane deflection due to the gravity force, assuming the ratio of gravity to pressure and the center height of the membrane to be small. The analytical expressions for the deflection and the surface error of the membrane strip subjected to pressure and gravity are obtained. It is found that the effect of gravity on the surface error increases as the ratio of gravity to pressure and the center height of the strip increases, and as the rigidity (Young Modulus) of the membrane decreases. It is also found that if the membrane strip is not so rigid (Young Modulus is not so high), the effect of gravity on the deflection is smallest with the membrane vertically placed. On the other hand if the membrane strip is rigid enough, the effect of gravity is smallest with the membrane horizontally placed.