Search NASA⌕ Search

SEARCH · Search NASA

Results for “Rigidity function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24

Dynamics and control of orbiting flexible beams and platforms under the influence of solar radiation and thermal effects

Expressions for thermal deflections of uniform thin beams and plates exposed to solar heating are obtained as a function of the properties of the material and the solar incidence angle. The major effect of the solar radiation pressure interacting with the thermally deformed structure is found to give rise to disturbance moments on the structure. The thermal deformations of the structures are assumed to be within 0.1 percent of the characteristic length of the structure. With the assumed thermal deformations, the resulting uncontrolled transient responses of these geosynchronous orbiting structures to the solar radiation pressure induced disturbances are simulated. The resulting rigid modal oscillations are found to be an order of magnitude larger than for those cases previously considered in which only the solar radiation pressure effect on vibrating structures was treated. Modifications of control laws and/or the feedback gain values are considered in order to improve the transient response characteristics under the thermally induced disturbances.

Krishna, R.↗

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗

Variation in the modal parameters of space structures

An analytic and experimental study of gravity and suspension influences on space structural test articles is presented. A modular test article including deployable, erectable, and rotary modules was assembled in three one- and two-dimensional structures. The two deployable modules utilized cable diagonal bracing rather than rigid cross members; within a bay of one of the deployable modules, the cable preload was adjustable. A friction lock was used on the alpha joint to either allow or prohibit rotary motion. Suspension systems with plunge fundamentals of 1, 2, and 5 Hz were used for ground testing to evaluate the influences of suspension stiffness. Assembly and reassembly testing was performed, as was testing on two separate shipsets at two test sites. Trends and statistical variances in modal parameters are presented as a function of force amplitude, joint preload, reassembly, shipset and suspension. Linear finite element modeling of each structure provided analytical results for 0-g unsuspended and 1-g suspended models, which are correlated with the analytical model.

Crawley, Edward F.↗

Software for continuum modeling of controls-structures interactions

It is clear that computer software is needed to assist in the generation of the equations of motion for complex, flexible spacecraft. Daniel Poelaert of ESTEC has developed the software DISTEL with which he has modeled the structural dynamics for different satellites. He is interested in expanding the capabilities of DISTEL to include structural damping and control systems. Unfortunately, the software has not been released. The author has developed similar software, PDEMOD, which has been used to model the Spacecraft control Laboratory Experiment (SCOLE), the Solar Array Flight Experiment (SAFE), the Mini-MAST truss, and the LACE satellite. PDEMOD has been used also for optimal parameter estimation and integrated control-structures design. PDEMOD is also being extended to include structural damping and control systems which are imbedded into the same equations for the structural dynamics. This paper will address the formulation of the equations for the structural dynamics of spacecraft structures which are constructed of a 3-dimensional arrangement of rigid bodies and flexible beam elements. Control system dynamics are imbedded into the same equations so that model order reduction approximations are not necessary. The input data consists of the physical data of the elements and the topological information describing how the elements are connected. PDEMOD accomplishes the following: (1) automatically assembles the equations of motion for the entire structural model; (2) calculates the modal frequencies; (3) calculates the mode shapes; (4) generates perspective views of the mode shapes; and (5) forms selected transfer functions. The software PDEMOD continues to be developed to provide additional features to assist in analyzing and synthesizing control and structural systems for flexible spacecraft.

Taylor, Lawrence W., Jr.↗

The effect of surface roughness on the average film thickness between lubricated rollers

The Christensen theory of stochastic models for hydrodynamic lubrication of rough surfaces is extended to elastohydrodynamic lubrication between two rollers. The Grubin-type equation including asperity effects in the inlet region is derived. Solutions for the reduced pressure at the entrance as a function of the ratio of the average nominal film thickness to the rms surface roughness (in terms of standard deviation), have been obtained numerically. Results were obtained for purely transverse and purely longitudinal surface roughness for cases with or without slip. The reduced pressure is shown to decrease slightly by considering longitudinal surface roughness. Transverse surface roughness has a slight beneficial effect on the average film thickness at the inlet. The same approach was used to study the effect of surface roughness on lubrication between rigid rollers and lubrication of an infinitely-wide slider bearing. The effects of surface roughness are shown to be similar to those found in elastohydrodynamic contacts.

Chow, L. S. H.↗

Macroscopic and bulk-controlled elastic modes in an interaction of interstitial alcali metal cations within a face-centered cubic crystalline fullerine

The calculations in a majority of previous works for the fulleride (AqC-60) crystals were performed within the framework of the rigid-lattice model, neglecting the distortion relaxation of the host fullerene (C-60) crystal caused by the interstitial alkali-metal (A) cations. However, an each cation is a source of a static distortion field, and the resulting field is a superposition of such fields generated by all cations. This is a reason why the host-crystal distortions depend on the A-cations configurations, i.e. on a type of a spatial bulk distribution of interstitial cations. The given paper seeks to find a functional relation between the amplitudes of the doping-induced structure-distortion waves and of static concentration ones. A semiphenomenological model is constructed here within the scope of statistical-thermodynamic treatment and using the lattice-statistics simulation method(*). In this model the effects due to the presence of q solute A cations over available interstices (per unit cell) on the static inherent reorientation and/or displacements of the solvent molecules from the 'average-lattice' sites' as well as on the lattice parameter a of a elastically-anysotropic 'cubic' C-60 crystal are taken into account.

Tatarenko, Valentine A.↗

Effects of gravity-gradient torque on the rotational motion of a triaxial satellite in a precessing elliptic orbit.

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.

Cochran, J. E.↗

Effect of solar radiation disturbance on a flexible beam in orbit

The uncontrolled dynamics of an orbiting flexible beam in the presence of solar radiation pressure forces is considered. The effect of solar radiation forces and moments on the rigid and flexible modes of a free-free flexible beam is evaluated. It is found that moments result only from the flexible symmetric modal deformations. For small pitch amplitudes, and at near geosynchronous altitudes the solar radiation moments due to the deformations of the beam are seen to be greater than those due to the gravity-gradient. Within the linear range, simulated steady state dynamic responses show that the induced pitch amplitudes can be more significant than the induced amplitudes of the modal shape functions.

Krishna, R.↗

Formations of Tethered Spacecraft as Stable Platforms for Far IR and Sub-mm Astronomy

In this paper we describe current research in tethered formations for interferometry, and a roadmap to demonstrating the required key technologies via on-ground and in-orbit testing. We propose an integrated kilometer-size tethered spacecraft formation flying concept which enables Far IR and Sub-mm astronomy observations from space. A rather general model is used to predict the dynamics, control, and estimation performance of formations of spacecraft connected by tethers in LEO and deep space. These models include the orbital and tethered formation dynamics, environmental models, and models of the formation estimator/controller/commander. Both centralized and decentralized control/sensing/estimation schemes are possible, and dynamic ranges of interest for sensing/control are described. Key component/subsystem technologies are described which need both ground-based and in-orbit demonstration prior to their utilization in precision space interferometry missions using tethered formations. Defining an orbiting formation as an ensemble of orbiting spacecraft performing a cooperative task, recent work has demonstrated the validity of the tethering the spacecraft to provide both the required formation rigidity and satisfy the formation reconfiguration needs such as interferometer baseline control. In our concept, several vehicles are connected and move along the tether, so that to reposition them the connecting tether links must vary in length. This feature enables variable and precise baseline control while the system spins around the boresight. The control architecture features an interferometer configuration composed of one central combiner spacecraft and two aligned collector spacecraft. The combiner spacecraft acts as the formation leader and is also where the centralized sensing and estimation functions reside. Some of the issues analyzed with the model are: dynamic modes of deformation of the distributed structure, architecture of the formation sensor, and sources of dynamical perturbation that need to be mitigated for precision operation in space. Examples from numerical simulation of an envisioned scenario in heliocentric orbit demonstrate the potential of the concept for space interferometry.

Quadrelli, Marco B.↗

Principal Effects of Axial Load on Moment-Distribution Analysis of Rigid Structures

This thesis presents the method of moment distribution modified to include the effect of axial load upon the bending moments. This modification makes it possible to analyze accurately complex structures, such as rigid fuselage trusses, that heretofore had to be analyzed by approximate formulas and empirical rules. The method is simple enough to be practicable even for complex structures, and it gives a means of analysis for continuous beams that is simpler than the extended three-moment equation now in common use. When the effect of axial load is included, it is found that the basic principles of moment distribution remain unchanged, the only difference being that the factors used, instead of being constants for a given member, become functions of the axial load. Formulas have been developed for these factors, and curves plotted so that their applications requires no more work than moment distribution without axial load. Simple problems have been included to illustrate the use of the curves.

James, Benjamin Wylie↗

Contaminated Solar Array Handrail Samples Retrieved From Mir Analyzed

In January 1998 during the shuttle STS 89 mission, an eight-section Russian solar array panel was retrieved after more than 10 years of exposure to the orbital space environment on Mir. The array was deployed June 16, 1987, and removed on November 3, 1997. It had been actively used as a source of electrical power for 8 years. This operational array had been located on the Mir core module, located directly above the Kvant-2 module. Its retrieval provided a unique opportunity to study the effects of the low-Earth-orbit environment on a functional solar array. The intact solar array underwent scientific inspections and preliminary tests by a joint team of U.S. and Russian investigators to evaluate the effects of long-term space exposure. Upon initial examination, significant contamination was observed over most components of the array. One panel, panel 8, was provided to the U.S. scientists for further evaluation. As part of the U.S. investigations, two solar array handrail samples from panel 8 were evaluated for contamination at the NASA Glenn Research Center at Lewis Field. One is a section of a rigid handrail, and the other is a section of woven fabric tape that was overwrapped around a flexible handhold. Both the flexible handhold woven fabric and the rigid handrail were significantly darkened after 10 years of space exposure. They were evaluated with optical microscopy, field emission scanning electron microscopy (FESEM), and energy-dispersive spectroscopy. Solar absorptance and room-temperature emittance values also were obtained. The returned contaminated solar array segment is very similar in design to the solar arrays being supplied by the Russians for the International Space Station. Therefore, it was desirable to determine what the contaminants on various surfaces are and what the sources of the contamination were.

deGroh, Kim K.↗

Circumferential pressure probe

A probe for measuring circumferential pressure inside a body cavity is disclosed. In the preferred embodiment, a urodynamic pressure measurement probe for evaluating human urinary sphincter function is disclosed. Along the length of the probe are disposed a multiplicity of deformable wall sensors which typically comprise support tube sections with flexible side wall areas. These are arranged along the length of the probe in two areas, one just proximal to the tip for the sensing of fluid pressure inside the bladder, and five in the sensing section which is positioned within the urethra at the point at which the urinary sphincter constricts to control the flow of urine. The remainder of the length of the probe comprises multiple rigid support tube sections interspersed with flexible support tube sections in the form of bellows to provide flexibility.

Holmes, Harlan K.↗

Robonaut 2 - IVA Experiments On-Board ISS and Development Towards EVA Capability

Robonaut 2 (R2) has completed its fixed base activities on-board the ISS and is scheduled to receive its climbing legs in early 2014. In its continuing line of firsts, the R2 torso finished up its on-orbit activities on its stanchion with the manipulation of space blanket materials and performed multiple tasks under teleoperation control by IVA astronauts. The successful completion of these two IVA experiments is a key step in Robonaut's progression towards an EVA capability. Integration with the legs and climbing inside the ISS will provide another important part of the experience that R2 will need prior to performing tasks on the outside of ISS. In support of these on-orbit activities, R2 has been traversing across handrails in simulated zero-g environments and working with EVA tools and equipment on the ground to determine manipulation strategies for an EVA Robonaut. R2 made significant advances in robotic manipulation of deformable materials in space while working with its softgoods task panel. This panel features quarter turn latches that secure a space blanket to the task panel structure. The space blanket covers two cloth cubes that are attached with Velcro to the structure. R2 was able to open and close the latches, pull back the blanket, and remove the cube underneath. R2 simulated cleaning up an EVA worksite as well, by replacing the cube and reattaching the blanket. In order to interact with the softgoods panel, R2 has both autonomously and with a human in the loop identified and localized these deformable objects. Using stereo color cameras, R2 identified characteristic elements on the softgoods panel then extracted the location and orientation of the object in its field of view using stereo disparity and kinematic transforms. R2 used both vision processing and supervisory control to successfully accomplish this important task. Teleoperation is a key capability for Robonaut's effectiveness as an EVA system. To build proficiency, crewmembers have attempted increasingly difficult tasks using R2 inside the Station. After donning motion capture equipment and a virtual reality visor, Expedition 34/35 flight engineer Tom Marshburn began operations with simple hand movements. Having gained confidence, Marshburn guided R2's arms in a leader-follower exercise with crewmate Chris Cassidy. He was also able to use the hand to grab a tumbling roll of tape, a task only demonstrable in microgravity. Later efforts saw Cassidy handle softgoods through shared control with ground operators, mimicking an activity previously achieved using only autonomy. Robotic climbing through the ISS on handrails requires both precision motion and compliant grasps in order to both position grippers on handrails/seat track and prevent large internal forces. R2 climbs using actively controlled compliance and torque limiting to meet both the precision and softness requirements. During a step, the attached leg is controlled to be strong and stiff in order to maintain precision trajectory tracking. The swing leg is controlled to be stiff but weak to minimize unintentional impact forces while maintaining precision. During a simulated dual limb grasp (as shown in Figure 1), the R2 controller maintains one limb rigid and one limb soft to prevent large internal forces from building up. R2's grippers also use a form of force control to limit grip force while not fully closed on either a handrail or seat track thus limiting unintentional forces on cables/objects that may be present in R2's translational path. The on-board torso R2 safety system relies on a single end-effector velocity limit to prevent potential impact forces from exceeding Station maximum load requirements. R2's mobile configuration required modifications to the velocity limiting safety function due to its large, dynamic inertia. R2's legs maneuver the robot's mass creating configuration dependent, joint-relative inertias. A single all-encompassing velocity limit to cover worst case inertia is prohibitively low. The upgraded R2 control and safety systems solve this problem using momentum limiting, momentum control, and kinetic energy minimization. Momentum and kinetic energy take the robot mass into account relieving low velocity restrictions on low inertia end-effectors while ensuring that the overall mass of R2 is limited from hazardous velocities. The momentum of R2's five safety nodes (each of the four end-effectors and the body) is monitored and compared to a single momentum limit. If any of the five nodes exceeds the safety limit, the motor power is removed and the robot comes to a stop. Momentum control/limiting also provides a simple, reliable method to integrate hand held tools into the safety system by providing the tool mass to the control system thus automatically reducing the allowable velocity of the end-effector with the tool. Work on the ground continues to build the skill set for an EVA Robonaut. Recent experiments (Figure 2) demonstrate how a teleoperator can use R2 to manipulate a tether hook, an important safety precaution on spacewalks. Another task displayed Robonaut's ability to pull back a protective jacket over a hose and search for damage, as well as inspect a quick-disconnect fitting for debris. Demonstrations such as these are indicative of EVA work done on ISS, specifically seen during a series of spacewalks over 2012 and 2013 where astronauts searched for an ammonia leak in one of the external cooling loops. Through experiments both on ISS and on the ground, R2 is evolving and providing the information needed to plan out the upgrades that will make an EVA Robonaut an effective tool. With the addition of legs, R2 will start climbing inside the space station and supply invaluable information on how the climbing strategies and task stabilization techniques must be refined. Ground R2 systems will continue to work with additional EVA tools and equipment in preparation for onboard IVA testing and future EVA applications.

Diftler, Myron↗

New Variational Formulations of Hybrid Stress Elements

In the variational formulations of finite elements by the Hu-Washizu and Hellinger-Reissner principles the stress equilibrium condition is maintained by the inclusion of internal displacements which function as the Lagrange multipliers for the constraints. These versions permit the use of natural coordinates and the relaxation of the equilibrium conditions and render considerable improvements in the assumed stress hybrid elements. These include the derivation of invariant hybrid elements which possess the ideal qualities such as minimum sensitivity to geometric distortions, minimum number of independent stress parameters, rank sufficient, and ability to represent constant strain states and bending moments. Another application is the formulation of semiLoof thin shell elements which can yield excellent results for many severe test cases because the rigid body nodes, the momentless membrane strains, and the inextensional bending modes are all represented.

Pian, T. H. H.↗

Mathematical modelling of flow distribution in the human cardiovascular system

The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.

NASA Center JSC↗

The Extensional Rheology of Non-Newtonian Materials

The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions are measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar, et al. The solutions are polystyrene-based (PS) Boger fluids that are stretched at constant strain rates ranging from 0.6 less than or equal to epsilon(0) less than or equal to 4s(exp -1) and to Hencky strains of epsilon greater than 4. The test fluids all strain harden and Trouton ratios exceeding 1000 are obtained at high strains. The experimental data strain hardens at lower strain levels than predicted by bead-spring FENE models. In addition to measuring the transient tensile stress growth, we also monitor the decay of the tensile viscoelastic stress difference in the fluid column following cessation of uniaxial elongation as a function of the total imposed Hencky strain and the strain rate. The extensional stresses initially decay very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation, and deviate significantly from FENE relaxation predictions. The relaxation at long times t is greater than or equal to 5 s, is compromised by gravitational draining leading to non-uniform filament profiles. For the most elastic fluids, partial decohension of the fluid filament from the endplates of the rheometer is observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. Flow visualization experiments using a modified stretching device show that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the nonhomogeneous region of highly deformed fluid near the rigid endplate.

Spiegelberg, Stephen H.↗

30-kW SEP Spacecraft as Secondary Payloads for Low-Cost Deep Space Science Missions

The Solar Array System contracts awarded by NASA's Space Technology Mission Directorate are developing solar arrays in the 30 kW to 50 kW power range (beginning of life at 1 AU) that have significantly higher specific powers (W/kg) and much smaller stowed volumes than conventional rigid-panel arrays. The successful development of these solar array technologies has the potential to enable new types of solar electric propulsion (SEP) vehicles and missions. This paper describes a 30-kW electric propulsion vehicle built into an EELV Secondary Payload Adapter (ESPA) ring. The system uses an ESPA ring as the primary structure and packages two 15-kW Megaflex solar array wings, two 14-kW Hall thrusters, a hydrazine Reaction Control Subsystem (RCS), 220 kg of xenon, 26 kg of hydrazine, and an avionics module that contains all of the rest of the spacecraft bus functions and the instrument suite. Direct-drive is used to maximize the propulsion subsystem efficiency and minimize the resulting waste heat and required radiator area. This is critical for packaging a high-power spacecraft into a very small volume. The fully-margined system dry mass would be approximately 1120 kg. This is not a small dry mass for a Discovery-class spacecraft, for example, the Dawn spacecraft dry mass was only about 750 kg. But the Dawn electric propulsion subsystem could process a maximum input power of 2.5 kW, and this spacecraft would process 28 kW, an increase of more than a factor of ten. With direct-drive the specific impulse would be limited to about 2,000 s assuming a nominal solar array output voltage of 300 V. The resulting spacecraft would have a beginning of life acceleration that is more than an order of magnitude greater than the Dawn spacecraft. Since the spacecraft would be built into an ESPA ring it could be launched as a secondary payload to a geosynchronous transfer orbit significantly reducing the launch costs for a planetary spacecraft. The SEP system would perform the escape from Earth and then the heliocentric transfer to the science target.

Dawn spacecraft↗

Departure from corotation of the Io plasma torus - Local plasma production

The departure of the Jovian magnetosphere from rigid corotation is adequately explained by outward plasma transport at distances where L is greater than approximately 10. The departure of 5% observed in the Io plasma torus, however, is too large to be accounted for simply by plasma transport. Local plasma production is proposed as the main factor determining the corotation lag in the torus. The outward pick-up current provided by ionization of neutral atoms is calculated and related to the current produced in the ionosphere by the corotation lag. This leads to an expression giving the corotation lag of the torus as a function of radial distance. Charge transfer is found to be an important process, allowing the majority of the torus mass to be ejected from the magnetosphere in a neutral state. Thus, the mass loading rate is found to be several times that inferred from examination of the corotation lag associated with outward plasma transport.

Pontius, D. H., Jr.↗