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NASA NTRS1985

Nonlinear dynamic analysis of deploying flexible space booms

The dynamics of the planar deployment and lock-up of two flexible boom-type appendages on a spacecraft are analyzed by establishing nonlinear equations of motion for the deployment phase and linear for the post-lock-up phase. Nondimensional parameters and threshold values are identified in terms of boom tip deflections, deployment time and root moments for appendages with tip masses attached to a central rigid body through a rotational spring; an account is taken of the nonlinear kinematic and structural terms. It was found that, in general, the solution is influenced only by two mass ratios and one nondimensional stiffness parameter.

Mcgowan, P. E.↗

NASA NTRS1989

Derivation of a Tappered p-Version Beam Finite Element

A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.

Hinnant, Howard E.↗

NASA NTRS1991

Dynamic modelling and analysis of a magnetically suspended flexible rotor

A 12-state lumped-element model is presented for a flexible rotor supported by two attractive force electromagnetic journal bearings. The rotor is modeled as a rigid disk with radial mass unbalance mounted on a flexible, massless shaft with internal damping (Jeffcott rotor). The disk is offset axially from the midspan of the shaft. Bearing dynamics in each radial direction are modeled as a parallel combination of a negative (unstable) spring and a linear current-to-force actuator. The model includes translation and rotation of the rigid mass and the first and second bending models of the flexible shaft, and it simultaneously includes internal shaft damping, gyroscopic effects, and the unstable nature of the attractive force magnetic bearings. The model is used to analyze the dependence of the system transmission zeros and open-loop poles on system parameters. The dominant open-loop poles occur in stable/unstable pairs with bandwidth dependent on the ratios of bearing (unstable) stiffnesses to rotor mass and damping dependent on the shaft spin rate. The zeros occur in complex conjugate pairs with bandwidth dependent on the ratios of shaft stiffness to rotor mass and damping dependent on the shaft spin rate. Some of the transmission zeros are non-minimum phase when the spin rate exceeds the shaft critical speed. The transmission zeros and open-loop poles impact the design of magnetic bearing control systems. The minimum loop cross-over frequency of the closed-loop system is the speed of the unstable open-loop poles. For the supercritical shaft spin rates, the presence of non-minimum phase zeros limits the distribution rejection achievable at frequencies near or above the shaft critical speed. Since non-minimum phase transmission zeros can only be changed by changing the system inputs and/or outputs, closed-loop performance is limited for supercritical spin rates unless additional force or torque actuators are added.

Mccallum, Duncan C.↗

NASA NTRS2012

International Space Station 2A Array Modal Analysis

On December 9th 2009, the International Space Station (ISS) 2A solar array mast experienced prolonged longeron shadowing during a Soyuz undocking. Analytical reconstruction of induced thermal and dynamic structural loads showed an exceedance of the mast buckling limit. Possible structural damage to the solar array mast could have occurred during this event. A Low fidelity video survey of the 2A mast showed no obvious damage of the mast longerons or battens. The decision was made to conduct an on-orbit dynamic test of the 2A array on December 18th, 2009. The test included thruster pluming on the array while photogrammetry data was recorded. The test was similar to other Dedicated Thruster Firings (DTFs) that were performed to measure structural frequency and damping of a solar array. Results of the DTF indicated lower frequency mast modes than model predictions, thus leading to speculation of mast damage. A detailed nonlinear analysis was performed on the 2A array model to assess possible solutions to modal differences. The setup of the parametric nonlinear trade study included the use of a detailed array model and the reduced mass and stiffness matrices of the entire ISS being applied to the array interface. The study revealed that the array attachment structure is nonlinear and thus was the source of error in the model prediction of mast modes. In addition, a detailed study was performed to determine mast mode sensitivity to mast longeron damage. This sensitivity study was performed to assess if the ISS program has sufficient instrumentation for mast damage detection.

Laible, Michael↗

NASA NTRS1990

Dynamic substructuring by the boundary flexibility vector method of component mode synthesis

Component mode synthesis (CMS) is a method of dynamic analysis, for structures having a large number of degrees of freedom (DOF). These structures often required lengthy computer CPU time and large computer memory resources, if solved directly by the finite-element method (FEM). In CMS, the structure is divided into independent components in which the DOF are defined by a set of generalized coordinates defined by displacement shapes. The number of the generalized coordinates are much less than the original number of physical DOF, in the component. The displacement shapes are used to transform the component property matrices and any applied external loads, to a reduced system of coordinates. Reduced system property matrices are assembled, and any type of dynamic analysis is carried out in the reduced coordinate system. Any obtained results are back transformed to the original component coordinate systems. In all conventional methods of CMS, the mode shapes used for components are dynamic mode shapes, supplemented by static deflected shapes. Historically, all the dynamic mode shapes used in conventional CMS are the natural modes (eigenvectors) of components. A new method of CMS, namely the boundary flexibility vector method of CMS, is presented. The method provides for the incorporation of a set of static Ritz vectors, referred to as boundary flexibility vectors, as a replacement and/or supplement to conventional eigenvectors, as displacement shapes for components. The generation of these vectors does not require the solution of a costly eigenvalue problem, as in the case of natural modes in conventional CMS, and hence a substantial saving in CPU time can be achieved. The boundary flexibility vectors are generated from flexibility (or stiffness) properties of components. The formulation presented is for both free and fixed-interface components, and for both the free and forced vibration problems. Free and forced vibration numerical examples are presented to verify the accuracy of the method and the saving in CPU time. Compared to conventional methods of CMS, the results indicate that by using the new method, more accurate results can be obtained with a substantial saving in CPU time.

Abdallah, Ayman Ahmed↗

NASA NTRS1991

Determination of Rotordynamic Coefficients for Labyrinth Seals and Application to Rotordynamic Design Calculations

In today's rotordynamic calculations, the input parameters for a finite element analysis (FEA) determine very much the reliability of eigenvalue and eigenmode predictions. While modeling of an elastic structure by means of beam elements etc. is relatively straightforward to perform and the input data for journal bearings are usually known exactly enough, the determination of stiffness and damping for labyrinth seals is still the subject of many investigations. Therefore, the rotordynamic influence of labyrinths is often not included in FEA for rotating machinery because of a lack of computer programs to calculate these parameters. This circumstance can give rise to severe vibration problems especially for high performance turbines or compressors, resulting in remarkable economic losses. The forces generated in labyrinths can be described for small motions around the seal center with a linearized force-motion relationship. Several years ago, we started with the development of computer codes for the determination of rotordynamic seal coefficients. Our different approaches to evaluate the dynamic fluid forces generated by turbulent, compressible seal flow are introduced.

Weiser, P.↗

NASA NTRS1988

Evaluation of a methodology for model identification in the time domain

A model identification methodology for structural dynamics has been applied to simulated vibrational data as a first step in evaluating its accuracy. The evaluation has taken into account a wide variety of factors which affect the accuracy of the procedure. The effects of each of these factors were observed in both the response time histories and the estimates of the parameters of the model by comparing them with the exact values of the system. Each factor was varied independently but combinations of these have also been considered in an effort to simulate real situations. The results of the tests have shown that for the chain model, the procedure yields robust estimates of the stiffness parameters under the conditions studied whenever uniqueness is ensured. When inaccuracies occur in the results, they are intimately related to non-uniqueness conditions inherent in the inverse problem and not to shortcomings in the methodology.

Beck, R. T.↗

NASA NTRS1994

Sensitivity of lag-damping correlations to structural and aerodynamic approximations of isolated experimental rotors in forward flight

The predictions of regressive lag-mode damping levels are correlated with the database of an isolated, soft-inplane, three-blade rotor operated untrimmed. The database was generated at the Army Aeroflightdynamics Directorate at Ames. The correlation covers a broad range of data, from near-zero thrust conditions in hover to high-thrust and highly stalled conditions in forward flight with advance ratio as high as 0.55 and shaft angle as high as 20 degrees. In the experimental rotor, the airfoil or blade portion has essentially uniform mass and stiffness distributions, but the root flexure has highly nonuniform mass and stiffness distributions. Accordingly, the structural approximations refer to four models of root-flexure-blade assembly. They range from a rigid flap-lag model to three elastic flap-lag-torsion models, which differ in modeling the root flexure. The three models of root-flexure are: three root springs in which the bending-torsion couplings are fully accounted for; a finite-length beam element with some average mass and stiffness distributions such that the fundamental frequencies match those of the experimental model; and accurate modal representation in which the actual mass and stiffness distributions of the experimental root-flexure-blade assembly are used in calculating the nonrotating mode shapes. The four models of root-flexure-blade assembly are referred to as the rigid flap-lag model, spring model, modified model and modal model. For each of these four models of the root-flexure-blade assembly, the predictions are based on the following five aerodynamic theories: ear theory, which accounts for large angle-of-attack and reverse-flow effects on lift, and has constant drag and pitching moment; quasisteady stall theory, which includes quasisteady stall lift, drag and pitching moment characteristics of the airfoil section, dynamics stall theory, which uses the ONERA dynamic stall models of lift, drag and pitching moment; dynamic wake theory, which is based on a finite-state three-dimensional wake model and includes all wake effects including both shed and trailing vorticity; and dynamics and wake theory, which combines both dynamic stall theory and dynamic wake theory and is a relatively complete aerodynamic representation.

Gaonkar, G. H.↗

NASA NTRS1981

Flap-lag-torsional dynamic modelling of rotor blades in hover and in forward flight, including the effect of cubic nonlinearities

The differential equations of motion, and boundary conditions, describing the flap-lead/lag-torsional motion of a flexible rotor blade with a precone angle and a variable pitch angle, which incorporates a pretwist, are derived via Hamilton's principle. The meaning of inextensionality is discussed. The equations are reduced to a set of three integro partial differential equations by elimination of the extension variable. The generalized aerodynamic forces are modelled using Greenberg's extension of Theodorsen's strip theory. The equations of motion are systematically expanded into polynomial nonlinearities with the objective of retaining all terms up to third degree. The blade is modeled as a long, slender, of isotropic Hookean materials. Offsets from the blade's elastic axis through its shear center and the axes for the mass, area and aerodynamic centers, radial nonuniformaties of the blade's stiffnesses and cross section properties are considered and the effect of warp of the cross section is included in the formulation.

Crespodasilva, M. R. M.↗

NASA NTRS2011

A Quasi-Steady Flexible Launch Vehicle Stability Analysis Using Steady CFD with Unsteady Aerodynamic Enhancement

Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin is caused by an undamping of the aerodynamics in one of the lower frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic lineloads derived from steady rigid computational fluid dynamics (CFD). However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers where experiment or unsteady computational aeroelastic (CAE) analysis show a reduced or even negative aerodynamic damping. This paper will present a method of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics. The enhanced formulation uses unsteady CFD to compute the response of selected lower frequency modes. The response is contained in a time history of the vehicle lineloads. A proper orthogonal decomposition of the unsteady aerodynamic lineload response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping and mass matrices. The results of the enhanced quasi-static aeroelastic stability analysis are compared with the damping and frequency computed from unsteady CAE analysis and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady CAE analysis.

Bartels, Robert E.↗

NASA NTRS1992

Update on the advanced Stirling conversion system project for 25 kW dish Stirling applications

Technology development for Stirling convertors directed toward a dynamic power source for space applications is examined. The free-piston Stirling engine has the potential for both solar and nuclear space power applications. Two parallel design directions feature a solar receiver/liquid metal heat transport system, and a free-piston Stirling convertor which incorporates a linear alternator to directly provide the electrical output of about 25 kW to a utility grid. The Cummins Engine Company (CEC) free-piston Stirling convertor incorporates a linear alternator along with hydrodynamic gas bearings to provide noncontacting, wear-free support to the pistons. The Stirling Technology Company design incorporates linear alternator technology with flexures that provide noncontacting support while also supplying much of the spring stiffness needed to obtain proper resonance.

Shaltens, Richard K.↗

NASA NTRS2005

Active Aeroelastic Wing Aerodynamic Model Development and Validation for a Modified F/A-18A

A new aerodynamic model has been developed and validated for a modified F/A-18A used for the Active Aeroelastic Wing (AAW) research program. The goal of the program was to demonstrate the advantages of using the inherent flexibility of an aircraft to enhance its performance. The research aircraft was an F/A-18A with wings modified to reduce stiffness and a new control system to increase control authority. There have been two flight phases. Data gathered from the first flight phase were used to create the new aerodynamic model. A maximum-likelihood output-error parameter estimation technique was used to obtain stability and control derivatives. The derivatives were incorporated into the National Aeronautics and Space Administration F-18 simulation, validated, and used to develop new AAW control laws. The second phase of flights was used to evaluate the handling qualities of the AAW aircraft and the control law design process, and to further test the accuracy of the new model. The flight test envelope covered Mach numbers between 0.85 and 1.30 and dynamic pressures from 600 to 1250 pound-force per square foot. The results presented in this report demonstrate that a thorough parameter identification analysis can be used to improve upon models that were developed using other means. This report describes the parameter estimation technique used, details the validation techniques, discusses differences between previously existing F/A-18 models, and presents results from the second phase of research flights.

Cumming, Stephen B.↗

NASA NTRS2005

Active Aeroelastic Wing Aerodynamic Model Development and Validation for a Modified F/A-18A Airplane

A new aerodynamic model has been developed and validated for a modified F/A-18A airplane used for the Active Aeroelastic Wing (AAW) research program. The goal of the program was to demonstrate the advantages of using the inherent flexibility of an aircraft to enhance its performance. The research airplane was an F/A-18A with wings modified to reduce stiffness and a new control system to increase control authority. There have been two flight phases. Data gathered from the first flight phase were used to create the new aerodynamic model. A maximum-likelihood output-error parameter estimation technique was used to obtain stability and control derivatives. The derivatives were incorporated into the National Aeronautics and Space Administration F-18 simulation, validated, and used to develop new AAW control laws. The second phase of flights was used to evaluate the handling qualities of the AAW airplane and the control law design process, and to further test the accuracy of the new model. The flight test envelope covered Mach numbers between 0.85 and 1.30 and dynamic pressures from 600 to 1250 pound-force per square foot. The results presented in this report demonstrate that a thorough parameter identification analysis can be used to improve upon models that were developed using other means. This report describes the parameter estimation technique used, details the validation techniques, discusses differences between previously existing F/A-18 models, and presents results from the second phase of research flights.

Cumming, Stephen B.↗

NASA NTRS2011

Enhanced Correlation of SMART Active Flap Rotor Loads

This is a follow-on study to a 2010 correlation effort. Measured data from the SMART rotor test in the NASA Ames 40- by 80- Foot Wind Tunnel are compared with CAMRAD II calculations. As background, during the wind tunnel test, unexpectedly high inboard loads were encountered, and it was hypothesized at that time that due to changes in the flexbeams over the years, the flexbeam properties used in the analysis needed updating. Boeing Mesa, recently updated these properties. This correlation study uses the updated flexbeam properties. Compared to earlier studies, the following two enhancements are implemented: i) the inboard loads (pitchcase and flexbeam loads) correlation is included for the first time (reliable prediction of the inboard loads is a prerequisite for any future anticipated flight-testing); ii) the number of blade modes is increased to better capture the flap dynamics and the pitchcase-flexbeam dynamics. Also, aerodynamically, both the rolled-up wake model and the more complex, multiple trailer wake model are used, with the latter slightly improving the blade chordwise moment correlation. This sensitivity to the wake model indicates that CFD is needed. Three high-speed experimental cases, one uncontrolled free flap case and two commanded flap cases, are considered. The two commanded flap cases include a 2o flap deflection at 5P case and a 0o flap deflection case. For the free flap case, selected modifications to the HH-06 section flap airfoil pitching moment table are implemented. For the commanded 2o flap case, the experimental flap variation is approximately matched by increasing the analytical flap hinge stiffness. This increased flap hinge stiffness is retained for the commanded 0o flap case also, which is treated as a free flap case, but with larger flap hinge stiffness. The change in the mid-span and outboard loads correlation due to the updating of the flexbeam properties is not significant. Increasing the number of blade modes results in an effective, commanded flap hinge stiffness of 4X baseline, not 3X as reported earlier. The inboard loads correlation is reasonable, but needs further study. Overall, the free flap case correlation is reasonable, thus confirming the basic correctness of the current semi-empirical modifications; the correlation for the commanded 2o flap at 5P case and the 0o flap case is also reasonable.

Kottapalli, Sesi↗

NASA NTRS1998

A Magnetic Suspension and Excitation System for Spin Vibration Testing of Turbomachinery Blades

The Dynamic Spin Rig (DSR) is used to perform vibration tests of turbomachinery blades and components under spinning conditions in a vacuum. A heteropolar radial active magnetic bearing was integrated into the DSR to provide non-contact magnetic suspension and mechanical excitation of the rotor to induce turbomachinery blade vibrations. The magnetic bearing replaces one of the two existing conventional radial ball bearings. Prior operation of the DSR used two voice-coil type linear electromagnetic shakers which provided axial excitation of the rotor. The new magnetic suspension and excitation system has provided enhanced testing capabilities. Tests were performed at high rotational speeds for longer duration and higher vibration amplitudes. Some characteristics of the system include magnetic bearing stiffness values up to 60,000 lb./in., closed loop control bandwidth around 500 Hz, and multi-directional radial excitation of the rotor. This paper reports on the implementation and operation of this system and presents some test results using this system.

Johnson, Dexter↗

NASA NTRS1999

Hubble Space Telescope (HST) Solar Array Damper

This paper describes the design of a solar array damper that will be built into each of two new solar arrays to be installed on the Hubble Space Telescope (HST) during Servicing Mission 3. On this mission, currently scheduled for August, 2000, two "rigid" solar array wings will replace the "flexible" wings currently providing power for HST. Dynamic interaction of these wings with the telescope spacecraft can affect the Pointing Control System. The damper, which is integral to the mast of the solar array, suppresses the fundamental bending modes of the deployed wings at 1.2 Hz (in-plane) and 1.6 Hz (out-of-plane). With the flight version of the damper, modal damping of 2.3% of critical is expected over the temperature range of -4 C to 23 C with a peak damping level of 3.9%. The unique damper design is a combination of a titanium spring and viscoelastic-shear-lap dashpot. The damper was designed using a system finite element model of the solar array wing and measured viscoelastic material properties. Direct complex stiffness (DCS) testing was performed to characterize the frequency- and temperature-dependent behavior of the damping prior to fixed-base modal testing of the wing at NASA/Goddard Space Flight Center (NASA/GSFC).

Maly, J. R.↗

NASA NTRS1987

Evaluation of seals for high-performance cryogenic turbomachines

An approach to computing flow and dynamic characteristics for seals or bearings is discussed. The local average velocity was strongly influenced by inlet and exit effects and fluid injection, which in turn drove zones of secondary flow. For the restricted three-dimensional model considered, the integral averaged results were in reasonable agreement with selected data. Unidirectional pressure measurements alone were insufficient to define such flow variations. However, for seal and bearing leakage correlations the principles of corresponding states were found to be useful. Also discussed are three phenomena encountered during testing of three eccentric nonrotating seal configurations for the Space Shuttle Main Engine (SSME) Program. Fluid injection, choking within a seal, and pressure profile crossover are related to postulated zones of secondary flow or separation and to direct stiffness.

Hendricks, R. C.↗

NASA NTRS1977

Dynamic blade loading in the ERDA/NASA 100 kW and 200 kW wind turbines

Dynamic blade loads, including aerodynamic, gravitational, and inertial effects, are presented for two large horizontal-axis wind turbines: the ERDA-NASA 100 kW Mod-0 and 200 kw Mod-0A wind power systems. Calculated and measured loads are compared for an experimental Mod-0 machine in operation. Predicted blade loads are also given for the higher power Mod-0A wind turbine now being assembled for operation as part of a municipal power plant. Two major structural modifications have been made to the Mod-0 wind turbine for the purpose of reducing blade loads. A stairway within the truss tower was removed to reduce the impulsive aerodynamic loading caused by the tower wake on the downwind rotor blades. Also, the torsional stiffness of the yaw drive mechanism connecting the turbine nacelle to the tower was doubled to reduce rotor-tower interaction loads. Measured reductions in load obtained by means of these two modifications equaled or exceeded predictions.

Spera, D. A.↗