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NASA NTRS1996

Comparison of Code Predictions to Test Measurements for Two Orifice Compensated Hydrostatic Bearings at High Reynolds Numbers

Rotordynamic coefficients obtained from testing two different hydrostatic bearings are compared to values predicted by two different computer programs. The first set of test data is from a relatively long (L/D=1) orifice compensated hydrostatic bearing tested in water by Texas A&M University (TAMU Bearing No.9). The second bearing is a shorter (L/D=.37) bearing and was tested in a lower viscosity fluid by Rocketdyne Division of Rockwell (Rocketdyne 'Generic' Bearing) at similar rotating speeds and pressures. Computed predictions of bearing rotordynamic coefficients were obtained from the cylindrical seal code 'ICYL', one of the industrial seal codes developed for NASA-LeRC by Mechanical Technology Inc., and from the hydrodynamic bearing code 'HYDROPAD'. The comparison highlights the difference the bearing has on the accuracy of the predictions. The TAMU Bearing No. 9 test data is closely matched by the predictions obtained for the HYDROPAD code (except for added mass terms) whereas significant differences exist between the data from the Rocketdyne 'Generic' bearing the code predictions. The results suggest that some aspects of the fluid behavior in the shorter, higher Reynolds Number 'Generic' bearing may not be modeled accurately in the codes. The ICYL code predictions for flowrate and direct stiffness approximately equal those of HYDROPAD. Significant differences in cross-coupled stiffness and the damping terms were obtained relative to HYDROPAD and both sets of test data. Several observations are included concerning application of the ICYL code.

Keba, John E.↗

NASA NTRS1996

The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals

A two-control volume is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the through flow and a 'capacitance accumulator' model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals can not be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transfer functions are required to account for the reaction forces, and calculated here as a lead-lag term for the direct force function and a lag term for the cross-coupled function. These first order functions are simple compared to transfer functions for magnetic bearings or foundations, For synchronous response to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamic codes. Correct predictions for stability and transient response will require more general algorithms, pressumably using a state-space format.

Childs, Dara W.↗

NASA NTRS1996

Large deflection analysis of a tension-foil bearing

The rolling element bearings (REB's) which support many turbomachinery rotors offer high load capacity, low power requirements, and durability. Two disadvantages of REB's are as follows: rolling or sliding contact within the bearing has life-limiting consequences; and REB's provide essentially no damping. The REB's in the Space Shuttle Main Engine (SSME) turbopumps must sustain high static and dynamic loads, at high speeds, with a cryogenic fluid as lubricant and coolant. The pump end ball bearings limit the life of the SSME high pressure oxygen turbopump (HPOTP). Compliant foil bearing (CFB) manufacturers have proposed replacing turbopump REB's with CFB's. CFB's work well in aircraft air cycle machines, auxiliary power units, and refrigeration compressors. In a CFB, the rotor only contacts the foil support structure during start up and shut down. CFB damping is higher than REB damping. However, the load capacity of the CFB is low, compared to a REB. Furthermore, little stiffness and damping data exist for the CFB. A rotordynamic analysis for turbomachinery critical speeds and stability requires the input of bearing stiffness and damping coefficients. The two basic types of CFB are the tension-dominated bearing and the bending-dominated bearing. Many investigators have analyzed and measured characteristics of tension-dominated foil bearings, which are applied principally in magnetic tape recording. The bending-dominated CFB is used more in rotating machinery. Recently, a new tension-foil bearing configuration has been proposed for turbomachinery applications.

Elrod, David A.↗

NASA NTRS1996

Predictions of Control Inputs, Periodic Responses and Damping Levels of an Isolated Experimental Rotor in Trimmed Flight

Since the early 1990s the Aeroflightdynamics Directorate at the Ames Research Center has been conducting tests on isolated hingeless rotors in hover and forward flight. The primary objective is to generate a database on aeroelastic stability in trimmed flight for torsionally soft rotors at realistic tip speeds. The rotor test model has four soft inplane blades of NACA 0012 airfoil section with low torsional stiffness. The collective pitch and shaft tilt are set prior to each test run, and then the rotor is trimmed in the following sense: the longitudinal and lateral cyclic pitch controls are adjusted through a swashplate to minimize the 1/rev flapping moment at the 12 percent radial station. In hover, the database comprises lag regressive-mode damping with pitch variations. In forward flight the database comprises cyclic pitch controls, root flap moment and lag regressive-mode damping with advance ratio, shaft angle and pitch variations. This report presents the predictions and their correlation with the database. A modal analysis is used, in which nonrotating modes in flap bending, lag bending and torsion are computed from the measured blade mass and stiffness distributions. The airfoil aerodynamics is represented by the ONERA dynamic stall models of lift, drag and pitching moment, and the wake dynamics is represented by a state-space wake model. The trim analysis of finding, the cyclic controls and the corresponding, periodic responses is based on periodic shooting with damped Newton iteration; the Floquet transition matrix (FTM) comes out as a byproduct. The stabillty analysis of finding the frequencies and damping levels is based on the eigenvalue-eigenvector analysis of the FTM. All the structural and aerodynamic states are included from modeling to trim analysis. A major finding is that dynamic wake dramatically improves the correlation for the lateral cyclic pitch control. Overall, the correlation is fairly good.

Gaonkar, G. H.↗

NASA NTRS1995

Global Dynamic Modeling of Space-Geodetic Data

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

Bird, Peter↗

NASA NTRS1995

Experimental Verification of a Progressive Damage Model for IM7/5260 Laminates Subjected to Tension-Tension Fatigue

The durability and damage tolerance of laminated composites are critical design considerations for airframe composite structures. Therefore, the ability to model damage initiation and growth and predict the life of laminated composites is necessary to achieve structurally efficient and economical designs. The purpose of this research is to experimentally verify the application of a continuum damage model to predict progressive damage development in a toughened material system. Damage due to monotonic and tension-tension fatigue was documented for IM7/5260 graphite/bismaleimide laminates. Crack density and delamination surface area were used to calculate matrix cracking and delamination internal state variables to predict stiffness loss in unnotched laminates. A damage dependent finite element code predicted the stiffness loss for notched laminates with good agreement to experimental data. It was concluded that the continuum damage model can adequately predict matrix damage progression in notched and unnotched laminates as a function of loading history and laminate stacking sequence.

Coats, Timothy W.↗

NASA NTRS1996

An Interactive Software for Conceptual Wing Flutter Analysis and Parametric Study

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well-defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed for Macintosh or IBM compatible personal computers, on MathCad application software with integrated documentation, graphics, data base and symbolic mathematics. The analysis method was based on non-dimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, taper ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The parametric plots were compiled in a Vought Corporation report from a vast data base of past experiments and wind-tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended-Wing-Body concept, proposed by McDonnell Douglas Corp. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗

NASA NTRS1997

Effects of Compression, Staging, and Braid Angle on Braided Rope Seal Performance

Future turbine engines and industrial systems will be operating at increased temperatures to achieve more demanding efficiency and performance goals. In the highest temperature sections of the engine new material systems such as ceramics and intermetallics are being considered to withstand the harsh thermal environment. Components constructed of these low expansion-rate materials experience thermal strains and a resulting reduction of life when rigidly attached to high expansion-rate, superalloy support structures. Seals are being designed to both seal and to serve as compliant mounts allowing for relative thermal growths between high temperature but brittle primary structures and the surrounding support structures. Previous seal research yielded several braided rope seal designs which demonstrated the ability to both seal and serve as a compliant mount. The hybrid seal was constructed of an all-ceramic (alumina-silica) core overbraided with a superalloy wire sheath (cobalt based superalloy). The all ceramic seal was constructed of an all-ceramic (alumina-silica) core overbraided with multiple ceramic (alumina-silica) sheath layers. Program goals for braided rope seals are to improve flow resistance and/or seal resilience. To that end, the current report studies the test results of: baseline and modified hybrid seals; two stage hybrid and two stage all-ceramic seal configurations; and single stage hybrid and single stage all-ceramic seal configurations for a range of seal crush conditions. Hybrid seal modifications include increasing the sheath braid angle and core coverage. For the same percent seal cross-sectional crush, results show that increasing the hybrid seal braid angle increased seal stiffness and seal unit load, resulting in flows approximately one third of the baseline hybrid seal flows. For both hybrid and all-ceramic seals, two stage seal configurations significantly outperformed single stage configurations. Two stage seal flows were at least 30% less than the single stage seal flows for the same seal crush. Furthermore, test results of single stage seals indicate that for both all-ceramic and hybrid seals, a specific seal crush condition exists at which minimum flows are achieved (i.e. increasing seal crush beyond a certain point does not result in better flow performance). Flow results are presented for a range of pressures and temperatures from ambient to 1300 F, before and after scrubbing. Compression tests results show that for both all-ceramic and hybrid seals, seal preload and stiffness increase with seal crush, but residual seal interference remains constant.

Steinetz, Bruce M.↗

NASA NTRS1994

Aeroelastic Stability of Modern Bearingless Rotors: A Parametric Investigation

The University of Maryland Advanced Rotorcraft Code (UMARC) is utilized to study the effects of blade design parameters on the aeroelastic stability of an isolated modern bearingless rotor blade in hover. The McDonnell Douglas Advanced Rotor Technology (MDART) Rotor is the baseline rotor investigated. Results indicate that kinematic pitch-lag coupling introduced through the control system geometry and the damping levels of the shear lag dampers strongly affect the hover inplane damping of the baseline rotor blade. Hub precone, pitchcase chordwise stiffness, and blade fundamental torsion frequency have small to moderate influence on the inplane damping, while blade pre-twist and placements of blade fundamental flapwise and chord-wise frequencies have negligible effects. A damperless configuration with a leading edge pitch-link, 15 deg of pitch-link cant angle, and reduced pitch-link stiffness is shown to be stable with an inplane damping level in excess of 2.7 percent critical at the full hover tip speed.

Nguyen, Khanh Q.↗

NASA NTRS1994

Dynamically Tuned Blade Pitch Links for Vibration Reduction

A passive vibration reduction device in which the conventional main rotor blade pitch link is replaced by a spring/damper element is investigated using a comprehensive rotorcraft analysis code. A case study is conducted for a modern articulated helicopter main rotor. Correlation of vibratory pitch link loads with wind tunnel test data is satisfactory for lower harmonics. Inclusion of unsteady aerodynamics had little effect on the correlation. In the absence of pushrod damping, reduction in pushrod stiffness from the baseline value had an adverse effect on vibratory hub loads in forward flight. However, pushrod damping in combination with reduced pushrod stiffness resulted in modest improvements in fixed and rotating system hub loads.

Milgram, Judah↗

NASA NTRS1997

Development of a Model Based Technique for Gear Diagnostics using the Wigner-Ville method

Imperfections in gear tooth geometry often result from errors in the manufacturing process or excessive material wear during operation. Such faults in the gear tooth geometry can result in large vibrations in the transmission system, and, in some cases, may lead to early failure of the gear transmission system. This report presents the study of the effects of imperfection in gear tooth geometry on the dynamic characteristics of a gear transmission system. The faults in the gear tooth geometry are modeled numerically as the deviation of the tooth profile from its original involute geometry. The changes in gear mesh stiffness due to various profile and pattern variations are evaluated numerically. The resulting changes in the mesh stiffness are incorporated into a computer code to simulate the dynamics of the gear transmission system. A parametric study is performed to examine the sensitivity of gear tooth geometry imperfections on the vibration of a gear transmission system. The parameters variations in this study consist of the magnitude of the imperfection, the pattern of the profile variation, and the total number of teeth affected. Numerical results from the dynamic simulations are examined in both the time and the frequency domains. A joint time-frequency analysis procedure using the Wigner-Ville Distribution is also introduced to identify the location of the damaged tooth from the vibration signature. Numerical simulations of the system dynamics with gear faults were compared to experimental results. An optimal tracker was introduced to quantify the level of damage in the gear mesh system. Conclusions are drawn from the results of this numerical study.

Choy, F.↗

NASA NTRS1998

Free-Suspension Residual Flexibility Testing of Space Station Pathfinder: Comparison to Fixed-Base Results

Application of the free-suspension residual flexibility modal test method to the International Space Station Pathfinder structure is described. The Pathfinder, a large structure of the general size and weight of Space Station module elements, was also tested in a large fixed-base fixture to simulate Shuttle Orbiter payload constraints. After correlation of the Pathfinder finite element model to residual flexibility test data, the model was coupled to a fixture model, and constrained modes and frequencies were compared to fixed-base test. modes. The residual flexibility model compared very favorably to results of the fixed-base test. This is the first known direct comparison of free-suspension residual flexibility and fixed-base test results for a large structure. The model correlation approach used by the author for residual flexibility data is presented. Frequency response functions (FRF) for the regions of the structure that interface with the environment (a test fixture or another structure) are shown to be the primary tools for model correlation that distinguish or characterize the residual flexibility approach. A number of critical issues related to use of the structure interface FRF for correlating the model are then identified and discussed, including (1) the requirement of prominent stiffness lines, (2) overcoming problems with measurement noise which makes the antiresonances or minima in the functions difficult to identify, and (3) the use of interface stiffness and lumped mass perturbations to bring the analytical responses into agreement with test data. It is shown that good comparison of analytical-to-experimental FRF is the key to obtaining good agreement of the residual flexibility values.

Tinker, Michael L.↗

NASA NTRS1961

An Analytical Treatment of Aircraft Propeller Precession Instability

An analytical investigation is made of a precession-type instability which can occur in a flexibly supported aircraft-engine-propeller combination. By means of an idealized mathematical model which is comprised of a rigid power-plant system flexibly mounted in pitch and yaw to a fixed backup structure, the conditions required for neutral stability are determined. The paper also examines the sensitivity of the stability boundaries to changes in such parameters as stiffness, damping, and asymmetries in the engine mount, propeller speed, airspeed, Mach number, propeller thrust, and location of pitch and yaw axes. Stability is found to depend strongly on the damping and stiffness in the system. With the use of nondimensional charts, theoretical stability boundaries are compared with experimental results obtained in wind-tunnel tests of an aeroelastic airplane model. In general, the theoretical results, which do not account for wing response, show the same trends as observed experimentally; however, for a given set of conditions calculated airspeeds for neutral stability are consistently lower than the measured values. Evidently, this result is due to the fact that wing response tends to add damping to the system.

Reed, Wilmer H., III↗

NASA NTRS1976

Environmental Effects on Graphite-Epoxy Fatigue Properties

Effects of torsional and flexural fatigue on the long-time Integrity of advanced graphite-epoxy structural composites have been investigated. Torsional fatigue tests were run at stress ratios of R = 0 (zero to maximum, repeated) and R = -1 (zero mean stress) on unidirectional, angleply, and woven graphite fiber materials in air and water at room temperature and at 74 C. Flexural fatigue tests (four-point bending) with R = -1 were run in air and water at room temperature, and with R = 0 in air. Results show that, in torsional cycling, both water environment and higher test temperature contribute to significant degradation of torsional stiffness. The degradation of stiffness from torsional stress cycling was observed to be much greater with R = -1 than with simple R = 0 cycling. The effect of environment also is greater in the fully reversed cycling. Flexural fatigue results on +/- 30 deg material show a large fatigue effect, with fatigue limits of less than 50% and 30% of the static failure strength for specimens tested under stress ratios of R = 0 and R = -1, respectively. Compliance measurements indicate that the final failures are preceded by damage initiation and accumulation, which begins at about 1% of the specimen life.

Sumsion, H. T.↗

NASA NTRS1960

Some Divergence Characteristics of Low-Aspect-Ratio Wings at Transonic and Supersonic Speeds

The problem of chordwise, or camber, divergence at transonic and supersonic speeds is treated with primary emphasis on slender delta wings having a cantilever support at the trailing edge. Experimental and analytical results are presented for four wing models having apex half-angles of 5 deg, 10 deg, 15 deg, and 20 deg. A Mach number range from 0.8 to 7.3 is covered. The analytical results include calculations based on small-aspect-ratio theory, lifting-surface theory, and strip theory. A closed-form solution of the equilibrium equation is given, which is based on low-aspect-ratio theory but which applies only to certain stiffness distributions. Also presented is an iterative procedure for use with other aerodynamic theories and with arbitrary stiffness distribution.

Woolston, Donald S.↗

NASA NTRS1959

Comparison of Measured Flapwise Structural Bending Moments on a Teetering Rotor Blade With Results Calculated From the Measured Pressure Distribution

Flapwise bending moments were calculated for a teetering rotor blade using a reasonably rapid theoretical method in which airloads obtained from wind-tunnel tests were employed. The calculated moments agreed reasonably well with those measured with strain gages under the same test conditions. The range of the tests included one hovering and two forward-flight conditions. The rotor speed for the test was very near blade resonance, and difficult-to-calculate resonance effects apparently were responsible for the largest differences between the calculated and measured harmonic components of blade bending moments. These differences, moreover, were largely nullified when the harmonic components were combined to give a comparison of the calculated and measured blade total- moment time histories. The degree of agreement shown is therefore considered adequate to warrant the use of the theoretical method in establishing and applying methods of prediction of rotor-blade fatigue loads. At the same time, the validity of the experimental methods of obtaining both airload and blade stress measurement is also indicated to be adequate for use in establishing improved methods for prediction of rotor-blade fatigue loads during the design stage. The blade stiffnesses and natural frequencies were measured and found to be in close agreement with calculated values; however, for a condition of blade resonance the use of the experimental stiffness values resulted in better agreement between calculated and measured blade stresses.

Mayo, Alton P.↗

NASA NTRS1998

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Koppenhoefer, Kyle C.↗

NASA NTRS1976

The Effects of Variable Mass and Geometry, Pretwist, Shear Deformation and Rotatory Inertia on the Resonant Frequencies of Intact Long Bones: A Finite Element Model Analysis

The influence of pretwist, nonuniformities in mass and flexural stiffness, rotatory inertia and shear deformation on the natural frequencies of intact bones is evaluated by means of a linear elastic, finite-element model which has been programmed for solution on the digital computer. Theoretical results are compared to the results on the forced vibration of intact canine radii obtained experimentally by Thompson. Surprisingly, inclusion of fairly large pretwist angles (from -14 to 12 deg for one specimen) had little affect on the first three frequencies of transverse vibration in either the cranial or lateral directions. Inclusion of shear deformation reduced the third-mode frequency in the stiffest (lateral) direction by about six percent, otherwise shear deformation played a minor role in determining natural frequencies. Similarly. rotatory inertia had negligible influence up to the third natural frequency. The predominant influence on the first three natural frequencies of transverse vibration could be attributed to the variations in mass and flexural stiffness along the length of the test specimens. Different effective moduli of elasticity are required to yield correct absolute values for the frequencies which correspond to experimental findings. thus implying the presence of some inhomogeneities in material properties around the bone cross-section and/or along its length.

Young, Donald R.↗