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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Telescope for x ray and gamma ray studies in astrophysics

Imaging of x-rays has been achieved by various methods in astrophysics, nuclear physics, medicine, and material science. A new method for imaging x-ray and gamma-ray sources avoids the limitations of previously used imaging devices. Images are formed in optical wavelengths by using mirrors or lenses to reflect and refract the incoming photons. High energy x-ray and gamma-ray photons cannot be reflected except at grazing angles and pass through lenses without being refracted. Therefore, different methods must be used to image x-ray and gamma-ray sources. Techniques using total absorption, or shadow casting, can provide images in x-rays and gamma-rays. This new method uses a coder made of a pair of Fresnel zone plates and a detector consisting of a matrix of CsI scintillators and photodiodes. The Fresnel zone plates produce Moire patterns when illuminated by an off-axis source. These Moire patterns are deconvolved using a stepped sine wave fitting or an inverse Fourier transform. This type of coder provides the capability of an instantaneous image with sub-arcminute resolution while using a detector with only a coarse position-sensitivity. A matrix of the CsI/photodiode detector elements provides the necessary coarse position-sensitivity. The CsI/photodiode detector also allows good energy resolution. This imaging system provides advantages over previously used imaging devices in both performance and efficiency.

Weaver, W. D.↗
NASA NTRS1994

Gain weighted eigenspace assignment

This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

Davidson, John B.↗
NASA NTRS1995

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Oh, K. S.↗
NASA NTRS2001

Seismic Study of the Solar Interior: Inferences from SOI/MDI Observations During Solar Activity

We have continued in collaboration with Dr. Eff-Darwich (University of La Laguna, Tenerife, Spain) the study of the structure, asphericity and dynamics of the solar interior from p-mode frequencies and frequency splittings. In March 2001, Dr. Eff-Darwich came for 3 weeks visit to CfA. During this visit we completed our work on the inversion of the internal solar rotation rate, and submitted a paper describing this work to the Astrophysical Journal. This paper has been recently revised in response to the referee comments and I expect that it will be accepted for publication very soon. We also have analyzed helioseismic data looking for temporal variations of the solar stratification near the base of the convection zone. We have expanded on the initial work that was presented at the SOHO-10/GONG-2000 meeting (October 2000, Tenerife), and are in the process of writing this up. Substantial progress towards the characterization of high-degree p-modes has been achieved. Indeed, in collaboration Dr. Rabello-Soares (Stanford University), we have gained a clear conceptual understanding of the various elements that affect the leakage matrix of the SOI/MDI instrument. This was presented in an invited talk at the SOHO-10/GONG-2000 meeting (October 2000, Tenerife). Once we will have successfully migrated from a qualitative to a quantitative assessment of these effects, we should be able to generate high-degree p-modes frequencies so crucial in the diagnostic of the layers just below solar surface.

Korzennik, Sylvain G.↗
NASA NTRS2004

Lunar and Planetary Science XXXV: Chondrules: The Never-Ending Story

The session "Chondrules: The Never-Ending Story" included the following reports:Dust Size Distribution in Solar Nebula Inferred from Shock-Wave Heating Model for Chondrule Formation; Collisional Destruction of Chondrules in Shock Waves and Inferred Dust to Gas Mass Ratio; Evaporation and Accompanying Isotopic Fractionation of Sulfur from Fe-S Melt During Shock Wave Heating ; Evaporation During Chondrule Formation, Recondensation as Fine Particles, and the Condensation of S and Other Volatile Elements; Fe Isotopes and the Formation of Chondrules; Pristine and Processed Metal in CR Chondrites: Condensation in the Solar Nebula and Partial Reequilibration During Chondrule Formation; Variation of the Condensation Path of Supercooled Silicate Melt; Volatile and Moderately Volatile Trace Element Composition of Chondrules and Matrix from CM Chondrites: Implications for Chondrule Formation; Opaque Mineral Assemblages at Chondrule Boundaries in the Vigarano CV Chondrite: Evidence for Gas-Solid Reactions Following Chondrule Formation; Forsterite and Olivine in Sahara-97210 (LL3.2) and Chainpur (LL3.4) Chondrules: Compositional Evolution and the Influence of Melting; The Vaguries of Pyroxene Nucleation and the Resulting Chondrule Textures; Contemporaneous Formation of Chondrules in the Al-26-Mg-26 System for Ordinary and CO Chondrites; and Al-Mg Isotopic Systematics in Ferromagnesian Chondrules from the Unequilibrated Ordinary Chondrite.

Source record↗
NASA NTRS2005

Seismic Study of the Solar Interior: Inferences from SOI/MDI Observations During Solar Activity

Work on the structure, asphericity and dynamics of the solar interior from p-mode frequencies and frequency splittings was carried out primarily in collaboration with Dr. Eff-Darwich (University of La Laguna, Tenerife). This ongoing collaboration produced new results for the inversion of the internal solar rotation rate and further development in inversion methodologies. It also resulted in inferences on the solar stratification. Substantial progress towards the characterization of high-degree p-modes has been achieved. In collaboration with Drs. Rabello-Soares and Schou (Stanford University), we have gained a clear conceptual understanding of the various elements that affect the leakage matrix of the SOI/MDI instrument. This work has precise implications on the properties and the characterization of the HMI instrument being developed for the SDO mission.

Korzennik, Sylvain G.↗
NASA NTRS2007

Development of a Tunable Electromechanical Acoustic Liner for Engine Nacelles

This report describes the development of a tunable electromechanical Helmholtz resonator (EMHR) for engine nacelles using smart materials technology. This effort addresses both near-term and long-term goals for tunable electromechanical acoustic liner technology for the Quiet Aircraft Technology (QAT) Program. Analytical models, i.e. lumped element model (LEM) and transfer matrix (TM) representation of the EMHR, have been developed to predict the acoustic behavior of the EMHR. The models have been implemented in a MATLAB program and used to compare with measurement results. Moreover, the prediction performance of models is further improved with the aid of parameter extraction of the piezoelectric backplate. The EMHR has been experimentally investigated using standard two-microphone method (TMM). The measurement results validated both the LEM and TM models of the EMHR. Good agreement between predicted and measured impedance is obtained. Short- and open circuit loads define the limits of the tuning range using resistive and capacitive loads. There is approximately a 9% tuning limit under these conditions for the non-optimized resonator configuration studied. Inductive shunt loads result in a 3 degree-of-freedom DOF) system and an enhanced tuning range of over 20% that is not restricted by the short- and open-circuit limits. Damping coefficient ' measurements for piezoelectric backplates in a vacuum chamber are also performed and indicate that the damping is dominated by the structural damping losses, such as compliant boundaries, and other intrinsic loss mechanisms. Based on models of the EMHR, a Pareto optimization design of the EMHR has been performed for the EMHR with non-inductive loads. The EMHR with non-inductive loads is a 2DOF system with two resonant fiequencies. The tuning ranges of the two resonant frequencies of the EMHR with non-inductive loads cannot be optimized simultaneously; a trade-off (i.e., a Pareto solution) must be reached. The Pareto solution provides the information for a designer that shows how design trade-offs can be used to satisfy specific design requirements. The optimization design of the EMHR with inductive loads aims at optimal tuning of these three resonant fiequencies. The results indicate that it is possible to keep the acoustic reactance of the resonator close to a constant over a given frequency range. An effort to mimic the second layer of the NASA 2DOF liner using a piezoelectric composite diaphragm has been made. The optimal acoustic reactance of the second layer of the NASA 2DOF liner is achieved using a thin PVDF composite diaphragm, but matching the acoustic resistance requires further investigation. Acoustic energy harvesting is achieved by connecting the EMHR to an energy reclamation circuit that converts the ac voltage signal across the piezoceramic to a conditioned dc signal. Energy harvesting experiment yields 16 m W continuous power for an incident SPL of 153 dB. Such a level is sufficient to power a variety of low power electronic devices. Finally, technology transfer has been achieved by converting the original NASA ZKTL FORTRAN code to a MATLAB code while incorporating the models of the EMHR. Initial studies indicate that the EMHR is a promising technology that may enable lowpower, light weight, tunable engine nacelle liners. This technology, however, is very immature, and additional developments are required. Recommendations for future work include testing of sample EMHR liner designs in NASA Langley s normal incidence dual-waveguide and the grazing-incidence flow facility to evaluating both the impedance characteristics as well as the energy reclamation abilities. Additional design work is required for more complex tuning circuits with greater performance. Poor electromechanical coupling limited the electromechanical tuning capabilities of the proof of concept EMHR. Different materials than those studies and perhaps novel composite material systems may dramatically improvehe electromechanical coupling. Such improvements are essential to improved mimicking of existing double layer liners.

Liu, Fei↗
NASA NTRS2018

Scattering and Extinction by Spherical Particles Immersed in an Absorbing Host Medium

Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum.

Far-field electromagnetic scattering; Absorbing ho↗
NASA NTRSDate not supplied

Unraveling Solar Wind Space Weathering of Carbon-Rich Asterods: Low-Flux VS. High-Flux Ion Irradiation of Murchison

Introduction: Space weathering processesalter the microstructural, compositional, and optical properties of airless planetary surfaces.Solar wind space weatheringforms ion-damaged rims within the outermost ~100 nm of regolith grains through atomic-displacements and implantation of energetic H+and He+ions[1]. Transmission electron microscope(TEM)studies of space weathered Itokawa and lunar olivine particles reveal predominantly nanocrystalline solar wind-damaged rims with only minor regions of amorphization[2-5]. This finding differs from laboratoryion irradiation experiments in which samples become amorphous at fluences 2-3 orders of magnitude lower than the independentlyconstrained fluences for still-crystalline natural samples [6-7].Ion flux is generally considered to have a secondaryeffectcompared to fluence in these irradiation experiments. However, solar wind irradiation of natural samples occurs at a flux that is ~4-5 orders of magnitude lower than whatisused inlaboratory simulations (e.g., [6,8-9]). Constraining how the very low ion flux of solar wind influences the microstructural, chemical, and spectral alteration of silicate minerals will improve our understanding of solar wind space weathering and aid in the analysis of returned samples from the Hayabusa2 and OSIRIS-REx missions. Here we report results from low-and high-flux ion irradiation experiments on the Murchison (CM2)meteoritewithcomparable total fluences. Methods: We performed low-flux and high-flux He+(4 keV) and H+(1 keV) irradiation experiments on separate, dry-cut Murchison slabs. Low-flux He+irradiation reached a total fluence of 2.1 x 1016ions/cm2(~400 years of exposure at Bennu) using a flux of 3.6 x 1011ions/cm2/s; low-flux H+irradiation reached a total fluence of 3.9 x 1016ions/cm2(~30 years) using a flux of 6.6 x 1011ions/cm2/s. High-flux He+irradiation reached a total fluence of 2.0 x 1016ions/cm2(~400 years)using a flux of 9.1 x 1012ions/cm2/s; high-flux H+irradiation reached a total fluence of 5.8 x 1016ions/cm2(~50 years)using flux of 8.4 x 1012ions/cm2/s. By irradiating to similar total fluences in both the low-flux and high-flux experiments, we can better isolate and evaluatethe effects of ion flux. Differences between unirradiatedand irradiated surfaces are determined using threeanalytical techniques:(1) in situX-ray photoelectron spectroscopy(XPS) reveals changes in surface chemistry,(2) visible to near-infrared spectroscopy (VNIR; 0.35-2.5 μm) highlights changes in spectraltrends, such as albedo and slope, and (3) TEM and energy-dispersive X-ray spectroscopy (EDS) identifieschanges in nanoscale structure and elemental composition within olivine and matrix electron-transparent thin sections prepared using focused ion beam scanning electron microscopy (FIB-SEM). Results and Discussion: XPS analyses of the low-fluxand high-fluxHe+-and H+-irradiated samples showa minorreduction in surface carbon contentand chemicalreduction ofFe3+to Fe2+. The latter result is consistent with the higher Fe2+/Fe3+ratios observed in phyllosilicate-rich space weathered rims of Ryugu grains [10].VNIR analyses suggest that the low-flux H+-irradiated spectrum has a slightly bluer slope (over 0.65-2.5 μm) compared to the unirradiated VNIR spectrum from [9] while the low-flux He+-irradiated spectral slope is comparable to the unirradiated surface. Both the high-flux He+-and H+-irradiated VNIR spectra exhibitslightlyhigheralbedos at shorter wavelengths relativeto their unirradiated counterparts, with He+irradiation yielding a greater change. Thus far, the low-flux He+-irradiated matrix and olivine FIBsections as well as the low-flux H+-irradiated olivine FIBsection have been examined with TEM. The surfaces of all three samplesshowless vesiculation than high-flux/high-fluenceirradiated matrix and olivine samples from [9]. The depth of phyllosilicate amorphization in thelow-fluxHe+-irradiated matrix FIBsection varieslaterally, with crystalline domains occurring as shallow as ~25 nm in some regions. Thelow-flux He+-irradiated olivine FIBsection has acontinuous,~40-90 nm thick ion-affected layer with polycrystalline and amorphous microstructures. The low-flux H+-irradiated olivine sampleexhibits a distinct, ~10-40 nm ion-affected layer whose uppermost ~20 nmin thicker regions is predominantly amorphous.Continuing to compare results from this work to those from [9] will provide a comprehensive understanding of how ion flux impacts the microstructural, chemical, and optical modification of various mineral phases and, in turn,help identify space weathering features from parent body alteration in Hayabusa2 and OSIRIS-REx returned samples.

D L Laczniak↗
DOE OSTI2020

High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

In this work, we present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrix-free operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrix-free operator evaluations utilize GPU-accelerated sum-factorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a low-order refined methodology with parallel subspace corrections, as described for diffusion problems in [1]. The saddle-point Stokes system is solved using block-preconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible Navier-Stokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

On the equinoctial orbit elements.

This paper investigates the equinoctial orbit elements for the two-body problem, showing that the associated matrices are free from singularities for zero eccentricities and zero and ninety degree inclinations. The matrix of the partial derivatives of the position and velocity vectors with respect to the orbit elements is given explicitly, together with the matrix of inverse partial derivatives, in order to facilitate construction of the matrizant (state transition matrix) corresponding to these elements. The Lagrange and Poisson bracket matrices are also given. The application of the equinoctial orbit elements to general and special perturbations is discussed.

Broucke, R. A.↗
DOE OSTI2025

Solute Redistribution During Aging in a Laser-Based Powder Bed Fusion-Produced Fe-18Ni-9Co-5Mo-Ti Maraging Steel

Solute distribution during the laser-based powder bed fusion of metals process is highly complex because of solidification. This study builds on a previous investigation of how solute heterogeneities across different scales influence phase distribution and aging physical phenomena in a Fe-18Ni-9Co-5Mo-Ti maraging steel (Santana et al. in Addit Manuf 104494, 2024). Previous work using energy-dispersive X-ray spectroscopy revealed heterogeneous Ni and Mo enrichment at intercellular regions. Using X-ray diffraction, 8 ± 3% retained austenite was quantified in as-built samples. Additionally, electron backscatter diffraction analysis exposed the location of retained austenite along cell boundaries. In this work, scanning transmission electron microscopy results revealed the presence of non-enriched retained austenite in the as-built condition. With increased aging temperature, Ni and Mo enrichment in austenite increased, especially at the austenite/martensite boundary. Solute diffusion was simulated in DICTRA Thermo-Calc® software to assess solute redistribution between the matrix and second phases and to comprehend whether elemental diffusion processes are interconnected. Three different scenarios were considered: (1) solute diffusion in the matrix; (2) diffusion with enriched austenite in the intercellular region; (3) diffusion with non-enriched austenite in the intercellular region. Results showed that Ni partitioning controls austenite growth and that boundary regions exhibit higher element enrichment than the core.

42 ENGINEERING↗
DOE OSTI2021

Application of HRGS for forensic characterization of uranium oxides, pure uranium metals and uranium alloys

A nondestructive iterative method for uranium-bearing material characterization with HRGS developed earlier in (J. appl. Rad. Isotopes, 166 (2020) 109433) is applied to determine matrix densities and uranium isotope masses of a variety of uranium materials, namely uranium ore, UO 2 and U 3 O 8 powders, fuel elements in the form of UO2 microspheres, uranium metal and uranium alloys. It is shown that U 3 O 8 powders with uranium mass fraction of about 84% can be distinguished from the powders of UO 2 with uranium mass fraction of about 87%; uranium products in the form of liquid or loose powder with matrix density of 0.5-2.0 g/cm 3 can be distinguished from uranium products in the form of compacted fuel elements with matrix density of 6.0-10.0 g/cm 3 and from pure metal uranium and uranium alloys with matrix density of 14.0- 19.0 g/cm 3 . In fuel microspheres based on UO2 the uranium mass fraction 88.02% measured by HRGS is consistent, within the measurement uncertainties, with the results of isotope dilution mass spectrometry 87.76±0.64 % and also is confirmed by X-ray diffraction technique. The uranium mass fraction of the uranium ore estimated as 0.08% by HRGS is consistent, within the measurement uncertainties, with the value 0.09±0.01% determined with WDXRF. Densities of two different uranium metal samples, estimated as 18.42 g/cm 3 and 19.33 g/cm 3 by HRGS are consistent with values 18.24±0.55 g/cm 3 and 18.86±0.59 g/cm 3 , respectively, obtained by the gas pycnometry technique.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Fully stretchable active-matrix organic light-emitting electrochemical cell array

Intrinsically and fully stretchable active-matrix-driven displays are an important element to skin electronics that can be applied to many emerging fields, such as wearable electronics, consumer electronics and biomedical devices. Here, we show for the first time a fully stretchable active-matrix-driven organic light-emitting electrochemical cell array. Briefly, it is comprised of a stretchable light-emitting electrochemical cell array driven by a solution-processed, vertically integrated stretchable organic thin-film transistor active-matrix, which is enabled by the development of chemically-orthogonal and intrinsically stretchable dielectric materials. Our resulting active-matrix-driven organic light-emitting electrochemical cell array can be readily bent, twisted and stretched without affecting its device performance. When mounted on skin, the array can tolerate to repeated cycles at 30% strain. This work demonstrates the feasibility of skin-applicable displays and lays the foundation for further materials development.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dependence of Heat Removal Rate of Pebble-Based Rods on Inter-Pebble Matrix Fill Fraction

Carbon pebble rods are a promising candidate for use in high heat flux regions of magnetic fusion energy reactor walls. Under high (10 – 50 MW/m 2 ) heat loads, carbon pebble rods release hot pebbles from the exposed surface, carrying away heat as the pebble rod surface recedes. In this work, we show that the surface recession rate during heating can be adjusted by changing the mechanical strength of the extruded rods, modifying the heat removal rate; this is accomplished here by varying the fill fraction of the inter-pebble matrix. A three-dimensional finite element model is presented that captures many experimental observations, including the sphere temperature and the surface recession rate. The model predicts that pebble release is caused by thermally driven crack propagation through the matrix and that the matrix strength against breaking is the single most important material parameter setting the pebble release rate; this prediction is supported by experimental results.

36 MATERIALS SCIENCE↗
NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗
NASA NTRS1990

Vibration transmission through rolling element bearings in geared rotor systems

A new mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element description, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. Experimental results have shown that the casing plate motion is primarily flexural. Here, this issue is clarified qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 to model precision rolling element bearings using basic principles. The proposed bearing stiffness matrix is partially verified using available analytical and experimental data, and is completely characterized. The study extends the proposed bearing formulation to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques.

Singh, Rajendra↗
NASA NTRS1991

Vibration transmission through rolling element bearings. III - Geared rotor system studies

The bearing matrix formulations proposed by Lim and Singh (1990) are extended to analyze the overall dynamics of a geared rotor system which includes a spur gear pair, shafts, rolling-element bearings, a motor, a load, a casing, and flexible or rigid mounts. For this purpose, discrete vibration models are developed and used to predict vibration transmission through the bearings and to investigate the effects of the bearing, casing, and mount dynamics on the dynamic characteristics of the internal rotating system. Analytical predictions show that the theory is capable of predicting the bearing and mount moment transmissibilities in addition to the force transmissibilities. The predicted flexural vibrations of the casing plate are in good agreement with measurements conducted on an experimental set-up that consisted of a high-precision beam and pinion, and four identical rolling element bearings contained in a flexible casing mounted rigidly on a massive foundation.

Lim, T. C.↗