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NASA NTRS2003

Finite-Element Methods for Real-Time Simulation of Surgery

Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.

Basdogan, Cagatay↗
NASA NTRS2012

Forming Human-Robot Teams Across Time and Space

NASA pushes telerobotics to distances that span the Solar System. At this scale, time of flight for communication is limited by the speed of light, inducing long time delays, narrow bandwidth and the real risk of data disruption. NASA also supports missions where humans are in direct contact with robots during extravehicular activity (EVA), giving a range of zero to hundreds of millions of miles for NASA s definition of "tele". . Another temporal variable is mission phasing. NASA missions are now being considered that combine early robotic phases with later human arrival, then transition back to robot only operations. Robots can preposition, scout, sample or construct in advance of human teammates, transition to assistant roles when the crew are present, and then become care-takers when the crew returns to Earth. This paper will describe advances in robot safety and command interaction approaches developed to form effective human-robot teams, overcoming challenges of time delay and adapting as the team transitions from robot only to robots and crew. The work is predicated on the idea that when robots are alone in space, they are still part of a human-robot team acting as surrogates for people back on Earth or in other distant locations. Software, interaction modes and control methods will be described that can operate robots in all these conditions. A novel control mode for operating robots across time delay was developed using a graphical simulation on the human side of the communication, allowing a remote supervisor to drive and command a robot in simulation with no time delay, then monitor progress of the actual robot as data returns from the round trip to and from the robot. Since the robot must be responsible for safety out to at least the round trip time period, the authors developed a multi layer safety system able to detect and protect the robot and people in its workspace. This safety system is also running when humans are in direct contact with the robot, so it involves both internal fault detection as well as force sensing for unintended external contacts. The designs for the supervisory command mode and the redundant safety system will be described. Specific implementations were developed and test results will be reported. Experiments were conducted using terrestrial analogs for deep space missions, where time delays were artificially added to emulate the longer distances found in space.

Hambuchen, Kimberly↗
NASA NTRS2012

Using NASA's Giovanni System to Simulate Time-Series Stations in the Outflow Region of California's Eel River

Oceanographic time-series stations provide vital data for the monitoring of oceanic processes, particularly those associated with trends over time and interannual variability. There are likely numerous locations where the establishment of a time-series station would be desirable, but for reasons of funding or logistics, such establishment may not be feasible. An alternative to an operational time-series station is monitoring of sites via remote sensing. In this study, the NASA Giovanni data system is employed to simulate the establishment of two time-series stations near the outflow region of California s Eel River, which carries a high sediment load. Previous time-series analysis of this location (Acker et al. 2009) indicated that remotely-sensed chl a exhibits a statistically significant increasing trend during summer (low flow) months, but no apparent trend during winter (high flow) months. Examination of several newly-available ocean data parameters in Giovanni, including 8-day resolution data, demonstrates the differences in ocean parameter trends at the two locations compared to regionally-averaged time-series. The hypothesis that the increased summer chl a values are related to increasing SST is evaluated, and the signature of the Eel River plume is defined with ocean optical parameters.

Acker, James G.↗
NASA NTRS2012

Time-Resolved Data Acquisition for In Situ Subsurface Planetary Geochemistry

The current gamma-ray/neutron instrumentation development effort at NASA Goddard Space Flight Center aims to extend the use of active pulsed neutron interrogation techniques to probe the subsurface geochemistry of planetary bodies in situ. All previous NASA planetary science missions, that used neutron and/or gamma-ray spectroscopy instruments, have relied on a constant neutron source produced from galactic cosmic rays. One of the distinguishing features of this effort is the inclusion of a high intensity 14.1 MeV pulsed neutron generator synchronized with a custom data acquisition system to time each event relative to the pulse. With usually only one opportunity to collect data, it is difficult to set a priori time-gating windows to obtain the best possible results. Acquiring time-tagged, event-by-event data from nuclear induced reactions provides raw data sets containing channel/energy, and event time for each gamma ray or neutron detected. The resulting data set can be plotted as a function of time or energy using optimized analysis windows after the data are acquired. Time windows can now be chosen to produce energy spectra that yield the most statistically significant and accurate elemental composition results that can be derived from the complete data set. The advantages of post-processing gamma-ray time-tagged event-by-event data in experimental tests using our prototype instrument will be demonstrated.

Bodnarik, Julia Gates↗
NASA NTRS2012

Adaptive Sampling of Time Series During Remote Exploration

This work deals with the challenge of online adaptive data collection in a time series. A remote sensor or explorer agent adapts its rate of data collection in order to track anomalous events while obeying constraints on time and power. This problem is challenging because the agent has limited visibility (all its datapoints lie in the past) and limited control (it can only decide when to collect its next datapoint). This problem is treated from an information-theoretic perspective, fitting a probabilistic model to collected data and optimizing the future sampling strategy to maximize information gain. The performance characteristics of stationary and nonstationary Gaussian process models are compared. Self-throttling sensors could benefit environmental sensor networks and monitoring as well as robotic exploration. Explorer agents can improve performance by adjusting their data collection rate, preserving scarce power or bandwidth resources during uninteresting times while fully covering anomalous events of interest. For example, a remote earthquake sensor could conserve power by limiting its measurements during normal conditions and increasing its cadence during rare earthquake events. A similar capability could improve sensor platforms traversing a fixed trajectory, such as an exploration rover transect or a deep space flyby. These agents can adapt observation times to improve sample coverage during moments of rapid change. An adaptive sampling approach couples sensor autonomy, instrument interpretation, and sampling. The challenge is addressed as an active learning problem, which already has extensive theoretical treatment in the statistics and machine learning literature. A statistical Gaussian process (GP) model is employed to guide sample decisions that maximize information gain. Nonsta tion - ary (e.g., time-varying) covariance relationships permit the system to represent and track local anomalies, in contrast with current GP approaches. Most common GP models are stationary, e.g., the covariance relationships are time-invariant. In such cases, information gain is independent of previously collected data, and the optimal solution can always be computed in advance. Information-optimal sampling of a stationary GP time series thus reduces to even spacing, and such models are not appropriate for tracking localized anomalies. Additionally, GP model inference can be computationally expensive.

Thompson, David R.↗
NASA NTRS2013

The CACAO Method for Smoothing, Gap Filling, and Characterizing Seasonal Anomalies in Satellite Time Series

Consistent, continuous, and long time series of global biophysical variables derived from satellite data are required for global change research. A novel climatology fitting approach called CACAO (Consistent Adjustment of the Climatology to Actual Observations) is proposed to reduce noise and fill gaps in time series by scaling and shifting the seasonal climatological patterns to the actual observations. The shift and scale CACAO parameters adjusted for each season allow quantifying shifts in the timing of seasonal phenology and inter-annual variations in magnitude as compared to the average climatology. CACAO was assessed first over simulated daily Leaf Area Index (LAI) time series with varying fractions of missing data and noise. Then, performances were analyzed over actual satellite LAI products derived from AVHRR Long-Term Data Record for the 1981-2000 period over the BELMANIP2 globally representative sample of sites. Comparison with two widely used temporal filtering methods-the asymmetric Gaussian (AG) model and the Savitzky-Golay (SG) filter as implemented in TIMESAT-revealed that CACAO achieved better performances for smoothing AVHRR time series characterized by high level of noise and frequent missing observations. The resulting smoothed time series captures well the vegetation dynamics and shows no gaps as compared to the 50-60% of still missing data after AG or SG reconstructions. Results of simulation experiments as well as confrontation with actual AVHRR time series indicate that the proposed CACAO method is more robust to noise and missing data than AG and SG methods for phenology extraction.

LAI↗
NASA NTRS2014

Time-Spectral Rotorcraft Simulations on Overset Grids

The Time-Spectral method is derived as a Fourier collocation scheme and applied to NASA's overset Reynolds-averaged Navier-Stokes (RANS) solver OVERFLOW. The paper outlines the Time-Spectral OVERFLOWimplementation. Successful low-speed laminar plunging NACA 0012 airfoil simulations demonstrate the capability of the Time-Spectral method to resolve the highly-vortical wakes typical of more expensive three-dimensional rotorcraft configurations. Dealiasing, in the form of spectral vanishing viscosity (SVV), facilitates the convergence of Time-Spectral calculations of high-frequency flows. Finally, simulations of the isolated V-22 Osprey tiltrotor for both hover and forward (edgewise) flight validate the three-dimensional Time-Spectral OVERFLOW implementation. The Time-Spectral hover simulation matches the time-accurate calculation using a single harmonic. Significantly more temporal modes and SVV are required to accurately compute the forward flight case because of its more active, high-frequency wake.

Rotocraft↗
NASA NTRS2012

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10 - 24deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large-separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel-time difference [outward-going time minus inward-going time] in the separation range delta= 10 - 24deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, 5.1+/-0.1 seconds, is constant over the distance range. This magnitude of the signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 ms(exp−1) extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 ms(exp−1) at a depth of 2.3 Mm and a peak horizontal flow of 700 ms(exp−1) at a depth of 1.6 Mm.

convection↗
NASA NTRS2015

Probabilistic Survivability Versus Time Modeling

This technical paper documents Kennedy Space Centers Independent Assessment team work completed on three assessments for the Ground Systems Development and Operations (GSDO) Program to assist the Chief Safety and Mission Assurance Officer (CSO) and GSDO management during key programmatic reviews. The assessments provided the GSDO Program with an analysis of how egress time affects the likelihood of astronaut and worker survival during an emergency. For each assessment, the team developed probability distributions for hazard scenarios to address statistical uncertainty, resulting in survivability plots over time. The first assessment developed a mathematical model of probabilistic survivability versus time to reach a safe location using an ideal Emergency Egress System at Launch Complex 39B (LC-39B); the second used the first model to evaluate and compare various egress systems under consideration at LC-39B. The third used a modified LC-39B model to determine if a specific hazard decreased survivability more rapidly than other events during flight hardware processing in Kennedys Vehicle Assembly Building (VAB).Based on the composite survivability versus time graphs from the first two assessments, there was a soft knee in the Figure of Merit graphs at eight minutes (ten minutes after egress ordered). Thus, the graphs illustrated to the decision makers that the final emergency egress design selected should have the capability of transporting the flight crew from the top of LC 39B to a safe location in eight minutes or less. Results for the third assessment were dominated by hazards that were classified as instantaneous in nature (e.g. stacking mishaps) and therefore had no effect on survivability vs time to egress the VAB. VAB emergency scenarios that degraded over time (e.g. fire) produced survivability vs time graphs that were line with aerospace industry norms.

Joyner, James J., Sr.↗
NASA NTRS2015

Characterizing the Effects of a Vertical Time Threshold for a Class of Well-Clear Definitions

A fundamental requirement for the integration of unmanned aircraft into civil airspace is the capability of aircraft to remain well clear of each other and avoid collisions. This requirement has led to a broad recognition of the need for an unambiguous, formal definition of well clear. It is further recognized that any such definition must be interoperable with existing airborne collision avoidance systems (ACAS). A particular class of well-clear definitions uses logic checks of independent distance thresholds as well as independent time thresholds in the vertical and horizontal dimensions to determine if a well-clear violation is predicted to occur within a given time interval. Existing ACAS systems also use independent distance thresholds, however a common time threshold is used for the vertical and horizontal logic checks. The main contribution of this paper is the characterization of the effects of the decoupled vertical time threshold on a well-clear definition in terms of (1) time to well-clear violation, and (2) interoperability with existing ACAS. The paper provides governing equations for both metrics and includes simulation results to illustrate the relationships. In this paper, interoperability implies that the time of well-clear violation is strictly less than the time a resolution advisory is issued by ACAS. The encounter geometries under consideration in this paper are initially well clear and consist of constant-velocity trajectories resulting in near-mid-air collisions.

Upchurch, Jason M.↗
NASA NTRS2016

Clasp/SJ Observation of Time Variations of Lyman-Alpha Emissions in a Solar Active Region

The Chromospheric Lyman-alpha SpectroPolarimeter (CLASP) is a sounding rocket experiment launched on September 3, 2015 to investigate the solar chromosphere, and the slit-jaw (SJ) optical system took Lyα images with the high time cadence of 0.6 s. By the CLASP/SJ observation, many time variations in the solar chromosphere with the time scale of <1 minute were discovered (see the poster by Kubo et al., Pa-13). We focused on an active region and investigated the short (<30 s) time variations and relation to the coronal structure observed by SDO/AIA. We compared the Ly(alpha) time variations at footpoints of coronal magnetic fields observed by AIA 211 Å (approx.2 MK) and AIA 171 Å (0.6 MK), and non-loop regions. As the result, we found the <30 s Ly(alpha) time variations had more in the footpoint regions. On the other hand, the <30 s time variations had no dependency on the temperature of the loop.

CLASP↗
NASA NTRS2016

Routing Based on Length of Time of Available Connection

In an embodiment, a method of routing packets at a first node in an ad-hoc network is provided. The method includes receiving, at the first node, a plurality of route-alive messages corresponding to a destination, each of the plurality of route-alive messages including a route time indicating a length of time in which a communicative connection is available between the second node that sent the respective route-alive message and the destination. The method also includes determining an updated route time for each second node. The updated route time corresponds to a length of time in which a communication connection is available between the first node and the destination through the respective second node. A second node is selected for sending a packet to based on the updated route time for each of the second nodes, wherein a node having a longer updated route time is given higher priority for selection.

Anandappan, Thanga↗
NASA NTRS2017

STROBE-X: X-Ray Timing Spectroscopy on Dynamical Timescales from Microseconds to Years

We describe a probe-class mission concept that provides an unprecedented view of the X-ray sky, performing timing and 0.2-30 keV spectroscopy over timescales from microseconds to years. The Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X) comprises three primary instruments. The first uses an array of lightweight optics (3-m focal length) that concentrate incident photons onto solid state detectors with CCD-level (85-130 eV) energy resolution, 100 ns time resolution, and low background rates to cover the 0.2-12 keV band. This technology is scaled up from NICER, with enhanced optics to take advantage of the longer focal length of STROBE-X. The second uses large-area collimated silicon drift detectors, developed for ESA's LOFT, to cover the 2-30 keV band. These two instruments each provide an order of magnitude improvement in effective area compared with its predecessor (NICER and RXTE, respectively). Finally, a sensitive sky monitor triggers pointed observations, provides high duty cycle, high time resolution, high spectral resolution monitoring of the X-ray sky with approx. 20 times the sensitivity of the RXTE ASM, and enables multi-wavelength and multi-messenger studies on a continuous, rather than scanning basis.For the first time, the broad coverage provides simultaneous study of thermal components, non-thermal components, iron lines, and reflection features from a single platform for accreting black holes at all scales. The enormous collecting area allows detailed studies of the dense matter equation of state using both thermal emission from rotation-powered pulsars and harder emission from X-ray burst oscillations. The combination of the wide-field monitor and the sensitive pointed instruments enables observations of potential electromagnetic counterparts to LIGO and neutrino events. Additional extragalactic science, such as high quality spectroscopy of clusters of galaxies and unprecedented timing investigations of active galactic nuclei, is also obtained.

STROBE-X X-ray↗
NASA NTRS2011

Failure Modes in Capacitors When Tested Under a Time-Varying Stress

Steady step surge testing (SSST) is widely applied to screen out potential power-on failures in solid tantalum capacitors. The test simulates the power supply's on and off characteristics. Power-on failure has been the prevalent failure mechanism for solid tantalum capacitors for decoupling applications. On the other hand, the SSST can also be reviewed as an electrically destructive test under a time-varying stress. It consists of rapidly charging the capacitor with incremental voltage increases, through a low resistance in series, until the capacitor under test is electrically shorted. Highly accelerated life testing (HALT) is usually a time-efficient method for determining the failure mechanism in capacitors; however, a destructive test under a time-varying stress like SSST is even more effective. It normally takes days to complete a HALT test, but it only takes minutes for a time-varying stress test to produce failures. The advantage of incorporating specific time-varying stress into a statistical model is significant in providing an alternative life test method for quickly revealing the failure modes in capacitors. In this paper, a time-varying stress has been incorporated into the Weibull model to characterize the failure modes. The SSST circuit and transient conditions to correctly test the capacitors is discussed. Finally, the SSST was applied for testing polymer aluminum capacitors (PA capacitors), Ta capacitors, and multi-layer ceramic capacitors with both precious metal electrode (PME) and base-metal-electrodes (BME). It appears that testing results are directly associated to the dielectric layer breakdown in PA and Ta capacitors and are independent on the capacitor values, the way the capacitors being built, and the manufactures. The testing results also reveal that ceramic capacitors exhibit breakdown voltages more than 20 times the rated voltage, and the breakdown voltages are inverse proportional to the dielectric layer thickness. The possibility of ceramic capacitors in front-end decoupling applications to block the surge noise from a power supply is also discussed.

Liu, David (Donhang)↗
NASA NTRS2018

STROBE-X: X-ray Timing & Spectroscopy on Dynamical Timescales from Milliseconds to Years

We describe a probe-class mission concept that provides an unprecedented view of the X-ray sky, performing timing and 0.2-30 keV spectroscopy over timescales from microseconds to years. The Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X) comprises three primary instruments. The first uses an array of lightweight optics (3-m focal length) that concentrate incident photons onto solid state detectors with CCD-level (85-130 eV) energy resolution, 100 ns time resolution, and low background rates to cover the 0.2-12 keV band. This technology is scaled up from NICER [1], with enhanced optics to take advantage of the longer focal length of STROBE-X. The second uses large-area collimated silicon drift detectors, developed for ESA's LOFT [2], to cover the 2-30 keV band. These two instruments each provide an order of magnitude improvement in effective area compared with its predecessor (NICER and RXTE, respectively). Finally, a sensitive sky monitor triggers pointed observations, provides high duty cycle, high time resolution, high spectral resolution monitoring of the X-ray sky with approx. 20 times the sensitivity of the RXTE ASM, and enables multi-wavelength and multi-messenger studies on a continuous, rather than scanning basis. For the first time, the broad coverage provides simultaneous study of thermal components, non-thermal components, iron lines, and reflection features from a single platform for accreting black holes at all scales. The enormous collecting area allows detailed studies of the dense matter equation of state using both thermal emission from rotation-powered pulsars and harder emission from X-ray burst oscillations. The combination of the wide-field monitor and the sensitive pointed instruments enables observations of potential electromagnetic counterparts to LIGO and neutrino events. Additional extragalactic science, such as high quality spectroscopy of clusters of galaxies and unprecedented timing investigations of active galactic nuclei, is also obtained

STROBE-↗
NASA NTRS2018

Magnetosheath Propagation Time of Solar Wind Directional Discontinuities

Observed delays in the ground response to solar wind directional discontinuities have been explained as the result of larger than expected magnetosheath propagation times. Recently, Samsonov et al. (2017, https://doi.org/10.1002/2017GL075020) showed that the typical time for a southward interplanetary magnetic field (IMF) turning to propagate across the magnetosheath is 14 min. Here by using a combination of magnetohydrodynamic simulations, spacecraft observations, and analytic calculations, we study the dependence of the propagation time on solar wind parameters and near-magnetopause cutoff speed. Increases in the solar wind speed result in greater magnetosheath plasma flow velocities, decreases in the magnetosheath thickness and, as a result, decreases in the propagation time. Increases in the IMF strength result in increases in the magnetosheath thickness and increases in the propagation time. Both magnetohydrodynamic simulations and observations suggest that propagation times are slightly smaller for northward IMF turnings. Magnetosheath flow deceleration must be taken into account when predicting the arrival times of solar wind structures at the dayside magnetopause.

Samsonov, A. A.↗
NASA NTRS2016

Reducing Departure Delays for Adjacent Center Airports using Time-Based Flow Management Scheduler: Checkbox On or Off?

The Federal Aviation Administration (FAA) has enhanced the Time-Based Flow Management (TBFM) scheduling tool with a "Checkbox ON" vs. "OFF" function which allows Traffic Management Coordinators (TMCs) to make room in a crowded arrival stream for a departure. When scheduling a departure, having the checkbox ON can delay the Scheduled Times of Arrivals (STAs) of the airborne flights upstream of the TBFM freeze horizons and can compress these flights to their minimum required spacing, thereby creating a slot for a departure. Hence, having the checkbox ON can reduce the frequent ground delays of aircraft departing near high volume airports but can increase delays for airborne arrivals. A Human-in-the-Loop (HITL) simulation compared arrival and departure delays to Newark Airport (EWR) with the checkbox ON vs. OFF as the default position. Three other conditions in this HITL involved various National Airspace System (NAS)-wide approaches for timely delivery of aircraft to the TBFM region. These conditions were: Baseline, using current Mile-in-Trail (MIT) spacing restrictions; Integrated Demand Management (IDM), where all aircraft were given departure times (Expect Departure Clearance Times, or EDCTs), ultimately based on the EWR Airport Arrival Rate; and IDM plus Required Time of Arrival (RTA), a flight deck tool which allowed some aircraft to meet a controlled time of arrival to the TBFM area more precisely. Results showed that the checkbox tool was powerful: with the checkbox ON, departure delays decreased and airborne delays increased, as predicted. However, assuming that the cost ratio of a minute of airborne delay to a minute of departure delay is in the range of 1.2 to 3, as commonly indicated by the literature, checkbox ON and checkbox OFF conditions showed approximately equal total delay costs, i.e., the cost of delays in the air balanced the cost of the delay on the ground. The three scheduling conditions also had approximately equal total delay costs, although a simulation artifact may have reduced the delays in the Baseline condition. In the debrief following the simulation, the TMCs concluded that the checkbox should be used flexibly depending on the current delay situation, and suggested modifications to the checkbox tool which would help them use it in this way, along with enhanced training. The relatively similar total cost of both checkbox default options in this simulation indicates that this might be a fruitful approach, and replace the necessity to have the checkbox rigidly set to either ON or OFF.

departure delay↗
NASA NTRS2019

Real-Time Modeling of Thermal Interactions in Cryogenic Ball Bearings

Based on the integration of classical differential equations of motion of bearing elements, a real-time dynamic simulation of ball bearing performance is coupled with simultaneous modeling of thermal interactions between the bearing elements. The transient heat generations are time averaged over a significantly larger time step before they are used to compute the changes in bearing temperature fields. Such an averaging algorithm eliminates the numerical difficulties associated with simultaneous integration of mechanical thermal differential equations with vastly different time scales. Under stable operation, the step change in temperatures at each thermal time step converges to a steady-state solution. Following is a list of accomplishments in the present investigation: (1) A real-time dynamic performance of both 440C and hybrid ball bearings in a LOX environment is modeled in both transient and steady-state time domains, as the inner race accelerates to a prescribed operating speed. (2) The frictional interactions at the ball to race contacts are modeled by experimentally measured traction coefficients as a function of slide-to-roll ratios. (3) Bearing heat generation, as defined by the heat transferred to circulating LOX, is validated against experimental values determined by measured LOX temperatures under prescribed pressures and flow rates. The predicted heat generation is in good agreement with the experimental values. (4) The steady-state solutions are shown to be independent of initial conditions. This establishes convergence of the numerical integration of a differential equation of motion of the bearing elements. (5) Churning and drag losses in the circulating LOX constitutes the majority of bearing heat generation under the experimental test conditions. (6) The heat dissipated in frictional interactions in hybrid bearings is significantly lower in hybrid bearings in comparison to that simulated in all-steel bearings, while the churning and drag losses are relatively unchanged.

Gupta, P. K.↗