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NASA NTRS2002

Evaluation of Standard Gear Metrics in Helicopter Flight Operation

Each false alarm made by a machine monitoring system carries a high price tag. The machine must be taken out of service, thoroughly inspected with possible disassembly, and then made ready for service. Loss of use of the machine and the efforts to inspect it are costly. In addition, if a monitoring system is prone to false alarms, the system will soon be turned off or ignored. For aircraft applications, one growing concern is that the dynamic flight environment differs from the laboratory environment where fault detection methods are developed and tested. Vibration measurements made in flight are less stationary than those made in a laboratory, or test facility, and thus a given fault detection method may produce more false alarms in flight than might be anticipated. In 1977. Stewart introduced several metrics, including FM0 and FM4, for evaluating the health of a gear. These metrics are single valued functions of the vibration signal that indicate if the signal deviates from an ideal model of the signal. FM0 is a measure of the ratio of the peak-to-peak level to the harmonic energy in the signal. FM4 is the kurtosis of the signal with the gear mesh harmonics and first order side bands removed. The underlying theory is that a vibration signal from a gear in good condition is expected to be dominated by a periodic signal at the gear mesh frequency. If one or a small number of gear teeth contain damage or faults, the signal will change, possibly showing increased amplitude, local phase changes or both near the damaged region of the gear. FM0 increases if a signal contains a local increase in amplitude. FM4 increases if a signal contains a local increase in amplitude or local phase change in a periodic signal. Over the years, other single value metrics were also introduced to detect the onset and growth of damage in gears. These various metrics have detected faults in several gear tests in experimental test rigs. Conditions in these tests have been steady state in the sense that the rpm, torque and forces on the gear have been held steady. For gears used in a dynamic environment such as that occurring in aircraft, the rpm, torque and forces on the gear are constantly changing. The authors have measured significant variation in rpm and torque in the transmissions of helicopters in controlled steady flight conditions flown by highly proficient test pilots. Statistical analyses of the data taken in flight show significant nonstationarity in the vibration measurements. These deviations from stationarity may increase false alarms in gear monitoring during aircraft flight. In the proposed paper, the authors will study vibration measurements made in flight on an AH- 1 Cobra and an OH-58C Kiowa helicopters. The primary focus will be the development of a methodology to assess the impact of nonstationarity on false alarms. Issues to be addressed include how time synchronous averages are constructed from raw data as well as how lack of stationarity effects the behavior of single value metrics. Emphasis will be placed on the occurrence of false alarms with the use of standard metrics. In order to maintain an acceptable level of false alarms in the flight environment, this study will also address the determination of appropriate threshold levels, which may need to be higher than for test rigs.

Mosher, M.↗

NASA NTRS1995

Boundary layer transition studies

A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated holes in the impervious test plate that used to establish the Blasius base flow. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance, for conditions corresponding to strong suction and without suction. The technique was enhanced by using up to nine multiple probes to reduce the experimental run-time. In both cases, 3D contour surfaces in the vicinity of the hole show highly 3D TS waves which fan out in the spanwise direction forming bow-shaped waves downstream. The case without suction has proved useful for evaluating calculation methods. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the TS waves in the far field are similar to the case without suction. Downstream, the contour surfaces of the TS waves develop spanwise irregularities which eventually form into clumps. The spanwise clumping is evidence of a secondary instability that could be associated with suction vortices. Designers of porous surfaces use Goldsmith's Criterion to minimize cross-stream interactions. It is shown that partial TS wave cancellation is possible, depending on the hole spacing, disturbance frequency and free-stream velocity. New high-performance Constant Temperature Hot-Wire Anemometers were designed and built, based on a linear system theory analysis that can be extended to arbitrary order. The motivation was to achieve the highest possible frequency reponse while ensuring overall system stability. The performance is equal to or superior to commercially available instruments at about 10% of the cost. Details, such as fabrication drawings and a parts list, have been published to enable the instrument to be construced by others.

Watmuff, Jonathan H.↗

NASA NTRS1996

Independent Pixel and Two Dimensional Estimates of LANDSAT-Derived Cloud Field Albedo

A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on cloud albedo bias. A two-dimensional (2D) version of the Spherical Harmonic Discrete Ordinate Method (SHDOM) is used to estimate the albedo bias of the plane parallel (PP-IPA) and independent pixel (IPA-2D) approximations for a wide range of 2D cloud fields obtained from LANDSAT. They include single layer trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus boundary layer cloud fields over ocean. Findings are presented on a variety of averaging scales and are summarized as a function of cloud fraction, mean cloud optical depth, cloud aspect ratio, standard deviation of optical depth, and the gamma function parameter Y (a measure of the width of the optical depth distribution). Biases are found to be small for small cloud fraction or mean optical depth, where the cloud fields under study behave linearly. They are large (up to 0.20 for PP-IPA bias, -0.12 for IPA-2D bias) for large v. On a scene average basis PP-IPA bias can reach 0.30, while IPA-2D bias reaches its largest magnitude at -0.07. Biases due to horizontal transport (IPA-2D) are much smaller than PP-IPA biases but account for 20% RMS of the bias overall. Limitations of this work include the particular cloud field set used, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to 2D radiative transport. The LANDSAT data used may also be affected by radiative smoothing.

Chambers, L. H.↗

NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗

NASA NTRS1992

Tests of a simple data merging algorithm for the GONG project

The GONG (Global Oscillation Network Group) project proposes to reduce the impact of diurnal variations on helioseismic measurements by making long-term observations of solar images from six sites placed around the globe. The sun will be observed nearly constantly for three years, resulting in the acquisition of l+ terabyte of image data. To use the solar network to maximum advantage, the images from the sites must be combined into a single time series to determine mode frequencies, amplitudes, and line widths. Initial versions of combined, i.e., merged, time series were made using a simple weighted average of data from different sites taken simultaneously. In order to accurately assess the impact of the data merge on the helioseismic measurements, a set of artificial solar disk images was made using a standard solar model and containing a well known set of oscillation modes and frequencies. This undegraded data set and data products computed from it were used to judge the relative merits of various data merging schemes. The artificial solar disk images were subjected to various instrumental and atmospheric degradations, dependent on site and time, in order to create a set of images simulating those likely to be taken at the site. The degraded artificial solar disk images for the six observing sites were combined in various ways to form merged time series of images and mode coefficients. Various forms of a weighted average were used, including an equally-weighted average, an average with weights dependent upon air mass and averages with weights dependent on various quality assurance parameters. Both the undegraded solar disk image time series and several time series made up of various combinations of the degraded solar disk images from the six sites were subjected to standard helioseismic measurement processing. This processing consisted of coordinate remapping, detrending, spherical harmonic transformation, computation of power series for the oscillation mode coefficients, and mode frequency identification. Visual and statistical evaluation of the merged data sets themselves and differences between the merged and undegraded data set shows good agreement between the two data sets. Some slight differences in image scale and registration appear between the undegraded data set and the various merged data sets. In the set of power series made from the mode coefficients of the merged data sets, some power leakage is observed into the background and into slightly lower l-value modes, especially at higher l-value mode frequencies. The results of the comparison of time series and mode oscillation frequencies of the undegraded data with those of the data merged using weighted averages indicate that, at least for p-mode solar oscillations, a weighted average of either the detrended remapped images or the mode coefficients gives good determination of the mode frequencies and adequate-to-good determination of the amplitudes and widths of the mode frequency lines. This conclusion is most advantageous to the analysis of the massive amounts of data to be received by the GONG network.

Williams, W. E.↗

NASA NTRS1994

Contributions to the Earth's obliquity rate, precession, and nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The J(sub2) effects have generally been allowed for in past nutation theories and some procession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta phi plus out-of-phase contributions of 0.14 mas in Delta phi and -0.03 mas in Delta epsilon. The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C = 0.003 273 763 4 which, in combination with a satellite-derived J(sub2), gives a normalized polar moment of inertia C/MR(exp2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub2). Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗

NASA NTRS1994

Contributions to the Earth's Obliquity Rate, Precession, and Nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub 2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024 sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The effects have generally been allowed for in past nutation theories and some precession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta(psi) plus out-of-phase contributions of 0.14 mas in Delta(psi) and -0.03 mas in Delta(sub epsilon). The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C =0.003 273 763 4 which, in combination with a satellite-derived J(sub 2), gives a normalized polar moment of inertia C/MR(exp 2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub 2) Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗