The velocity synchronous discrete Fourier transform for order tracking in the field of rotating machinery

Diagnostics of rotating machinery has developed significantly in the last decades, and industrial applications are spreading in different sectors. Most applications are characterized by varying velocities of the shaft and in many cases transients are the most critical to monitor. In these variable speed conditions, fault symptoms are clearer in the angular/order domains than in the common time/frequency ones. In the past, this issue was often solved by synchronously sampling data by means of phase locked circuits governing the acquisition; however, thanks to the spread of cheap and powerful microprocessors, this procedure is nowadays rarer; sampling is usually performed at constant time intervals, and the conversion to the order domain is made by means of digital signal processing techniques. In the last decades different algorithms have been proposed for the extraction of an order spectrum from a signal sampled asynchronously with respect to the shaft rotational velocity; many of them (the so called computed order tracking family) use interpolation techniques to resample the signal at constant angular increments, followed by a common discrete Fourier transform to shift from the angular domain to the order domain. A less exploited family of techniques shifts directly from the time domain to the order spectrum, by means of modified Fourier transforms. This paper proposes a new transform, named velocity synchronous discrete Fourier transform, which takes advantage of the instantaneous velocity to improve the quality of its result, reaching performances that can challenge the computed order tracking.

A Theory of the Lifted Temperature Minimum on Calm Clear Nights

Numerous reports from several parts of the world have confirmed that on calm clear nights a minimum in air temperature can occur just above ground, at heights of the order of $\frac{1}{2}$ m or less. This phenomenon, first observed by Ramdas & Atmanathan (1932), carries the associated paradox of an apparently unstable layer that sustains itself for several hours, and has not so far been satisfactorily explained. We formulate here a theory that considers energy balance between radiation, conduction and free or forced convection in humid air, with surface temperature, humidity and wind incorporated into an appropriate mathematical model as parameters. A complete numerical solution of the coupled air-soil problem is used to validate an approach that specifies the surface temperature boundary condition through a cooling rate parameter. Utilizing a flux-emissivity scheme for computing radiative transfer, the model is numerically solved for various values of turbulent friction velocity. It is shown that a lifted minimum is predicted by the model for values of ground emissivity not too close to unity, and for sufficiently low surface cooling rates and eddy transport. Agreement with observation for reasonable values of the parameters is demonstrated. A heuristic argument is offered to show that radiation substantially increases the critical Rayleigh number for convection, thus circumventing or weakening Rayleigh-Benard instability. The model highlights the key role played by two parameters generally ignored in explanations of the phenomenon, namely surface emissivity and soil thermal conductivity, and shows that it is unnecessary to invoke the presence of such particulate constituents as haze to produce a lifted minimum.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Minimum power consumption for drag reduction on a circular cylinder by tangential surface motion

We investigate the effect of a prescribed tangential velocity on the drag force on a circular cylinder in a spanwise uniform cross flow. Using a combination of theoretical and numerical techniques we make an attempt at determining the optimal tangential velocity profiles which will reduce the drag force acting on the cylindrical body while minimizing the net power consumption characterized through a non-dimensional power loss coefficient (C-PL). A striking conclusion of our analysis is that the tangential velocity associated with the potential flow, which completely suppresses the drag force, is not optimal for both small and large, but finite Reynolds number. When inertial effects are negligible (R e << 1), theoretical analysis based on two-dimensional Oseen equations gives us the optimal tangential velocity profile which leads to energetically efficient drag reduction. Furthermore, in the limit of zero Reynolds number (Re -> 0), minimum power loss is achieved for a tangential velocity profile corresponding to a shear-free perfect slip boundary. At finite Re, results from numerical simulations indicate that perfect slip is not optimum and a further reduction in drag can be achieved for reduced power consumption. A gradual increase in the strength of a tangential velocity which involves only the first reflectionally symmetric mode leads to a monotonic reduction in drag and eventual thrust production. Simulations reveal the existence of an optimal strength for which the power consumption attains a minima. At a Reynolds number of 100, minimum value of the power loss coefficient (C-PL = 0.37) is obtained when the maximum in tangential surface velocity is about one and a half times the free stream uniform velocity corresponding to a percentage drag reduction of approximately 77 %; C-PL = 0.42 and 0.50 for perfect slip and potential flow cases, respectively. Our results suggest that potential flow tangential velocity enables energetically efficient propulsion at all Reynolds numbers but optimal drag reduction only for Re -> infinity. The two-dimensional strategy of reducing drag while minimizing net power consumption is shown to be effective in three dimensions via numerical simulation of flow past an infinite circular cylinder at a Reynolds number of 300. Finally a strategy of reducing drag, suitable for practical implementation and amenable to experimental testing, through piecewise constant tangential velocities distributed along the cylinder periphery is proposed and analysed.

Optimal Guidance for Accurate Lunar Soft Landing with Minimum Fuel Consumption using Model Predictive Static Programming

In this paper the soft lunar landing with minimum fuel expenditure is formulated as a nonlinear optimal guidance problem. The realization of pinpoint soft landing with terminal velocity and position constraints is achieved using Model Predictive Static Programming (MPSP). The high accuracy of the terminal conditions is ensured as the formulation of the MPSP inherently poses final conditions as a set of hard constraints. The computational efficiency and fast convergence make the MPSP preferable for fixed final time onboard optimal guidance algorithm. It has also been observed that the minimum fuel requirement strongly depends on the choice of the final time (a critical point that is not given due importance in many literature). Hence, to optimally select the final time, a neural network is used to learn the mapping between various initial conditions in the domain of interest and the corresponding optimal flight time. To generate the training data set, the optimal final time is computed offline using a gradient based optimization technique. The effectiveness of the proposed method is demonstrated with rigorous simulation results.

Influence of Coulomb potential for photoionization of H atoms in an elliptically polarized laser field: Velocity gauge versus length gauge

We theoretically study the influence of Coulomb potential for photoionization of hydrogen atoms in an intense laser field with elliptical polarization. The total ionization rates, photoelectron energy spectra, and photoelectron angular distributions are calculated with the Coulomb-Volkov wave functions in the velocity gauge and compared with those calculated in the length gauge as well as those calculated with the Volkov wave functions. By comparing the results obtained by the Coulomb-Volkov and Volkov wave functions, we find that for linear polarization the influence of Coulomb potential is obvious for low-energy photoelectrons, and as the photoelectron energy and/or the laser intensity increase, its influence becomes smaller. This trend, however, is not so clear for the case of elliptical polarization. We also find that the twofold symmetry in the photoelectron angular distributions for elliptical polarization is caused by the cooperation of Coulomb potential and interference of multiple transition channels. About the gauge issue, we show that the difference in the photoelectron angular distributions obtained by the velocity and length gauges becomes rather obvious for elliptical polarization, while the difference is generally smaller for linear polarization.

Anomaly in photoelectron angular distributions

The recently observed anomaly in photoelectron angular distributions (PADs), the disappearance of the main lobes of PADs which should be usually in the direction of laser polarization, is reinterpreted as a minimum of generalized Bessel functions in the laser-polarization direction with the theory of nonperturbative quantum electrodynamics. The reinterpretation has no artificial fitting parameters and explains more features of the experimentally observed PADs, in contrast to the existing interpretation in which the anomaly is interpreted as a quantum interference of angular momentum partial waves. Some hierarchy anomalies are predicted for further experimental observations.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.

Comparison of acoustic velocity perturbation measurements using PIV vs. two-microphone technique

Understanding combustion instabilities requires accurate measurements of the acoustic velocity perturbation into injectors. This is often accomplished via the use of the two microphone technique, as this only requires two pressure transducers. However, measurements of the actual velocities emerging from the injectors are not often taken, leaving questions regarding the assumptions about the acoustic velocity. A comparison of velocity measured at downstream of the injector with that of two-microphone technique can show the accuracy and limitations of two-microphone technique. In this paper, velocity measurements are taken using both particle image velocimetry (PIV) and the two-microphone technique in a high pressure facility designed for aeroengine injector measurements. The flow is excited using an area modulation device installed on the choked end of the combustion chamber, with PIV measurements enabled by optical access downstream of the injector through a quartz tube and windows. Acoustic velocity perturbations at the injector are determined by considering the Fourier transformed pressure fluctuations for two microphones installed at a known distance upstream of the injector. PIV measurements are realized by seeding the air flow with micrometric water particles under 2.5 bar pressure at ambient temperature. Phase locked velocity fields are realized by synchronizing the acquisition of PIV images with the revolution of the acoustic modulator using the pressure signal measured at the face of injector. The mean velocity fluctuation is calculated as the difference between maximum and minimum velocities, normalized by the mean velocity of the unforced case. Those values are compared with the peak-to-peak velocity fluctuation amplitude calculated by the two-microphone technique. Although the ranges of velocity fluctuations for both techniques are similar, the variation of fluctuation with forcing frequencies diverges significantly with frequency. The differences can be attributed to several limitations associated with of both techniques, such as the quality of the signal, the signal/noise ratio, the accuracy of PIV measurements and the assumption of isentropic flow of the particle velocity from the plenum through the injector. We conclude that two-microphone methods can be used as a reference value for the velocity fluctuation in low order applications such as flame transfer functions, but not for drawing conclusions regarding the absolute velocity fluctuations in the injector. Copyright © 2013 by ASME.

Ultra-broadband optical parametric chirped-pulse amplification by matching of both group-velocity and pulse-front

Ultra-broadband optical parametric chirped-pulse amplification is analyzed based the compensation of phase-mismatch, which is achieved by matching of both group-velocity and pulse-front between signal and idler by the combination of the noncollinear-phase-match and pulse-front-tilt. The results show exactly matching of both group-velocity and pulse-front is the important criterion for constructing an UBOPCPA. Its general model is developed, in which the group velocities, noncollinear angles. spatial walk-off angles, linear angular spectral dispersion coefficients and pulse-front tilted angles are suitably linked to each other. Finally, specific numerical calculations and simulations are presented for beta-barium borate OPCPA with type-1 noncollinear angularly dispersed geometry. (C) 2005 Elsevier B.V. All rights reserved.

A velocity map ion-imaging study on C2H5SH and C3H7SH photodissociation at 243 nm

Photodissociation dynamics Of C2H5SH, i-C-3-H7SH and n-C3H7SH at 243.1 nm were investigated using velocity map ion-imaging method. H-atom photolysis products were detected by a (2 + 1) resonance enhanced ionization scheme. Both the angular distribution and translational energy distribution of the H-atom elimination processes were determined from the ion images of the H-atom products. The experimental results indicate that the H-atom eliminations from these molecules are mainly direct and fast dissociation processes from a repulsive potential energy state. And a more statistical dissociation process that likely occurs oil the ground state via internal conversion has also been observed. Dissociation energies of the S-H bonds are also derived from the H-atom product translational energy distributions. (C) 2002 Elsevier Science B.V. All rights reserved.

Multiwavelength observations of the M15 intermediate-velocity cloud

We present Westerbork Synthesis Radio Telescope HI images, Lovell telescope multibeam H I wide-field mapping, William Herschel Telescope long-slit echelle Ca II observations, Wisconsin Halpha Mapper (WHAM) facility images, and IRAS ISSA 60- and 100-mum co-added images towards the intermediate- velocity cloud (IVC) at + 70 km s(-1), located in the general direction of the M15 globular cluster. When combined with previously published Arecibo data, the H I gas in the IVC is found to be clumpy, with a peak H I column density of similar to1.5 x 10(20) cm(-2), inferred volume density (assuming spherical symmetry) of similar to24 cm(-3)/D (kpc) and a maximum brightness temperature at a resolution of 81 x 14 arcsec(2) of 14 K. The major axis of this part of the IVC lies approximately parallel to the Galactic plane, as does the low- velocity H I gas and IRAS emission. The H I gas in the cloud is warm, with a minimum value of the full width at half-maximum velocity width of 5 km s(-1) corresponding to a kinetic temperature, in the absence of turbulence, of similar to540 K. From the H I data, there are indications of two-component velocity structure. Similarly, the Ca II spectra, of resolution 7 km s(-1), also show tentative evidence of velocity structure, perhaps indicative of cloudlets. Assuming that there are no unresolved narrow-velocity components, the mean values of log(10)[N(Ca II K) cm(2)] similar to 12.0 and Ca II/H I similar to2 5 x 10(-8) are typical of observations of high Galactic latitude clouds. This compares with a value of Ca II/H I>10(-6) for IVC absorption towards HD 203664, a halo star of distance 3 kpc, some 3.degrees1 from the main M15 IVC condensation. The main IVC condensation is detected by WHAM in Halpha with central local-standard-of-rest velocities of similar to60-70 km s(-1), and intensities uncorrected for Galactic extinction of up to 1.3 R, indicating that the gas is partially ionized. The FWHM values of the Halpha IVC component, at a resolution of 1degrees, exceed 30 km s(-1). This is some 10 km s(-1) larger than the corresponding H I value at a similar resolution, and indicates that the two components may not be mixed. However, the spatial and velocity coincidence of the Halpha and H I peaks in emission towards the main IVC component is qualitatively good. If the Halpha emission is caused solely by photoionization, the Lyman continuum flux towards the main IVC condensation is similar to2.7 x 10(6) photon cm(-2) s(-1). There is not a corresponding IVC Halpha detection towards the halo star HD 203664 at velocities exceeding similar to60 km s(- 1). Finally, both the 60- and 100-mum IRAS images show spatial coincidence, over a 0.675 x 0 625 deg(2) field, with both low- and intermediate-velocity H I gas (previously observed with the Arecibo telescope), indicating that the IVC may contain dust. Both the Halpha and tentative IRAS detections discriminate this IVC from high-velocity clouds, although the H I properties do not. When combined with the H I and optical results, these data point to a Galactic origin for at least parts of this IVC.

Angular distribution for the elastic scattering of electrons from Ar+(3s^2 3p^5 ^2P) above the first inelastic threshold

The measured angular differential cross section (DCS) for the elastic scattering of electrons from Ar+(3s2 3p5 2P) at the collision energy of 16 eV is presented. By solving the Hartree-Fock equations, we calculate the corresponding theoretical DCS including the coupling between the orbital angular momenta and spin of the incident electron and those of the target ion and also relaxation effects. Since the collision energy is above one inelastic threshold for the transition 3s2 3p5 2P–3s 3p6 2S, we consider the effects on the DCS of inelastic absorption processes and elastic resonances. The measurements deviate significantly from the Rutherford cross section over the full angular range observed, especially in the region of a deep minimum centered at approximately 75°. Our theory and an uncoupled, unrelaxed method using a local, spherically symmetric potential by Manson [Phys. Rev. 182, 97 (1969)] both reproduce the overall shape of the measured DCS, although the coupled Hartree-Fock approach describes the depth of the minimum more accurately. The minimum is shallower in the present theory owing to our lower average value for the d-wave non-Coulomb phase shift s2, which is due to the high sensitivity of s2 to the different scattering potentials used in the two models. The present measurements and calculations therefore show the importance of including coupling and relaxation effects when accurately modeling electron-ion collisions. The phase shifts obtained by fitting to the measurements are compared with the values of Manson and the present method.

The VLT-FLAMES survey of massive stars: atmospheric parameters and rotational velocity distributions for B-type stars in the Magellanic Clouds

Aims.We aim to provide the atmospheric parameters and rotational velocities for a large sample of O- and early B-type stars, analysed in a homogeneous and consistent manner, for use in constraining theoretical models. Methods: Atmospheric parameters, stellar masses, and rotational velocities have been estimated for approximately 250 early B-type stars in the Large (LMC) and Small (SMC) Magellanic Clouds from high-resolution VLT-FLAMES data using the non-LTE TLUSTY model atmosphere code. This data set has been supplemented with our previous analyses of some 50 O-type stars (Mokiem et al. 2006, 2007) and 100 narrow-lined early B-type stars (Hunter et al. 2006; Trundle et al. 2007) from the same survey, providing a sample of ~400 early-type objects. Results: Comparison of the rotational velocities with evolutionary tracks suggests that the end of core hydrogen burning occurs later than currently predicted and we argue for an extension of the evolutionary tracks. We also show that the large number of the luminous blue supergiants observed in the fields are unlikely to have directly evolved from main-sequence massive O-type stars as neither their low rotational velocities nor their position on the H-R diagram are predicted. We suggest that blue loops or mass-transfer binary systems may populate the blue supergiant regime. By comparing the rotational velocity distributions of the Magellanic Cloud stars to a similar Galactic sample, we find that (at 3s confidence level) massive stars (above 8 M?) in the SMC rotate faster than those in the solar neighbourhood. However there appears to be no significant difference between the rotational velocity distributions in the Galaxy and the LMC. We find that the v sin i distributions in the SMC and LMC can modelled with an intrinsic rotational velocity distribution that is a Gaussian peaking at 175 km s-1 (SMC) and 100 km s-1 (LMC) with a 1/e half width of 150 km s-1. We find that in NGC 346 in the SMC, the 10-25 M? main-sequence stars appear to rotate faster than their higher mass counterparts. It is not expected that O-type stars spin down significantly through angular momentum loss via stellar winds at SMC metallicity, hence this could be a reflection of mass dependent birth spin rates. Recently Yoon et al. (2006) have determined rates of GRBs by modelling rapidly rotating massive star progenitors. Our measured rotational velocity distribution for the 10-25 M? stars is peaked at slightly higher velocities than they assume, supporting the idea that GRBs could come from rapid rotators with initial masses as low as 14 M? at low metallicities.

High-velocity features: A ubiquitous property of Type Ia supernovae

Evidence of high-velocity features (HVFs) such as those seen in the near-maximum spectra of some Type Ia supernovae (SNe Ia; e. g., SN 2000cx) has been searched for in the available SN Ia spectra observed earlier than 1 week before B maximum. Recent observational efforts have doubled the number of SNe Ia with very early spectra. Remarkably, all SNe Ia with early data ( seven in our Research Training Network sample and 10 from other programs) show signs of such features, to a greater or lesser degree, in Ca II IR and some also in the Si II lambda 6355 line. HVFs may be interpreted as abundance or density enhancements. Abundance enhancements would imply an outer region dominated by Si and Ca. Density enhancements may result from the sweeping up of circumstellar material (CSM) by the highest velocity SN ejecta. In this scenario, the high incidence of HVFs suggests that a thick disk and/or a high-density companion wind surrounds the exploding white dwarf, as may be the case in single degenerate systems. Large-scale angular fluctuations in the radial density and abundance distribution may also be responsible: this could originate in the explosion and would suggest a deflagration as the more likely explosion mechanism. CSM interaction and surface fluctuations may coexist, possibly leaving different signatures on the spectrum. In some SNe, the HVFs are narrowly confined in velocity, suggesting the ejection of blobs of burned material.