Rotational Sidebands Research Articles

A Precise, General, Non-Invasive and Automatic Speed Estimation Method for MCSA Diagnosis and Efficiency Estimation of Induction Motors

Efficiency estimation and diagnosis via MCSA require precise knowledge of speed. In an industrial environment, speed must be obtained with a non-invasive, automatic and general method. Recent studies have shown that Sensorless Speed Estimation techniques based on detecting Rotational Frequency Sideband Harmonics (RFSHs) or Rotor Slot Harmonics (RSHs) are best suited to these purposes. RFSHs-based methods are easier to apply as they only depend on the number of poles. RSHs-based are much more accurate due to their wider bandwidth. Yet, their use is not trivial as they require to identify the RSHs family, assign to each RSH its order of the current harmonic ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\nu$</tex-math></inline-formula> ) and determine the number of rotor slots ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> ), a rarely known parameter. This paper ends with this trade-off between accuracy and applicability by proposing a novel RSHs-based technique that, for the first time in technical literature, eliminates the need to estimate the number of rotor slots and provides a reliable and automatic procedure to locate the RSHs family and determine their <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\nu$</tex-math></inline-formula> indices. Finally, the method is validated under all types of conditions and motor designs, by simulations, lab tests and with 105 industrial motors, highlighting its high accuracy (errors below 0.05 rpm), and applicability.

The Sun’s Mean Line-of-sight Field

In this paper, I regard the Sun-as-a-star magnetic field (i.e., the mean field) as a filter for the spherical harmonic components of the photospheric field, and then calculate the transmission coefficients of this filter. The coefficients for each harmonic, Y l m , are listed in three tables according to their dependence on B 0, the observer’s latitude in the star’s polar coordinate system. These coefficients are used to interpret the 46 yr sequence of daily mean-field measurements at the Wilcox Solar Observatory. I find that the nonaxisymmetric part of the field originates in the , , and a combination of the and harmonic components. The axisymmetric part of the field originates in plus a B 0-dependent combination of the and components. The power spectrum of the field has peaks at frequencies corresponding to the ∼27 day synodic equatorial rotation period and its second and third harmonics. Each of these peaks has fine structure on its low-frequency side, indicating magnetic patterns that rotate slowly under the influence of differential rotation and meridional flow. The sidebands of the fundamental mode resolve into peaks corresponding to periods of ∼28.5 and ∼30 days, which tend to occur at the start of sunspot maximum, whereas the ∼27 day period tends to occur toward the end of sunspot maximum. We might expect similar rotational sidebands to occur in magnetic observations of other Sun-like stars and to be a useful complement to asteroseismology studies of convection and magnetic fields in those stars.

Shapes, softness, and nonyrast collectivity in W186

Non-yrast, excited states in neutron-rich $^{186}$W were populated via inelastic-scattering reactions using beams of $^{136}$Xe nuclei accelerated to 725 and 800 MeV. Levels populated in the reactions were investigated via particle-$ \gamma $ coincidence techniques using the Gammasphere array of High-Purity Germanium detectors and the compact heavy-ion counter, CHICO2. The $ K^{\pi} = 2 ^{+} $ ($\gamma$), $ K^{\pi} = 0^{+}$ and $ K^{\pi} = 2^{-} $ (octupole) rotational side bands were extended to spins $ 14\hbar $, $ 12\hbar $, and $ 13\hbar $, respectively. A staggering pattern observed in the energies of levels in the $ K^{\pi} = 2^{+} $ band was found to be consistent with a potential that gets softer to vibration in the $ \gamma $ degree of freedom with increasing spin. The odd-even staggering of states in the $ K^{\pi} = 2^{-}$ band was found to exhibit a phase opposite to that seen in the $ \gamma $ band; an effect most probably associated with Coriolis coupling to other, unobserved octupole vibrational bands in $^{186}$W.

Flux-Based Detection and Classification of Induction Motor Eccentricity, Rotor Cage, and Load Defects

Motor current signature analysis (MCSA) has been accepted in the field as a reliable means of detecting faults in the rotor cage of induction motors. However, there are many limitations to MCSA-based detection for other types of faults including rotor eccentricity and load defects. Recently, there has been increasing interest in airgap or leakage flux monitoring as an alternative to replace or complement MCSA. Flux monitoring can provide a reliable means of detecting rotor faults since anomalies in the rotor magnetomotive force or airgap can be directly observed. In this article, a new method based on monitoring the attenuation of rotor rotational frequency sidebands in the flux spectra is proposed for reliable detection and classification of rotor cage and eccentricity faults. It is also shown that flux monitoring can provide detection of rotor faults that is insensitive to the load defects. An experimental study under controlled broken bar, eccentricity, misalignment, and load unbalance conditions are given to support the claims. The results show that rotor cage, eccentricity, and load defects can be detected and distinguished for cases where MCSA alone is ineffective. A comparative evaluation between the proposed flux monitoring method and existing methods (MCSA, vibration analysis) is also given.

Reliable Flux-Based Detection of Induction Motor Rotor Faults From the Fifth Rotor Rotational Frequency Sideband

Motor current signature analysis (MCSA) is widespread in the field as a means of providing remote, online monitoring of industrial induction motor rotor faults. However, numerous cases of false indications with MCSA produced due to asymmetries in the rotor structure or load leading to unnecessary inspection or forced outages have been reported. Although alternative test methods under motor standstill or starting transient immune to the false indications have been proposed, a reliable method capable of “online” monitoring is desirable. In this article, a new fault indicator in the airgap or stray flux capable of reliable online detection is proposed. It is shown that the fifth sideband of the rotor rotational speed frequency can provide detection of rotor faults immune to most of the false MCSA indications. Experimental results under the most common false indications are provided to verify the claims made for cases where online MCSA produces false indications. The proposed fault indicator is also shown to be immune to eccentricity and common load defects such as load unbalance and misalignment.

Search Coil-Based Detection of Nonadjacent Rotor Bar Damage in Squirrel Cage Induction Motors

Detection of rotor cage faults in induction motors based on motor current signature analysis (MCSA) is being extensively applied in the field for preventing forced outage of the motor and industrial process. Although MCSA is very effective for detecting broken bars that are adjacent to each other, it can fail if the broken bars are nonadjacent, which is common for applications with frequent starts. If multiple broken bars are spread out at locations where the rotor “electrical” asymmetry is canceled, the presence of broken bars is difficult to detect with MCSA. A false indication can lead to a catastrophic-forced outage, but the only known means of detecting this type of fault in the field is through rotor visual inspection. In this article, the feasibility of detecting nonadjacent broken rotor bars from the rotor rotational frequency sideband components in the internal and external search coil measurements during steady state and motor starting is evaluated. Experimental testing on a 7.5-hp induction motor shows that nonadjacent broken bars can be reliably detected from the analysis of flux measurements for cases where MCSA and all other electrical tests fail.

Single-Crystal 31P and 7Li NMR of the Ionic Conductor LiH2PO4

The electronic surroundings of phosphorus and lithium atoms in the ionic conductor lithium dihydrogen phosphate (LDP) have been studied by single-crystal nuclear magnetic resonance (NMR) spectroscopy at room temperature. From orientation-dependent NMR spectra of a large homegrown LDP single crystal, the full 31P chemical shift (CS) and 7Li quadrupole coupling (QC) tensor was determined, using a global fit over three rotation patterns. The resulting CS tensor is characterized by its three eigenvalues: δ 11 P A S = ( 67.0 ± 0.6 ) ppm, δ 22 P A S = ( 13.9 ± 1.5 ) ppm, and δ 33 P A S = ( − 78.7 ± 0.9 ) ppm. All eigenvalues have also been verified by magic-angle spinning NMR on a polycrystalline sample, using Herzfeld–Berger analysis of the rotational side band pattern. The resulting 7Li QC tensor is characterized by its quadrupolar coupling constant χ = Q 33 P A S = ( − 71 ± 1 ) kHz and the two eigenvalues Q 11 P A S = ( 22.3 ± 0.9 ) kHz, and Q 22 P A S = ( 48.4 ± 0.8 ) kHz. The initially unknown orientation of the mounted crystal, expressed by the orientation of the rotation axis in the orthorhombic crystal frame, was included in the global data fit as well, thus obtaining it from NMR data only.

Coherent Control of the Rotational Degree of Freedom of a Two-Ion Coulomb Crystal.

We demonstrate the preparation and coherent control of the angular momentum state of a two-ion crystal. The ions are prepared with an average angular momentum of 7850ℏ freely rotating at 100kHz in a circularly symmetric potential, allowing us to address rotational sidebands. By coherently exciting these motional sidebands, we create superpositions of states separated by up to four angular momentum quanta. Ramsey experiments show the expected dephasing of the superposition which is dependent on the number of quanta separating the states. These results demonstrate coherent control of a collective motional state described as a quantum rotor in trapped ions. Moreover, our Letter offers an expansion of the utility of trapped ions for quantum simulation, interferometry, and sensing.

Configuration-constrained calculations of high-&amp;lt;italic&amp;gt;K &amp;lt;/italic&amp;gt;rotational bands in even-even isotones around &amp;lt;italic&amp;gt;N&amp;lt;/italic&amp;gt;=100

Nuclear rotational spectroscopy has been extensively investigated in experimental and theoretical studies. In the collective model, a nucleus can be excited in two ways. One is by breaking pairs of nucleons and exciting nucleons to a higher level. An excited state with a higher K -value sometimes has a long lifetime. Usually those states with lifetimes longer than 1 ns are called isomeric state because of forbidden transitions from high K to low K state. The other way is by collective motions, like rotation and vibration. A rotational band built on the multi-particle state is called a sideband. In general, a nucleus can have more than one sideband. Investigations of sidebands can provide rich information about the nucleus structure, like single-particle level, nuclear shape, and electromagnetic transitions and so on. The traditional total Routhian surface method, which is a powerful tool for investigating nuclear rotation, has been successfully used to describe yrast bands. However, it often encounters non-convergence problems when calculating sidebands. To overcome this problem, we recently developed a configuration-constrained cranking Skyrme Hartree-Fock mean-field calculation with pairing treated by the particle-number-conserving (PNC) method for sidebands. The PNC pairing method follows the technique of a “standard” shell model, which diagonalizes the Hamiltonian in a truncated model space and guarantees the conservation of the particle number. The rare-earth ( Z =57−71) neutron-rich nuclides are good candidates for investigating the high- K rotational bands. In this mass region, nuclei with N ≥90 are known to be well deformed and many high- j orbitals exist near the neutron and proton Fermi surfaces. These orbitals can form various multi-particle configurations and lead to high- K rotational sidebands. We perform configuration-constrained cranking Skyrme Hartree-Fock mean-field calculations with pairing treated using the PNC method for the high- K rotational bands in even-even isotones near N =100. The K π=6− rotational bands in 160Sm, 164Dy, 166Er, 168Yb, 170Er, and 172Yb and the K π=4− rotational bands in 168Er and 170Yb have been observed during experiments. K π=6− isomers were first observed in very neutron-rich nuclei, i.e., 158Nd, 164Sm, and 166Gd. Further, K π=4− isomers were first observed in neutron-rich N =100 isotones, i.e., 160Nd, 162Sm, and 164Gd. Theoretically, several models have been used to study these neutron-rich nuclei, including the cranked shell model, projected shell model, deformed Hartree-Fock method, cranking PNC method, and quasiparticle random phase approximation. We systematically investigated these high- K rotational bands and the ground state bands in N =98, 100, and 102 isotones using the configuration-constrained cranking Skyrme Hartree-Fock mean-field calculation with PNC pairing. The Skyrme force of SKM* is adopted. The pairing strength is determined using the odd-even mass difference and a three-point formula, which includes the mean-field and blocking effects. The calculations reproduce the experimental moments of inertia of both the ground state and sidebands well. Configurations are assigned to the observed high- K rotational bands. Further, we predict possible high- K rotational bands in 158Nd, 162Gd, 160Nd, 162Sm, 164Gd, and 166Dy. This study on high- K rotational bands can provide new insights into the structure of the states, and the predictions may provide useful information for future experiments.

Dispersive Fourier transformation for megahertz detection of coherent stokes and anti-stokes Raman spectra

In many fields of study, from coherent Raman microscopy on living cells to time-resolved coherent Raman spectroscopy of gas-phase turbulence and combustion reaction dynamics, the need for the capability to time-resolve fast dynamical and nonrepetitive processes has led to the continued development of high-speed coherent Raman methods and new high-repetition rate laser sources, such as pulse-burst laser systems. However, much less emphasis has been placed on our ability to detect shot to shot coherent Raman spectra at equivalently high scan rates, across the kilohertz to megahertz regime. This is beyond the capability of modern scientific charge coupled device (CCD) cameras, for instance, as would be employed with a Czerny-Turner type spectrograph. As an alternative detection strategy with megahertz spectral detection rate, we demonstrate dispersive Fourier transformation detection of pulsed (∼90 ps) coherent Raman signals in the time-domain. Instead of reading the frequency domain signal out using a spectrometer and CCD, the signal is transformed into a time-domain waveform through dispersive Fourier transformation in a long single-mode fiber and read-out with a fast sampling photodiode and oscilloscope. Molecular O- and S-branch rotational sideband spectra from both N2 and H2 were acquired employing this scheme, and the waveform is fitted to show highly quantitative agreement with a molecular model. The total detection time for the rotational spectrum was 20 ns, indicating an upper limit to the detection frequency of ∼50 MHz, significantly faster than any other reported spectrally-resolved coherent anti-Stokes Raman detection strategy to date.

Dynamic features of three-dimensional helical gears under sliding friction with tooth breakage

Abstract Mass eccentric and mesh stiffness variation induced by tooth breakage will change the dynamic features of helical gears. However, the internal excitation in helical gears under sliding friction with tooth breakage is seldom considered to reveal the dynamic features. In this study, the calculation method of mesh stiffness in helical gears with tooth breakage is proposed based on the time-varying contact line. A three-dimensional analytical helical gear pair model is developed by considering the mass eccentric and mesh stiffness induced by tooth breakage with sliding friction. The effects of tooth breakage on the dynamic responses of helical gears are performed. The results show that the amplitude modulation phenomenon emerged in the dynamic transmission error by considering the mass eccentric caused by tooth breakage. The oscillation of the dynamic response change significantly in the tooth breakage area, especially with the growth of the breakage size. Sliding friction plays a certain role in inhibiting the amplitude of the frequency. Tooth breakage results in the presence of rotational frequency and sidebands around mesh frequency and its harmonics. The rotational frequency increases significantly by considering the mass eccentricity due to tooth breakage defect.

Near-infrared absorption gas sensing with metal-organic framework on optical fibers

Despite significant advantages in terms of portability and cost, near-infrared (NIR) gas sensing still remains a great challenge due to its relatively weak overtone absorption from the fundamental vibrational bond absorption at the mid-IR frequency. In this paper, we demonstrated ultra-sensitive NIR gas sensing for carbon dioxide (CO2) at 1.57μm wavelength through nanoporous Cu-BTC (BTC=benzene-1,3,5-tricarboxylate) metal-organic framework (MOF) coated single-mode optical fiber. For the first time, we obtained high-resolution NIR spectroscopy of CO2 sorbed in MOF without seeing any rotational side band, indicating that the tightly confined gas molecules in the MOF pores do not have any freedom of rotation. Real-time measurement of the mixed gas flow of CO2 and Ar showed different response time depending on the concentration of CO2, which is attributed to the complex sorption mechanism of CO2 in Cu-BTC MOF. Most importantly, we realized ultra-low detection limit of CO2 (<20ppm) with only 5cm long Cu-BTC MOF thin film coated on single-mode optical fibers.

Configuration-constrained cranking Hartree-Fock pairing calculations for sidebands of nuclei

Background: Nuclear collective rotations have been successfully described by the cranking Hartree-Fock-Bogoliubov (HFB) model. However, for rotational sidebands which are built on intrinsic excited configurations, it may not be easy to find converged cranking HFB solutions. The nonconservation of the particle number in the BCS pairing is another shortcoming. To improve the pairing treatment, a particle-number-conserving (PNC) pairing method was suggested. But the existing PNC calculations were performed within a phenomenological one-body potential (e.g., Nilsson or Woods-Saxon) in which one has to deal the double-counting problem.Purpose: The present work aims at an improved description of nuclear rotations, particularly for the rotations of excited configurations, i.e., sidebands.Methods: We developed a configuration-constrained cranking Skyrme Hartree-Fock (SHF) calculation with the pairing correlation treated by the PNC method. The PNC pairing takes the philosophy of the shell model which diagonalizes the Hamiltonian in a truncated model space. The cranked deformed SHF basis provides a small but efficient model space for the PNC diagonalization.Results: We have applied the present method to the calculations of collective rotations of hafnium isotopes for both ground-state bands and sidebands, reproducing well experimental observations. The first up-bendings observed in the yrast bands of the hafnium isotopes are reproduced, and the second up-bendings are predicted. Calculations for rotational bands built on broken-pair excited configurations agree well with experimental data. The band-mixing between two ${K}^{\ensuremath{\pi}}={6}^{+}$ bands observed in $^{176}\mathrm{Hf}$ and the $K$ purity of the $^{178}\mathrm{Hf}$ rotational state built on the famous 31 yr ${K}^{\ensuremath{\pi}}={16}^{+}$ isomer are discussed.Conclusions: The developed configuration-constrained cranking calculation has been proved to be a powerful tool to describe both the yrast bands and sidebands of deformed nuclei. The analyses of rotational moments of inertia help to understand the structures of nuclei, including rotational alignments, configurations, and competitions between collective and single-particle excitations.

Bearing fault diagnosis under unknown variable speed via gear noise cancellation and rotational order sideband identification

The interfering vibration signals of a gearbox often represent a challenging issue in rolling bearing fault detection and diagnosis, particularly under unknown variable rotational speed conditions. Though some methods have been proposed to remove the gearbox interfering signals based on their discrete frequency nature, such methods may not work well under unknown variable speed conditions. As such, we propose a new approach to address this issue. The new approach consists of three main steps: (a) adaptive gear interference removal, (b) fault characteristic order (FCO) based fault detection, and (c) rotational-order-sideband (ROS) based fault type identification. For gear interference removal, an enhanced adaptive noise cancellation (ANC) algorithm has been developed in this study. The new ANC algorithm does not require an additional accelerometer to provide reference input. Instead, the reference signal is adaptively constructed from signal maxima and instantaneous dominant meshing multiple (IDMM) trend. Key ANC parameters such as filter length and step size have also been tailored to suit the variable speed conditions, The main advantage of using ROS for fault type diagnosis is that it is insusceptible to confusion caused by the co-existence of bearing and gear rotational frequency peaks in the identification of the bearing fault characteristic frequency in the FCO sub-order region. The effectiveness of the proposed method has been demonstrated using both simulation and experimental data. Our experimental study also indicates that the proposed method is applicable regardless whether the bearing and gear rotational speeds are proportional to each other or not.

Effect of Rotational Couplings on Vibrational Spectrum Line Shape of the Bending Mode in Low-Density Supercritical Water: Density and Hydrogen Isotopes Dependencies

The effect of rotations on the line shape of the bending vibrational spectrum for supercritical water was analyzed using classical molecular dynamics simulation for the flexible point-charge SPC/Fw model. The experimental infrared spectrum of the bending mode at the low densities of 0.01–0.04 g·cm−3 and at 400 °C was essentially reproduced without any other assumptions. The spectrum line shape at low densities consists of two broad rotational bands due to the rotational couplings, as in the case of the O–H stretch mode. This is due to the time-scale separation breakdown but is not due to the presence of any definite clusters. The rotational couplings become more significant at higher temperatures. The separations between the bending band center and the rotational broad side-bands are found to be linearly correlated with the inverse of the total moment of inertia of the water isotopic species, which is clear molecular-level evidence for the rotational couplings.

Effect of heavy hydrogen isotopes on the vibrational line shape for supercritical water through rotational couplings

The rotational couplings, which determine the infrared spectral line shape in the low-density supercritical water, were analyzed as functions of the density and the temperature by applying molecular dynamics simulation to a flexible water model, SPC∕Fw and by varying the moment of inertia of the water through substitution for the H atom in H2O by heavy hydrogen isotopes. The differences in the frequency and the relative intensity between the sharp center peak and the rotational broad side-bands were analyzed for the O-H, O-D, and O-T stretch spectra. The frequency differences between the sharp center peak and the rotational broad side-bands are linearly correlated with the inverse of the moment of inertia of the isotope-substituted water species. The intensity of the sharp peak is associated with the long-time component of the reorientational time correlation function for the stretching bond vector. At 400 °C, where a substantial amount of hydrogen bonds are dynamically persisting, an intensity decrease in the rotational broad side-bands was observed with increasing density from 0.01 to 0.40 g cm(-3), respectively, corresponding to 0.56 and 22.2 M (=mol dm(-3)), orders of magnitude higher than the ideal gas densities. This arises from the decrease in the correlation time of the angular velocity and the rotational couplings due to an increase in the hydrogen-bonding perturbation. The intensity decrease of the rotational side-bands with increasing density is more significant for the water isotopes with heavier hydrogens. At a high temperature of 1200 °C, the rotational side-bands at 0.01 to 0.05 g cm(-3) were more distinct than those at 400 °C, and even at a medium density of 0.40 g cm(-3) a significant signal broadening due to the rotational couplings was clearly observed because of the accelerated rotational momentum. The vibrational spectrum cannot be decomposed into definite chemical clusters for the thermodynamic and kinetic analysis because of the dynamic origin.

Continuous-wave, multiple-order rotational Raman generation in molecular deuterium

We demonstrate the generation of ≈10 rotational sidebands using continuous-wave stimulated Raman scattering in molecular deuterium. The generation occurs inside a high-finesse cavity at molecular gas pressures of ≈0.1 atm.

Generation of high-order rotational Raman sidebands in the deep-ultraviolet region using molecular phase modulation induced by an intensity-modulated optical pulse

We demonstrated the efficient excitation of coherent molecular motion for the generation of high-order rotational Stokes and anti-Stokes Raman emissions using a femtosecond laser. Molecular phase modulation of a probe beam was efficiently induced by an optical beat of the pump beam emitting at two different frequencies, the separation of which corresponded to the multiplicative inverse of the period of molecular rotation. The spectral width of the probe pulse was expanded to 10 nm in the deep-ultraviolet region, suggesting the generation of a 10 fs pulse by Fourier synthesis of the emission lines.

The study of energy bands in nucleus 102Zr

Theoretical calculations of the energy bands in nucleus 102Zr are carried out by taking the projected shell model approach, which has reproduced the experimental data. In addition, by analyzing band-head energies, corresponding configurations of yrast band, quasi-particle rotational bands and side bands, we have worked out the microscopic formation mechanism of axially symmetric deformation bands: The low-excitation deformation bands are attributed to the high-j intruder states 1g7/2 and 1h11/2 in the N=4, 5 shells; the quasi-particles in the orbit v5/2-[532], v3/2+[411] and v3/2+[413] in particular play an important role in the deformation of 102Zr.

Solid state deuteron relaxation time anisotropy measured with multiple echo acquisition

The signal to noise ratio of solid state deuteron NMR line shapes can be significantly improved by recording multiple echoes, generated either by a quadrupole Carr-Purcell-Meiboom-Gill pulse train (QCPMG) or by magic angle spinning (MAS). It is shown in this article, theoretically and experimentally, that when these techniques are used to record partially relaxed spectra, the relaxation times of Zeeman order, T(1Z), and quadrupole order, T(1Q), measured for individual side bands in QCPMG experiments preserve relaxation time anisotropy, while rotational side bands in MAS spectra do not. The relaxation times of individual QCPMG sidebands are not identical to those measured at the same frequencies on partially relaxed quadrupole echo powder patterns, and must be computed by explicit simulation.