Sideband Characteristics Research Articles

Analysis of Vibration Characteristics of Planetary Gearbox with Broken Sun Gear Based on Phenomenological Model

To investigate the vibration properties in healthy and fault conditions of planetary gearboxes, a phenomenological model is constructed to present the vibration spectrum structure. First, the effects of the base deflection of the gear fillet and the flexibility between the root circle and the base circle on the time-varying meshing stiffness are considered in order to construct an equivalent model of time-varying mesh stiffness and broken tooth faults, exploring the law of variation for meshing stiffness when differently sized faults occur on the sun gear. Then, considering both the effect of the vibration transfer path and the meshing impacts, we establish phenomenological models of planetary gears under healthy and fault conditions. By comparing and analyzing the phenomenological model based on the cosine function to verify the effectiveness of the proposed model. The experimental results show that the error of the proposed model is 1.38% lower than that of the traditional phenomenological model, and the proposed model can accurately analyze the frequency, amplitude, and sideband characteristics of the vibration signals of sun gear with different degrees of broken tooth, which can be used for the local fault diagnosis of planetary gearboxes.

Water speciation and hydrogen isotopes in hydrous stishovite: implications for the deep Earth water cycle

Stishovite is a key mineral for understanding the deep Earth water cycle because of its potential as a main carrier for water into the transition zone and lower mantle. During subduction-related metamorphism of basaltic oceanic crust, stishovite stabilizes at 8–9 GPa and comprises 10–25 vol% of the bulk mineralogy, with some experimental studies indicating that stishovite can accommodate 3.5 wt% H2O or more in the transition zone and upper lower mantle. This large water solubility has been explained by a hydrogarnet substitution mechanism (1Si4+ ↔ 4H+) and/or the incorporation of interstitial molecular water. To investigate water speciation and hydrogen isotope behavior, we synthesized partially deuterated hydrous stishovite at 9 GPa and 450 °C in a multi-anvil press (MA). The hydrous stishovite contains on average 1.69 ± 0.05 wt% water, which is consistent with earlier MA studies but is significantly lower than the 3.5 wt% reported from in situ diamond anvil cell (DAC) studies made at higher pressures and temperatures. 1H MAS NMR spinning sideband characteristics suggest a high abundance of interstitial molecular water in hydrous stishovite, while the presence of a hydrogarnet defect cannot be ruled out. Unit-cell volumes and deuterium enrichment in the quenched hydrous stishovite indicate that ~ 45% of the water is lost from the stishovite upon quenching and decompression of the experiment, consistent with a higher solubility. This implies that the pristine water contents of a P–T–fO2 equilibrated hydrous stishovite cannot be quenched to 1 atm and room temperature from classical MA experiments. We further present a capillary-based recovery method for fluid from experimental capsules, allowing direct determination of the D/H ratio of the experimental fluid and indirect determination of the hydrous stishovite. Using Rayleigh modeling to account for the quench-related water loss, we find that, at 450 °C and 9 GPa, deuterium is 3.5–4.5 times enriched in hydrous stishovite relative to coexisting aqueous fluid. This is opposite of what is commonly observed for mineral–fluid pairs above 300 °C, rendering hydrous stishovite a potential sink for deuterium and decreasing the D/H ratio of coexisting aqueous fluids. Partial decomposition (30–60%) of hydrous stishovite during mantle upwelling and production of primary basaltic melts could be accompanied by high-temperature D/H fractionation, decreasing the hydrogen isotope composition of such melts towards “mantle-like” δD values between −75 and −220‰.

Dynamic Characteristics and Fault Mechanism of the Gear Tooth Spalling in Railway Vehicles under Traction Conditions

Gear tooth spalling is one of the inevitable fault modes in the long-term service of the traction transmission system of railway vehicles, which can worsen the dynamic load of the rotating mechanical system and reduce the operating quality. Therefore, it is necessary to study its fault mechanism to guide fault diagnosis scientifically. This paper established a planar railway vehicle model with a traction transmission system and an analytical time-varying meshing stiffness (TVMS) model of the spalling spur gear. Then, it analyzed the dynamic characteristics under traction conditions. The research found that the spalling length and depth affect the amplitude of the TVMS at the defect, while the width affects the range of the TVMS loss. The crest factor is the best evaluation indicator in ideal low-noise environments due to its sensitivity and linearity, but it is not good in strong-noise environments. Similarly, a time–frequency analysis tool cannot significantly detect the sideband characteristics that are excited by spalling. After high-pass filtering, the root mean square and variance exhibit excellent classification and vehicle speed independence in strong-noise environments. This research achievement can provide adequate theoretical support for feature selection and making strategies for fault diagnosis of railway vehicle gear systems.

Permanent magnet synchronous generator stator current AM-FM model and joint signature analysis for planetary gearbox fault diagnosis

Wind energy is renewable and wind power generation facilities have been growing rapidly around the world. Permanent magnet synchronous generators (PMSGs) and planetary gearboxes are commonly used in wind turbines (WTs). For planetary gearbox fault diagnosis, PMSG stator current signal analysis provides a potential alternative approach because stator current signals contain fault signatures with easier accessibility comparing to conventional vibration signals. Planetary gearbox faults result in PMSG input torque oscillations, leading to both amplitude modulation and frequency modulation (AM-FM) effects on stator current signals. To better reveal gear fault features in PMSG stator current signals, this paper proposes to diagnose planetary gearbox faults from three complementary analysis results of the PMSG stator current, i.e., Fourier spectrum, amplitude demodulated spectrum and frequency demodulated spectrum. For this purpose, an AM-FM current signal model is derived through mechanical-magnetic-electric interaction analysis. Explicit equation of Fourier spectrum is derived with its sideband characteristics investigated. Both amplitude and frequency demodulation analyses are proposed to compensate for or mitigate the difficulty in the intricate sideband analysis of Fourier spectrum. Due to its capability in signal mono-component decomposition for accurate estimation of instantaneous frequency, adaptive local iterative filtering is utilized in frequency demodulation analysis. Explicit equations of corresponding demodulated spectra are derived, and gear fault signatures in PMSG stator current signals are revealed. The theoretical derivations and proposed methods are validated through lab experiments by diagnosing localized faults on the sun, planet and ring gears.

Generation of soliton rain in a passive mode-locked Tm-doped fiber laser at 2 µm

In this paper, the experimental investigation and theoretical analysis on the soliton rain generated in the Tm-doped fiber laser have been carried out. On the basis of nonlinear polarization rotation technology, the fundamental and harmonic soliton rain pulses were obtained, the influence of net negative dispersion cavity length on the output performances of soliton rain pulse were studied, and the spectral sideband characteristics of soliton rain were numerically analyzed. By comparing the spectra of continuous wave mode-locking and soliton rain states, it can be found that the quasi-periodic modulation exists for the spectral sideband of soliton rain resulted from the complex interaction between the dispersive wave and the soliton wave. The interaction is one of the major factors for the formation of soliton rain. The research results are helpful for the better understanding of the soliton rain dynamics and mechanism in passive mode-locked fiber lasers.

Guided wave structure of spoof surface plasmon polaritons with ring cavities

The confined capability of the spoof surface plasmon polaritons (SSPPs) can be regulated by the periodic cell structure of the SSPP waveguide. In this paper, to further enhance the confinement to the SSPP interface fields and reduce the lateral dimension of the SSPP guided wave structure, the periodic unit loaded with rectangular ring cavities on both sides of the metal strip is proposed. The experimental results show that at a given periodic cell height, the proposed guided wave structure have a lower asymptotic frequency and steep sideband characteristics. That indicates it has good low-pass guided wave performance. Meanwhile, this structure is beneficial to device integration.

Spectral negentropy based sidebands and demodulation analysis for planet bearing fault diagnosis

Planet bearing vibration signals are highly complex due to intricate kinematics (involving both revolution and spinning) and strong multiple modulations (including not only the fault induced amplitude modulation and frequency modulation, but also additional amplitude modulations due to load zone passing, time-varying vibration transfer path, and time-varying angle between the gear pair mesh lines of action and fault impact force vector), leading to difficulty in fault feature extraction. Rolling element bearing fault diagnosis essentially relies on detection of fault induced repetitive impulses carried by resonance vibration, but they are usually contaminated by noise and therefor are hard to be detected. This further adds complexity to planet bearing diagnostics. Spectral negentropy is able to reveal the frequency distribution of repetitive transients, thus providing an approach to identify the optimal frequency band of a filter for separating repetitive impulses. In this paper, we find the informative frequency band (including the center frequency and bandwidth) of bearing fault induced repetitive impulses using the spectral negentropy based infogram. In Fourier spectrum, we identify planet bearing faults according to sideband characteristics around the center frequency. For demodulation analysis, we filter out the sensitive component based on the informative frequency band revealed by the infogram. In amplitude demodulated spectrum (squared envelope spectrum) of the sensitive component, we diagnose planet bearing faults by matching the present peaks with the theoretical fault characteristic frequencies. We further decompose the sensitive component into mono-component intrinsic mode functions (IMFs) to estimate their instantaneous frequencies, and select a sensitive IMF with an instantaneous frequency fluctuating around the center frequency for frequency demodulation analysis. In the frequency demodulated spectrum (Fourier spectrum of instantaneous frequency) of selected IMF, we discern planet bearing fault reasons according to the present peaks. The proposed spectral negentropy infogram based spectrum and demodulation analysis method is illustrated via a numerical simulated signal analysis. Considering the unique load bearing feature of planet bearings, experimental validations under both no-load and loading conditions are done to verify the derived fault symptoms and the proposed method. The localized faults on outer race, rolling element and inner race are successfully diagnosed.

Planetary Gearbox Fault Diagnosis via Torsional Vibration Signal Analysis in Resonance Region

Planetary gearbox torsional vibration signals are free from the extra amplitude modulation effect due to time-varying transmission paths and have simpler frequency structure than translational ones. Gear faults result in modulation on the torsional resonance vibration and are manifested by the modulation feature. These merits are exploited for planetary gearbox fault diagnosis in this paper. Gear fault induced torsional vibrations in resonance region are modelled as amplitude modulation and frequency modulation (AM-FM) processes, the explicit equation of Fourier spectrum is derived, and the sideband characteristics are summarized. To avoid complex sideband analysis, amplitude and frequency demodulation analysis methods are exploited. The equations of amplitude and frequency demodulated spectra are derived in closed form, and their frequency structures are revealed. For fault diagnosis based on above theoretical derivations, a resonance frequency identification approach is proposed through time-frequency analysis of torsional vibrations during variable speed processes, according to the independence nature of resonance frequency on running conditions. The theoretical derivations and proposed approach are illustrated by numerical simulated signal analysis and are further validated through dynamics modelling and lab experimental tests. Localized faults on the sun, planet, and ring gears are successfully diagnosed.

Time-Frequency Analysis of Torsional Vibration Signals in Resonance Region for Planetary Gearbox Fault Diagnosis Under Variable Speed Conditions

Translational vibration-based methods have been widely used for machinery fault diagnosis. However, because of the unique gear configuration and complex kinetics, planetary gearbox translational vibration signals have complex modulation features due to gear faults and time-varying vibration transmission paths. This results in complex frequency components of translational vibrations, and adds difficulty to gear fault signature extraction. Under variable speed conditions, the resultant time-variant frequency components and complex sidebands may overlap in frequency domain, thus making it more difficult to pinpoint fault features. To address this issue, torsional vibration signals are exploited, because they are free from the extra modulation effect due to time-varying transmission paths and have simpler frequency contents. Gear faults generate impacts, thus exciting resonances and leading to modulations on resonances. Therefore, torsional resonance frequency band is concentrated to extract gear fault information. The time-variant but symmetric sideband characteristics in the resonance region are derived based on the explicit time-varying amplitude modulation and frequency modulation signal model. Resonance frequencies are identified under variable speed conditions by virtue of their independence on running conditions. Furthermore, time-frequency analysis is utilized to extract time-variant gear fault frequencies. The proposed method is validated using both numerical simulation and lab experimental data. Localized faults of the sun, planet, and ring gears are diagnosed under variable speed conditions.

Sideband characterization and atmospheric observations with various 340 GHz heterodyne receivers

This paper describes sideband response measurements and atmospheric observations with a double sideband and two Single Sideband (SSB) receiver prototypes developed for the multi-beam limb sounder instrument stratosphere-troposphere exchange and climate monitor radiometer. We first show an advanced Fourier-Transform Spectroscopy (FTS) method for sideband response and spurious signal characterization. We then present sideband response measurements of the different prototype receivers and we compare the results of the SSB receivers with sideband measurements by injecting a continuous wave signal into the upper and lower sidebands. The receivers were integrated into a total-power radiometer and atmospheric observations were carried out. The observed spectra were compared to forward model spectra to conclude on the sideband characteristics of the different receivers. The two sideband characterization methods show a high degree of agreement for both SSB receivers with various local oscillator settings. The measured sideband response was used to correct the forward model simulations. This improves the agreement with the atmospheric observations and explains spectral features caused by an unbalanced sideband response. The FTS method also allows to quantify the influence of spurious harmonic responses of the receiver.

Modulation Spectroscopy of Acoustic Waves in Solids Containing Contact-Type Cracks

This study examined the characteristics of sidebands in modulation spectroscopy on a high-frequency wave interacting with a defect that imposes a simple switching type disruption caused by a low-frequency, high-amplitude vibration. A simple close form of sideband amplitude is obtained by convolution of a high-frequency probing wave with harmonics of a pulse wave. This study also proposes an experimental procedure based on sideband phases for determining the crack parameters.

Sidebands in Fourier transform ion cyclotron resonance mass spectra

Sidebands in mass spectra are an intrinsic feature of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). Appearance of the sidebands there is detrimental for the analytical performance, especially in case of complex mixtures analyzed at high resolution. Yet, the sidebands have a practical potential as well. Specifically, they can be applied for fine tuning of ICR cells and were previously employed to improve mass measurement accuracy for small molecules and atoms in fundamental physics experiments. Moreover, experimental characteristics of sidebands allow evaluating the theory of the ICR signal, which provides the metrological basis in FT-ICR MS. Here, we revisit the sidebands phenomenon in the conventional FT-ICR MS, specifically applied to macromolecules. We extend the previous reports on sidebands by examining the appearance of sidebands as functions of ICR cell trapping potentials, resolution, and number of charges for the first three harmonics of the reduced cyclotron frequency. Next, we develop an analytical model of sidebands that contributes to the existing theory of the ICR signal by showing the origin of sidebands to be the result of the broadband amplitude-phase modulation occurring in the ICR signal. Finally, we evaluate the theory of the ICR signal on the basis of the obtained experimental sidebands. Further progress in the theory of the ICR signal shall outline the way for further improvements in FT-ICR MS performance.

Generation Mechanism of Sidebands about Gear Mesh Vibration Considering Amplitudes Asymmetricity

Sidebands of mesh harmonic frequencies are considerable components in gear vibration spectrum. In this study, generation mechanism and characteristics of sidebands are investigated based on a single-degree-of-freedom vibration model of a cylindrical gear pair. Time-varying mesh stiffness and contribution of tooth surface form are formulated in the model. In addition to mesh harmonic components, the first order component of gear rotation is incorporated into each of the time-varying mesh stiffness and the tooth surface form as the effect of gear eccentricity. This model presents that the product of mesh harmonics and low order component of gear rotation frequency produces sidebands on either side of the mesh frequency. Asymmetrical property of sideband amplitudes about mesh frequency is dependent on frequency response function of gear vibration system. Vibration response curves of the sidebands have pseudo resonance peak. These sideband characteristics are verified by comparing simulation result of the gear model with experiment using a single-stage helical gearing.

3112 歯車のかみあい振動における側帯波の特徴把握 : 系がもつ非線形性について(S40-2 第14回卒業研究コンテスト(2),21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

The aim of this work is to investigate the characteristics of sidebands of gear mesh vibration. Because the sidebands of mesh harmonics occur owing to pitch error and gear eccentricity, they are synchronous with the rotation of the gear shaft. The dynamic relations between the sidebands and the gear errors are represented by the single-degree-of-freedom vibration model. Analytical result and experimental result show that the amplitude of the sideband rises to local maximum value when the mesh frequency equal to the natural frequency of the gear pair. This sideband characteristic is due to nonlinearity of the gear vibration, and different from that of the mesh harmonics.