Distribution Of Sidebands Research Articles

Experimental investigation on coupled-bunch instability and suppression for the upgrade of Beijing Electron-Positron Collider (BEPCII).

After touching the design collision luminosity of 1.0 × 1033cm-2s-1 in 2016, this target has not been reached again for the upgrade of Beijing Electron-Positron Collider during physical collision operation in subsequent years due to various factors, such as the collision background, noise, and equipment stability under high power operation. One of the most serious factors was the beam instability, especially the coupled-bunch instability, whose sideband distribution was clearly displayed on the spectrum analyzer when the feedback system was OFF. Experimental measurements on coupled-bunch instability and the damping from the feedback system were carried out over the past two years. These measurements were conducted by transiently turning off/on the feedback system, and the bunch-by-bunch oscillations were recorded to obtain the mode distribution and growth and damping rates. The experimental results demonstrate that the feedback damping is strong enough to suppress instability, and precise adjustments to the feedback system during physical collision operation can increase the collision luminosity, which has been verified in last year's physical run.

Maximum Likelihood Identification of Cavitation Instabilities in Axial Inducers

Abstract The article illustrates the results of an exploratory study on the effectiveness of maximum likelihood Bayesian estimation in the identification of cavitation instabilities in axial inducers using the blade-to-blade pressure measured by a single transducer flush-mounted on the impeller casing. The typical azimuthal distribution of the pressure in the blade channels is parameterized and modulated in space and time for theoretically reproducing the expected pressure generated by known forms of cavitation instabilities (cavitation surge auto-oscillations, n-lobed synchronous/asynchronous rotating cavitation, and higher-order surge/rotating cavitation modes). The power spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame, corrected for frequency broadening effects, and parametrically fitted by maximum likelihood estimation to the measurements of the pressure on the inducer casing just downstream of the blade leading edges. In addition to its fundamental frequency, each form of instability generates a characteristic spectral distribution of sidebands. The identification uses this information for successfully discriminating flow oscillation modes occurring simultaneously with intensities differing by up to one order of magnitude. The method returns the estimates of the model parameters and their standard errors, allowing one to assess the accuracy and statistical significance of the identification. The results first demonstrate that elementary maximum likelihood Bayesian identification is indeed capable to effectively detect and characterize the occurrence of flow instabilities in cavitating inducers at a fraction of the experimental and postprocessing costs and complexities of traditional cross-correlation methods.

Fault feature analysis and detection of progressive localized gear tooth pitting and spalling

Fault feature analysis of gear tooth spalling plays a vital role in gear fault diagnosis. Understanding how fault features evolve as a fault progresses is key to fault severity assessment. Due to the complicated nature of gear meshing, fault features and their development as the fault severity progresses remain mostly unknown. The assessment of fault severity is generally based on the hypothesis that ‘the more severe the fault, the stronger the fault symptom’, an assumption that has not been experimentally validated. This paper provides a comprehensive, experimental analysis of the evolution of fault vibration features of a gear transmission with progressive localized gear tooth spalling. The effects of rotational speed on the vibration features of the gear transmission are analysed. Changes in fault features (e.g. periodic impulses and sideband phenomena) under different fault severity levels and speed conditions are compared. Results indicate that the number, amplitude and distribution of sidebands increase nonlinearly as the fault progresses. Based on feature analysis, a new health indicator of the mean of the nth order peaks is proposed to detect progressive localized tooth spalling. Results indicate that the proposed indicator shows very good performance for tracking the severity of progressive tooth spalling under different speed conditions.

Modulation sidebands analysis of coupled bevel gear pair and planetary gear train system

This paper proposed a dynamic model based on the lumped parameter method and the Timoshenko beam theory to explore the sideband distribution law of the coupled bevel gear pair (BGP) and planetary gear train (PGT) system. The pass-effect of the PGT is simulated without adding extra window functions. A finite element method is proposed to solve the time-varying mesh stiffness (TVMS) of the BGP. The vibration signal of the system triggered by the TVMS of all gear pairs is obtained and validated by the experiment. It is observed that the carrier rotation frequency can modulate both the meshing frequency of the PGT and that of the BGP and their harmonics. Furthermore, the influence of the supporting state of the intermediate shaft on the sideband energy is studied. It is revealed that the farther the support positions of the intermediate shaft are from both ends, and the smaller the radial support stiffness of the bearing near the sun gear, the better it is to obtain smaller sideband energy near the meshing frequency of the BGP.

The Effect of Signal Propagation Delay on the Measured Vibration in Planetary Gearboxes

Modulation of the gear mesh vibration is a major field of research for the condition monitoring of planetary gearboxes. The modulation creates sidebands around the gearmesh frequency in the vibration spectrum, and the distribution of these sidebands has been researched in numerous papers. All publications on the subject assume that the effect of the time varying signal propagation delay between the main vibration source – the gear mesh point(s) – and the (usually fixed) transducer can beneglected. This paper investigates the validity of this assumption. To do so, a planetary gearbox with a transducer mounted on the (fixed) ring gear is studied, and the effect of the propagation delay is modelled as a phase modulation of the gear mesh vibration. General expressions are then derived for the distribution and strength of the modulation sidebands, and these expressions are applied to quantify the effect of the propagation delay on five industrial gearboxes. The results show that the amplitude of the sidebands is negligible and would not interfere with condition assessment based on analysis of the modulation of the gear mesh frequency, and thus the propagation delay can be neglected for practical purposes.

Maximum Likelihood Identification of Cavitation Instabilities in Axial Inducers

The article illustrates the application of maximum likelihood estimation to the identification of cavitation instabilities in axial inducers from the unsteady pressure readings measured on the impeller casing. The typical triangular pressure distribution in the blade channels of the impeller is parametrized and modulated in time and space in order to theoretically reproduce the expected pressure generated by known forms of cavitation instabilities (cavitation auto-oscillations, n-lobed sub/super-synchronous rotating cavitation, higher-order surge/rotating cavitation modes). The Fourier spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame and fitted by maximum likelihood estimation to the auto-correlation of the pressure measurements on the inducer casing. Each form of instability generates a characteristic spectral distribution of side bands in addition to its fundamental frequency. The identification makes use of this information for effective discrimination of simultaneous flow oscillations with significantly different intensities and partially overlapping frequencies. The method returns the estimates of the model parameters and their standard errors, allowing for both recognition of the forms of instabilities occurring in the inducer and assessment of the statistical significance of the results.

Phenomenon-model-based AM-FM vibration mechanism of faulty spur gear

Vibration responses of faulty gear contain modulation components that are commonly used as the indicators to detect the fault. The modulation mechanism has not been revealed clearly, especially the sideband distribution of amplitude modulation and frequency modulation. Aiming at the vibration modulation mechanism of fault gear, the gear meshing stiffness with frequency modulation components is deduced considering the actual speed fluctuation, as well as its influence on vibration responses. A series of phenomenon models of gear pair are built to research the sideband distribution features of vibration responses related to different types of gear faults. Both the steady-type and impact-type gear faults are proved to generate asymmetric amplitude-frequency modulation sidebands around harmonics of the meshing frequency. The marked difference lies in that the steady-type fault features distribute within a finite band while the impact-type fault features cover the entire frequency range and induce spurious resonance peaks. Sidebands with both amplitude and frequency modulations are wider than those with only amplitude modulation, and the product of two groups of frequency modulation components is proved to bring in amplitude modulation components. The phenomenon models of gear vibration responses contribute a deeper understanding of modulation mechanism of faulty spur gear, and the obtained sideband distribution features of amplitude-frequency modulation are an effective aid for gear fault diagnose.

Two-color XUV+NIR femtosecond photoionization of neon in the near-threshold region

Results of angle-resolved electron spectroscopy of near-threshold photoionization of Ne atoms by combined femtosecond extreme ultraviolet and near infrared fields are presented. The dressed-electron spectra show an energetic distribution into so-called sidebands, being separated by the photon energy of the dressing laser. Surprisingly, for the low kinetic energy (few eV) sidebands, the photoelectron energy varies as a function of the emission angle. Such behavior has not yet been observed in sideband creation and has not been predicted in commonly used theoretical descriptions such as strong field approximation and soft photon approach. Describing the photoionization with a time-dependent Schrödinger equation allows a qualitative description of the observed effect, as well as the prediction of fine structure in the sideband distribution.

Study of phase-locking of optoelectronic microwave oscillators considering amplitude perturbation

This paper presents a detailed study of the phase-locking phenomenon in single-loop optoelectronic microwave oscillators considering strong radio frequency (RF) signal injection. The analyses are made in terms of the lock-range, beat frequency and the spectral components of the unlocked-driven oscillator in presence of amplitude perturbation. An approximate expression for the amplitude perturbation of the oscillator is derived and the influence of amplitude perturbation on the phase-locking dynamics is analysed. The influence of external RF signal on the frequency pulling of the unlocked-driven optoelectronic oscillator (OEO) is also studied. It is shown that the unlocked-driven OEO output signal has a very non-symmetrical sideband distribution about the carrier. Also, analytical technique for studying the response characteristics of a phase-locked OEO to pure continuous wave amplitude modulated signal is presented. The simulation findings are also given in partial support of the conclusions of the analysis.

Phase-locking dynamics in optoelectronic oscillator

This paper analyzes the phase-locking phenomenon in single-loop optoelectronic microwave oscillators considering weak and strong radio frequency (RF) signal injection. The analyses are made in terms of the lock-range, beat frequency and the spectral components of the unlocked-driven oscillator. The influence of RF injection signal on the frequency pulling of the unlocked-driven optoelectronic oscillator (OEO) is also studied. An approximate expression for the amplitude perturbation of the oscillator is derived and the influence of amplitude perturbation on the phase-locking dynamics is studied. It is shown that the analysis clearly reveals the phase-locking phenomenon and the associated frequency pulling mechanism starting from the fast-beat state through the quasi-locked state to the locked state of the pulled OEO. It is found that the unlocked-driven OEO output signal has a very non-symmetrical sideband distribution about the carrier. The simulation results are also given in partial support to the conclusions of the analysis.

Spectral sideband distribution asymmetry in fiber laser

A ring fiber laser with SESAM mode-locking mechanism is constructed. The spectral sideband distribution asymmetry of solitons is observed in the fiber laser. There are different order sidebands distributed in two edges of the soliton spectrum. Through experimentally studying the effect of the different gain media lengths on the mode-locked solitons, it is found that the spectral sideband asymmetry occurs at the long wavelength band of erbium-doped fiber (EDF) gain profile. The origin of sideband asymmetry is owing to the secondary amplification gain profile of EDF, which is pumped by the first gain peak at 1530 nm. Furthermore, an extra in-line polarizer is imported in the cavity for studying the effect of the polarization bias on sidebands. It is found that the polarization bias in the cavity is an important control method to adjust the power and generate the spectral sidebands. However, the polarization bias does not decide the generation of spectral sideband distribution asymmetry.

Research on localization of the source of cyclostationary sound field

The conventional planar near-field acoustic holography technology cannot exactly refecact the modulation characteristics of cyclostationary sound field radiated from the rotating machineries,and the spurious energy distribution of sidebands exists in its hologram. When the cyclic spectral density (CSD), instead of the energy spectrum of sound pressure is adopted as a reconstructed physical quantity, the modulating wave and carrier wave components of the cyclostationary sound field can be extracted exactly. Focusing on the complicated nature of calculation and the accuracy of feature extracting, the CSD gathering slice method is proposed, and the effect of the additive white noise on the reconstruction is analyzed. The results of the simulation and experiments show that the method has the better anti-noise performance and sound source can be localized exactly.

Electrostatic plasma wave propagation in a density modulated plasma

A model which treats the formation of wave sidebands on a propagating electron plasma wave in the case where the plasma density is modulated by a low-frequency perturbation is developed. A new mechanism for production of an asymmetric distribution of sidebands appears, and circumstances under which the original wave may reconstitute itself are described. An experimental study of electrostatic plasma waves in a weakly ionized plasma, where the density is modulated either by external means or by the presence of an unstable drift wave, is in agreement with the model.

Wave modulation in a nonlinear dispersive medium

A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model.

Time impulse response and time frequency response of optical pupils.:Experimental confirmations and applications

Time impulse response and time frequency response of optical pupils.:Experimental confirmations and applications

Sideband Interpretation of Optical Information and the Diffraction Patterns of Unsymmetrical Pupil Functions*

This report shows how the pattern information in an object through which a coherent beam of light is passed can be transformed into information existing in the focal plane. The information in the focal plane can be interpreted as sidebands of a zero-frequency carrier. There is also a close connection between the sideband interpretation and the sampling theorem of information theory and this connection is derived and discussed.The mathematical methods used in the first (one-dimensional) part of the following analysis are an application to optics of certain classical methods in modulation and communication theory. These are the method of symmetrical and antisymmetrical sideband distribution, the method of paired echoes and sampling theorem analysis.In the two dimensional analysis, a more general method of separating functions into symmetrical and antisymmetrical parts is used. This leads to a new general analysis of the diffraction patterns of unsymmetrical pupil functions. In the course of the analysis a two-dimensional quadrature function is used. The quadrature function in one dimension is the Hilbert transform.