Resonant Frequency Band Research Articles

Dual-Guidance-Based Optimal Resonant Frequency Band Selection and Multiple Ridge Path Identification for Bearing Fault Diagnosis Under Time-Varying Speeds

To perform bearing fault diagnosis under variable speeds, the optimal resonant frequency (ORF) band selection and diagnosis strategy are pivotal. Indexes, such as kurtosis, crest factor (CF) and smoothness index (SI), are extensively used for guiding ORF selection. Due to that each index has unique advantages, the hybrid of such indexes has been developed. However, applications of the current index hybrid method are impeded by problems of: 1) ineffectiveness for signal corrupted by impulsive noises and 2) equal segmentation of frequency band with human intervention. This paper, therefore, firstly proposes a dual-guidance based scheme with an embedded tunable Q-factor wavelet transform (TQWT) to address the problems. The so-called dual-guidance scheme contains two guidance procedures: 1) the SI guided pre-process for obtaining weight vectors and 2) the index hybrid output guided scheme for ORF selection. The embedded TQWT is used for frequency band segmentation and sub-band signal acquisition without subjective interventions. With the proposed scheme, the ORF band can be determined for bearing fault feature extraction. Then, an algorithm for multiple instantaneous frequency (IF) ridge identification is exploited based on the peak search algorithm for diagnosis. To tackle the difficulty that, at each time instance, the amplitudes of IF ridges of interest do not always dominate the time frequency representation (TFR), a starting point search tactic with a synchronization step is explored. A diagnosis vector can subsequently be obtained by calculating the average ratios of the identified ridges and bearing fault diagnosis can then be done by matching the elements of the diagnosis vector with fault characteristic coefficient (FCC). Comparisons are performed to illustrate the superiority of the proposed method. The experimental analyses are also conducted to validate the proposed method for bearing fault diagnosis under variable speeds.

Rolling Element Bearings Fault Diagnosis Based on a Novel Optimal Frequency Band Selection Scheme

The squared envelope spectrum (SES) is one of the most effective methods in rolling element bearing fault diagnosis. Being a technique based on demodulation, the success of SES depends highly on the extraction of information caused by the bearings fault. Therefore, a preprocessing step of choosing an optimal frequency band (OFB), before the implementation of the SES, is absolutely needed and should always be taken prior. Fast kurtogram (FK), as the most commonly used method targeting resonance frequency band which is excited by the bearing fault, is applied as the benchmark tool for the selection of the OFB. However, recent theoretical works show that the kurtosis used as the criterion for OFB selection was both sensitive to the impulsiveness and cyclostationarity, which means irrelevant impulsive and cyclostationary components are able to mislead the kurtosis based OFB selection techniques and subsequently bring great difficulties in bearing fault diagnosis. To tackle this problem, in this paper, a novel statistical model parameter-based method, called Distcsgram, is proposed as a substitution to the traditional FK technique so that an OFB can be selected with the least influences from the irrelevant cyclostationary and impulsive interferences. Together with the SES, the Distcsgram is explained and validated in both simulation and experimental studies. Furthermore, through the comparisons with the traditional methods, the superiority of the proposed method over those traditional methods for the diagnosis of rolling element bearing is proved.

Extremely Large Oscillations of Cantilevers Subject to Motion Constraints

The nonlinear extremely large-amplitude oscillation of a cantilever subject to motion constraints is examined for the first time. In order to be able to model the large-amplitude oscillations accurately, the equation governing the cantilever centerline rotation is derived. This allows for analyzing motions of very large amplitude even when tip angle is larger than π/2. The Euler–Bernoulli beam theory is employed along with the centerline inextensibility assumption, which results in nonlinear inertial terms in the equation of motion. The motion constraint is modeled as a spring with a large stiffness coefficient. The presence of a gap between the motion constraint and the cantilever causes major difficulties in modeling and numerical simulations, and results in a nonsmooth resonance response. The final form of the equation of motion is discretized via the Galerkin technique, while keeping the trigonometric functions intact to ensure accurate results even at large-amplitude oscillations. Numerical simulations are conducted via a continuation technique, examining the effect of various system parameters. It is shown that the presence of the motion constraints widens the resonance frequency band effectively which is particularly important for energy harvesting applications.

Probabilistic Harmonic Resonance Assessment Considering Power System Uncertainties

The presence of power system uncertainties results in variations of the harmonic resonance behaviors. There is, therefore, a need to perform the probabilistic assessment in harmonic resonance study. In this paper, a systematic methodology for probabilistic harmonic resonance assessment considering power system uncertainties is presented. First, potential system uncertainties are analyzed and modeled. The stochastic behavior of harmonic resonance due to system uncertainties is then studied using both Monte Carlo approach and harmonic resonance mode analysis technique. A modified power iteration method is further used to efficiently reduce the calculation time. Three indices, including probabilistic expressions of 1) resonance frequency band, 2) modal impedances in the resonance band, and 3) sensitivity information at the bus-level and the element-level are used to represent the stochastic behaviors of harmonic resonance. In addition, the resonance mitigation scheme based on probabilistic resonance frequency band shift technique is described. The effectiveness of the proposed method is demonstrated through case studies in an uncertain power system. Its potential applications are also discussed.

Novel D SRR‐based dual band antenna for WiMAX/C applications

AbstractA novel miniaturized D shape split ring resonator (SRR) antenna is proposed for dual band (3.6 GHz and 4.7 GHz) applications. This proposed antenna structure has dimensions of 18 × 20 × 0.8 mm3 which is built on FR4 dielectric constant ( ε r=4.4). This antenna consists of top and bottom side dual SRR creating dual band resonant frequency which is excited from microstrip line as monopole and slotted partial ground plane for better impedance matching. The microstrip line (monopole) is creating a resonance frequency at 4.7 GHz and the SRR is responsible for creating resonance frequency at the frequency of 3.6 GHz. The parametric study of microstrip line and the position of SRR has been analyzed. The D shape SRR in the monopole is generating another resonating frequency at 3.6 GHz. The metamaterial property of proposed D shape SRR is also verified to validate the resonance frequency. The antenna radiation measurement is carried out in Antenna Research Centre (ARC) FKE, Universiti Teknologi MARA, Malaysia. Both simulated and measured results agreed well. Measured gain achieved with this dual band antenna is around 2‐3 dB.

Vibration reduction performance parameters matching for adaptive tunable vibration absorber

Based on the principle of vibration absorber, an adaptive tunable vibration absorber with the magnetorheological elastomer as the core intelligent component was designed to eliminate variable frequency vibration of the powertrain system. The simulation of the magnetic circuit of the adaptive tunable vibration absorber was carried out to ensure the magnetic field generated by the design with a closed magnetic circuit could meet the requirement. The transient dynamic simulation analysis of the adaptive tunable vibration absorber shows that the natural frequency of the vibration absorber could well follow the external excitation signal. The natural vibration sensitivity analysis of the 4-degree-of-freedom dynamic system of the powertrain system was performed to obtain the key moment of inertia that affects the natural frequencies of each stage and then the installation position of the adaptive tunable vibration absorber corresponding to external excitation near the resonant frequency band could be determined. Subsequently, taking the third natural vibration as an example, an adaptive tunable vibration absorber with corresponding variable-stiffness range was installed on the key moment of inertia affecting the vibration of this order. The transient changes of each natural vibration frequency of the powertrain system with the adaptive tunable vibration absorber were studied and then the best starting and stopping frequencies were determined. According to the optimal frequency tuning scheme, the variation range of the storage modulus required for the magnetorheological elastomer material in the limited magnetic field range was obtained. The relationship between the controllable current and the torsional stiffness of the vibration absorber is established. Aiming at the vibration problem near the third-order natural vibration, the best vibration reduction performance parameters were matched to the adaptive tunable vibration absorber. Finally, a time-frequency analysis was applied to the powertrain system with adaptive tunable vibration absorber, and the result shows that the best performance parameter matching for the adaptive tunable vibration absorber could effectively improve its vibration reduction performance.

Numerical Simulation and Vibration Analysis of Dynamically Loaded Bearing with Defect on Rolling Element

The external loading on a rolling element bearing is often not of pure static nature but has a dynamic component associated with it. In the present study, the analysis of vibration response of rolling element bearing with localized defect on its rolling element subjected to external dynamic loading has been carried out. The dynamic component of external loading considered is either harmonic or random in nature. The defect-induced vibration signals have been processed with the FFT of their enveloped signal obtained from the Hilbert transform of band-passed signal around the resonant frequency band. Numerical results have been obtained for the NJ 204 bearing for different amplitude contributions of dynamic components of external load. For harmonic loading, the vibration spectra show additional spectral components through loading frequency as sidebands about each significant spectral components result due to static load. The experimental investigation confirms the presence of these additional components in the spectra. In the case of random loading, the noise level tends to rise with an increase in the value of standard deviation. The rise in noise level becomes so significant that some spectral components are masked by the noise for higher values of standard deviation.

An advanced beamforming approach based on two-channel echo-train system to cancel interference within an NQR signal resonance spectrum

Abstract Interference can be a huge challenge for Nuclear Quadrupole Resonance (NQR) signal detection in real life settings. The problem is particularly challenging when interference is strong around the resonant frequency band of the targeted NQR signal (to which we refer as the NQR band). This paper first proves the beamforming characteristics of a designed two-channel echo-train (TE) data acquisition system, and then presents a novel beamforming approach which is based on the TE system and is able to cancel interference effectively within the NQR band. After interference cancellation, NQR signal detection can be done successfully by applying an ”echo train” approximate maximum likelihood (ETAML) algorithm to the residual data. The proposed algorithm is shown to be superior to previously proposed algorithms, including the classical beamforming algorithms/detectors constructed on the TE system, for detecting NQR signal polluted by interference.

A classical analogy for quantum band formation

Electrons in an atom are confined to distinct, quantized energy levels. When atoms form solids, the interaction of the electrons causes their energy levels to split into multiple closely spaced levels, or bands, separated by forbidden regions called band gaps. Each band contains a number of energy levels equal to the number of atoms in the solid. This model of the origin of band structure can be reproduced by using a classical array of harmonic oscillators (masses connected by springs). In this system, each oscillator plays the role of an atom and its resonant frequencies play the roles of electronic energy levels. When coupled, a system of oscillators yields a spectrum of resonant frequencies and when the number of oscillators becomes sufficiently large, the system exhibits the formation of “resonant frequency bands,” similar in structure to the energy bands of an atomic solid. We experimentally demonstrate band formation using coupled harmonic oscillators and highlight the effects of both number of oscillators and coupling strength on the band structure. Additionally, we show that experimental results of this band formation follow a theoretical analysis of the system.

Meshing frequency modulation (MFM) index-based kurtogram for planet bearing fault detection

Identifying the bearing fault-induced impulsive components in the frequency domain is a key step in the corresponding fault detection. However, gearbox vibration signals often significant interrupt the rolling bearing fault diagnosis, particularly in the detection of planet bearing faults under the background noise of the planetary gearbox. Except in the case of a high amplitude, a gear meshing-related vibration may also affect the identification of the planet bearing fault-induced resonance frequency band. To solve this problem, a meshing frequency modulation index (indexMFM)-based kurtogram utilizing a particular gearbox related phenomenon is proposed. The underlying mechanism is such that although the gear meshing-related spectral components are always more prominent in relatively higher-frequency band than the planet bearing-induced resonance frequency band in impulsiveness, the gear meshing-related impulsive components modulate the gear meshing frequency, yet the faulty bearing-induced one does not. Exploiting this difference, the planet bearing fault-induced impulsive components can be directly identified from the strong gear vibration interruption by determining the bearing fault-related resonance frequency band in the indexMFM-based kurtogram. The effectiveness of the proposed method is separately verified using simulated and experimental data.

Characteristics of the Magnetic Resonance WPT System Applying a Frequency Converter

Recently, studies on the commercialization of magnetic resonance wireless power transfer (WPT) systems are underway domestically and internationally. The magnetic resonance WPT technology enables power transmission between transmitter and receiver coils with the same resonance frequency. If the resonance frequencies of the transmitter coil and receiver coil are different, the efficiency of the WPT will rapidly decrease. Various organizations, such as A4WP, have been striving to standardize resonance frequencies, but the countries around the world are sticking to their own distinctive standards based on the frequency bands available in their territories. Therefore, each country uses a slightly different resonance frequency band. In this paper, a frequency converter that enables WPT when the transmitter and receiver coils have different resonance frequencies is proposed. The frequency converter consists of two coils, and its structure is very simple. The two coils transmit power using the magnetic induction method, and frequency variation is possible using variable capacitors. It was confirmed from the experiment that WPT is possible even if the resonance frequencies of the transmitter and receiver coils are different.

Stimulated Motion Suppression (STMS): a New Approach to Break the Resolution Barrier for Ion Trap Mass Spectrometry.

Ion trap is an excellent platform to perform tandem mass spectrometry (MS/MS), but has an intrinsic drawback in resolving power. Using ion resonant ejection as an example, the resolution degradation can be largely attributed to the broadening of the resonant frequency band (RFB) between ion motion and driving alternative-current (AC). To solve this problem, stimulated motion suppression (STMS) was developed. The key idea of STMS is the use of two suppression alternative-current (SAC) signals, which both have reversed initial phases to the main AC. The SACs can block the unexpected sideband ion resonances (or ejections), therefore playing a key role in sharpening the RFB. The proof-of-concept has been demonstrated through ion trajectory simulations and validated experimentally. STMS provides a new and versatile means for the improvement of the ion trap resolution, which for a long time has reached the bottleneck through conventional methods, e.g., increasing the radio-frequency (RF) voltage and decreasing the mass scan rate. At the end, it is worth noting that the idea of STMS is very general and principally can be applied in any RF device for the purposes of high-resolution mass analysis and ion isolation. Graphical Abstract ᅟ.

Teager Energy Entropy Ratio of Wavelet Packet Transform and Its Application in Bearing Fault Diagnosis.

Kurtogram can adaptively select the resonant frequency band, and then the characteristic fault frequency can be obtained by analyzing the selected band. However, the kurtogram is easily affected by random impulses and noise. In recent years, improvements to kurtogram have been concentrated on two aspects: (a) the decomposition method of the frequency band; and (b) the selection index of the optimal frequency band. In this article, a new method called Teager Energy Entropy Ratio Gram (TEERgram) is proposed. The TEER algorithm takes the wavelet packet transform (WPT) as the signal frequency band decomposition method, which can adaptively segment the frequency band and control the noise. At the same time, Teager Energy Entropy Ratio (TEER) is proposed as a computing index for wavelet packet subbands. WPT has better decomposition properties than traditional finite impulse response (FIR) filtering and Fourier decomposition in the kurtogram algorithm. At the same time, TEER has better performance than the envelope spectrum or even the square envelope spectrum. Therefore, the TEERgram method can accurately identify the resonant frequency band under strong background noise. The effectiveness of the proposed method is verified by simulation and experimental analysis.

Influence of nonlinear subunits on the resonance frequency band gaps of acoustic metamaterial

Recently, a significant attention has been directed toward so called ‘acoustic metamaterials’ which have large similarity with already-known ‘electromagnetic metamaterials’ which are applied for elimination of the electromagnetic waves. The stop of electromagnetic waves is realized with the negative refractive index, negative permittivity and negative permeability. Motivated by the mathematical analogy between acoustic and electromagnetic waves, the acoustic metamaterials are introduced. It was asked the material to have negative effective mass. To obtain the negative effective mass, the artificial material, usually composite, has to be designed. The basic unit is a vibration absorber which consists of a lumped mass attached with a spring to the basic mechanical system. The purpose of the unit is to give a band gap where some frequencies of acoustic wave are stopped. We investigated the nonlinear mass-in-mass unit excited with any periodic force. Mathematical model of the motion is a system of two coupled strongly nonlinear and nonhomogeneous second-order differential equations. The solution of equations is assumed in the form of the Ateb (inverse beta) periodic function. The frequency of vibration is obtained as the function of the parameters of the excitation force. The effective mass of the system is also determined. Regions of negative effective mass are calculated. For these values the motion of the forced mass stops. It is concluded that the stop frequency gaps are much wider for the nonlinear than for the linear system. Based on the obtained parameter values, the acoustic metamaterial could be designed.

Shannon Entropy of Binary Wavelet Packet Subbands and Its Application in Bearing Fault Extraction.

The fast spectrum kurtosis (FSK) algorithm can adaptively identify and select the resonant frequency band and extract the fault feature via the envelope demodulation method. However, the FSK method has some limitations due to its susceptibility to noise and random knocks. To overcome this shortage, a new method is proposed in this paper. Firstly, we use the binary wavelet packet transform (BWPT) instead of the finite impulse response (FIR) filter bank as the frequency band segmentation method. Following this, the Shannon entropy of each frequency band is calculated. The appropriate center frequency and bandwidth are chosen for filtering by using the inverse of the Shannon entropy as the index. Finally, the envelope spectrum of the filtered signal is analyzed and the faulty feature information is obtained from the envelope spectrum. Through simulation and experimental verification, we found that Shannon entropy is—to some extent—better than kurtosis as a frequency-selective index, and that the Shannon entropy of the binary wavelet packet transform method is more accurate for fault feature extraction.

Left‐handed meta‐surface loaded with ring resonator modelling for satellite application

SummaryA new geometry of compact meta‐surface, loaded with the ring resonator for satellite application (Ku‐band), is presented in this paper. The diamond‐shaped meta‐surface is designed by the metallic ring resonator with metallic ground plane separated by a dielectric substrate layer, while epoxy resin fibre is utilized as a dielectric substrate layer. The proposed meta‐surface structure is successfully simulated, fabricated, and measured. Effects of the design specifications on the surface current and field distribution are also investigated elaborately. Theoretical and simulated results show that the diamond‐shape structure resonance is at 15.84 GHz, whereas the measured results are slightly shifted around at 15.87 GHz. The designed meta‐surface structure also exhibits the left‐handed characteristics at 15.88 GHz, where the estimations of permittivity is −4 + 0.28j, permeability is −19.2 − 134.6j, and negative index is −5.51 − 3.86j. Further, the lumped element equivalent circuit model of the proposed meta‐surface unit cell is explained. Moreover, the 10 × 10 mm2 meta‐surface single‐unit‐cell prototype is compact in size and the impact on the performance by modifying the meta‐surface structure is investigated. Therefore, the meta‐surface integrated antenna shows resonance frequency bands from 14.0 to 14.50 GHz, which is used as INSAT‐4A communication satellite uplink frequency.

A novel energy harvesting device for ultralow frequency excitation

In recent decades, energy harvesting from external vibration with ultralow frequency has been investigated intensively. A novel energy harvesting device with adjustable nonlinearity for ultralow frequency excitation is proposed and analyzed in this study. The energy harvesting device is made of a mass attached to the base by Elastic Steel Slices (ESSs) and a pair of Quadrilateral-Linkage Structures (QLSs). With the mathematical model, theoretical studies are carried out. The analysis shows that the device is capable for ultralow-frequency vibration energy harvesting since it has adjustable resonance frequency band. With the appearance of the adjustable nonlinearity, the system has a wide band for resonance by the utilization of multi-steady states. Experimental prototypes are assembled and tested. The experimental results show that the beginning frequency of effective energy harvesting can be reduced by over 50% by assembling the QLSs to adjust the stiffness property of the system. In addition, although the stiffness of the device is expressed by nonlinear irrational function, we find that the output voltages generated are large, smooth and stable. The results of this study illustrate that the proposed device is a feasible design for collecting energy from ultralow frequency excitation.

Vicsek fractal slot substrate integrated waveguide leaky wave antenna for X-band application

A substrate integrated waveguide based leaky wave antenna with Vicsek-cross fractal shaped slot is proposed. Vicsek cross fractal is used here to obtain wide band and compact structure for wideband applications in X-band. The proposed design achieves a wide impedance bandwidth of 1.98 GHz ranging from 8.96 to 10.94 GHz. A near identical pattern bandwidth with peak realized gain of 8.41dBi is achieved over the resonance frequency band of the proposed antenna. A prototype in X-band of the proposed design is examined and measured for verification.

Performance Improvement for Reduction of Resonance in a Grid-Connected Inverter System Using an Improved DPWM Method

This paper proposes discontinuous pulse width modulation (DPWM) for a grid-connected inverter system using an LCL-filter which consists of two inductors and a capacitor that is connected in parallel per phase. The modulation signal is discontinuously changed, and the harmonic voltages are generated in the wide frequency range at the output terminal of the inverter when the conventional DPWM is used. If these harmonic voltages are present in the resonance frequency band by an LCL-filter, then the resonance problem of the grid current occurs. To suppress the resonance problem, the proposed DPWM injects the sixth harmonic to the modulation signal. Therefore, in the improved DPWM, harmonic voltages at the output terminal of the inverter are sufficiently reduced because the discontinuous change of the modulation signal disappears. The proposed DPWM method is verified by a Powersim (PSIM) simulation (Powersim Inc., Rockville, MD, USA) and experiments with a 3-kW neutral-point clamped (NPC)-type grid-connected inverter system.

Compound Fault Diagnosis of Bearings Using an Improved Spectral Kurtosis by MCDK

The fast spectrum kurtosis (FSK) algorithm can adaptively identify and select the resonant frequency band and extract the fault feature by the envelope demodulation method. However, in practical applications, the fault source may be located in different resonant frequency bands; plus in noise interference, the weak side of the compound fault is not easy to be identified by the FSK. In order to improve the accuracy of fast spectral kurtosis analysis method, a modified method based on maximum correlation kurtosis deconvolution (MCKD) is proposed. According to the possible fault characteristic frequencies, the period of MCKD is calculated, and the appropriate filter length is selected to filter the original compound fault signal. In this way, the compound fault located in different resonance bands is separated. Then, the signal after MCKD filtering is analyzed by FSK. Through the simulation and experimental analysis, the MCKD can separate the compound fault information in different frequency band and eliminate the noise interference; the FSK can accurately identify the resonance frequency and identify the weak fault characteristics of compound fault.