Sideband Components Research Articles

A New Criterion for the Quantification of Broken Rotor Bars in Induction Motors

This paper addresses itself to evaluate quantitatively the severity of broken rotor bar (BRB) fault, i.e., the number of BRBs in induction motors. Sideband components are induced in stator current if BRB fault is present and commonly used for diagnosis purposes. Filippetti criterion has been proposed and developed in the literature to quantify the severity of BRB fault by using sideband components, however, with unsatisfactory universality/accuracy. This paper briefly analyzes Filippetti criterion, and mathematically derives a new criterion for the quantification of BRBs, based on the electromagnetic mechanism of sideband components. Comparing to Filippetti criterion, the universality and accuracy of the new criterion are both improved. Moreover, the new criterion includes the influence from the interbar currents associated with BRB fault. The related experiment on a 3-kW, 380-V, 50-Hz induction motor has been conducted, and results show the superiority of the new criterion over Filippetti criterion.

Comparison between vibration and stator current analysis for the detection of bearing faults in asynchronous drives

This study deals with the application of vibration and motor current spectral analysis for the monitoring of rolling bearings damage in asynchronous drives. Vibration measurement is widely used to detect faulty bearings operations. However, this approach is expensive and cannot always be performed, while electrical quantities such as the machine stator current are often already measured for control and detection purposes. Signal processing methods and global indicators associated with bearing fault detection of vibration measurements are recalled. Compared to these methods, an automatic detector based on vibration spectral energy extraction is then proposed and its performances are discussed. Moreover, load torque measurements underlines that bearing faults also induce mechanical load torque oscillations. Therefore a theoretical stator current model in case of load torque oscillations is used to demonstrate the presence of phase modulation (PM) on stator currents. Frequency behaviour of the related sideband components is strongly investigated for monitoring purposes. Thus, a fault detector using the extraction of spectral energy of stator current is proposed to detect damaged bearings. This detector is then compared to the one defined on vibration signals.

Dynamic analysis of mixed eccentricity signatures at various operating points and scrutiny of related indices for induction motors

Load variation along with static and dynamic eccentricities degrees is one of the major factors affecting the dynamic behaviours of eccentricity signatures which is utilised for precise mixed eccentricity fault diagnosis. Without taking the effect of load variation into account properly and just by considering the change in the static and dynamic eccentricity degrees, inaccurate fault detection is acquired. This is of noticeable effects that load variations have on side-band components that are used as fault detection indices. These indices are extracted from the current spectrum of healthy and faulty motor. In this paper, all these factors are dealt in a unified framework by analysing various combinations both theoretically and experimentally. An incisive approach is developed to recognise mixed eccentricity and determine the static and dynamic eccentricities degrees individually at different load levels literally. In order to evaluate the impact of load-dependent indices on eccentricity detection and fault-severity estimation, a systematic relation between each other and eccentricity degree is proposed. Correlation coefficient and mutual information are applied to assess abilities of the obtained indices for eccentricity detection in terms of their relation to static and dynamic eccentricities, their degrees and dependency on the load of motor. The classification results indicate that the elicited indices estimate the eccentricity type and degree exactly. Since, the accuracy of calculated stator current, computed from simulated motor, has considerable effects on precise fault diagnosis, time-stepping finite element method (TSFEM) is employed to model the healthy and faulty induction motor.

Diagnosis and performance analysis of three-phase permanent magnet synchronous motors with static, dynamic and mixed eccentricity

Albeit permanent magnet synchronous motors (PMSMs) under static and dynamic eccentricity have been studied in few papers, so far mixed eccentricity has not been investigated. In this study, a novel index is introduced for dynamic and mixed eccentricity fault diagnosis in PMSM. This index is the amplitude of side-band components with a particular frequency pattern that is extracted from spectrum analysis of the motor torque. The index provides precise detection of the eccentricity occurrence, recognition of its type and determination of its degree. To evaluate the ability of the proposed index for the eccentricity diagnosis and estimation of its severity, first the correlation between indices, static and dynamic eccentricity degrees are calculated. The type of eccentricity is determined using k-nearest neighbour (KNN) classifier. At the next step, a three-layer artificial neural network is employed to estimate the eccentricity degree of torque profiles based on their type of eccentricity. After all, a white Gaussian noise is added to the simulated torque and robustness of the proposed index is analysed with respect to the noise variance. Meanwhile, the spectrum analysis of the stator current in faulty PMSM under static, dynamic and mixed eccentricities is studied and the influence of these eccentricities on ohmic, hysteresis and eddy current losses of PMSM are presented. In this examination, the time-domain elemental flux density waveforms and various time-domain waveforms of motor winding currents are computed using time stepping finite element method (TSFEM) for core loss and ohmic loss calculations punctually. The accuracy of obtained simulation results is verified using experimental results.

Automatic detection and classification of rotor cage faults in squirrel cage induction motor

The detection of broken rotor bars and broken end-ring in three-phase squirrel cage induction motors by means of improved decision structure. The structure consists of current signal analysis (CSA), Artificial Neural Network (ANN) and diagnosis algorithm. Effects of broken bars and end-ring on current signal and feature extraction are in the CSA. The rotor cage faults are classified by using ANN. And result matrixes of ANN are considered two different ways for diagnosis. Then the diagnoses are compared with each other. In this study six different rotor faults, which are one, two, three broken bars, bar with high resistance, broken end-ring and healthy rotor, are investigated. The effects of different rotor faults on current spectrum, in comparison with other fault conditions, are investigated by analyzing side-bands in current spectrum. To reduce bad effects of changing of distance between the side-band and main component on the detection and classification of the faults, the spectrum is achieved with low definition. Thus, the improved decision structure diagnoses faulted rotors with 100% accuracy and classified rotor faults 98.33% accuracy.

Diagnosis of Induction Machines' Rotor Faults in Time-Varying Conditions

Motor current signature analysis is the reference method for the diagnosis of induction machines' rotor faults; however, in time-varying conditions, it fails as slip and speed vary, and, thus, sideband components are spread in a bandwidth that is proportional to the variation. Variable speed drive applications are common in the aerospace, appliance, railway, and automotive industries and also in electric generators for wind turbines. In this paper, a simple and effective method is presented that allows the diagnosis of rotor faults for induction machine drives in time-varying conditions. It is tailored to direct rotor flux field-oriented controlled drives, where the control system provides suitable signals that are exploited for the demodulation to a constant frequency of time-varying signatures related to the rotor faults. Simulations and experiments are reported to validate the proposed method on a critical speed transient.

Static-, Dynamic-, and Mixed-Eccentricity Fault Diagnoses in Permanent-Magnet Synchronous Motors

Mixed-eccentricity (ME) fault diagnosis has not been so far documented for permanent-magnet (PM) synchronous motors (PMSMs). This paper investigates how the static eccentricity (SE), dynamic eccentricity (DE), and ME in three-phase PMSMs can be detected. A novel index for noninvasive diagnosis of these eccentricities is introduced for a faulty PMSM. The nominated index is the amplitude of sideband components with a particular frequency pattern which is extracted from the spectrum of stator current. Using this index makes it possible to determine the occurrence, as well as the type and percentage, of eccentricity precisely. Meanwhile, the current spectrum of the faulty PMSM during a large span is inspected, and the ability of the proposed index is exhibited to detect eccentricity in faulty PMSMs with different loads. A novel theoretical scrutiny based on a magnetic field analysis is presented to prove the introduced index and generalize the illustrated fault recognition method. To show the merit of this index in the eccentricity detection and estimation of its severity, first, the correlation between the index and the SE and DE degrees is determined. Then, the type of the eccentricity is determined by a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbor classifier. At the next step, a three-layer artificial neural network is employed to estimate the eccentricity degree and its type. After all, a white Gaussian noise is added to the simulated current, and the robustness of the proposed index is analyzed with respect to the noise variance. In this paper, the PMSM under magnetic fault (demagnetization) and electrical faults (short and open circuits) is modeled, and the current spectrum of the faulty PMSM under demagnetization, short circuit, and open circuit faults is analyzed. It is demonstrated that the proposed index, due to eccentricity fault, is not generated in the current spectrum due to magnetic and electrical faults. Indeed, it is exposed that the introduced index is only created due to eccentricity fault and it is not sensitive to other faults. To model the PMSM eccentricities, a time-stepping finite-element method, which takes into account all geometrical and physical characteristics of the machine components, nonuniform permeance of the air gap, and nonuniform characteristics of the PM material, is employed. This model facilitates the access to the demanded signals in order to have accurate processing. A comparison of simulation and experimental results validate the proposed index.

Scattering characteristics of non-linear loaded two-sided corner reflector

Method of integral equations of sideband component of surface currents and physical optics method can be used for calculation of non-linear corner reflector. Efficient equivalent areas of backward scattering at frequencies of incident field and sideband frequencies are calculated.

Effect of Magnetic Saturation on Static and Mixed Eccentricity Fault Diagnosis in Induction Motor

We have investigated the effect of magnetic saturation of core materials on the diagnosis of static and mixed-eccentricity faults in induction motors. We modeled the faults by using a modified winding function (MWF) and time-stepping finite-element (TSFE) methods to compute the stator currents of both healthy and faulty motors for processing. We then analyzed the stator signal spectra of the motors by the MWF and TSFE methods and estimated the amplitudes of sideband components attributable to the faults. The results obtained by TSFE agreed well with experimental measurements. However, there was considerable discrepancy between the MWF results and the experimental measurements. We investigated the reason for the discrepancy by analyzing the air gap magnetic field distribution in both healthy and faulty induction motors in order to determine their linear and actual magnetization characteristics. We found that, in a faulty motor, for fixed permeability, the analytic method yields a much larger magnetic flux amplitude than is actually the case. At the same time, the distribution of magnetic flux in the air gap is more asymmetric than the actual case. Here, we present our experimental results and those obtained with the MWF method, using the finite-element analysis package Opera2d 10.5, for two three-phase, four-pole, 60-Hz, 3-hp motors having 36 stator slots and 44 and 28 rotor slots, respectively.

Diagnosis of rotor asymmetries in induction motors based on the transient extraction of fault components using filtering techniques

The aim of this paper is to present and validate a methodology for diagnosing rotor asymmetries in cage motors, based on the analysis of the stator startup current. The method consists of the extraction of a harmonic component introduced by this fault – the left sideband component – from the stator startup current. Two alternative techniques developed by different research groups are proposed for the transient extraction of this component; the digital low-pass filtering (DLPF) and the discrete wavelet transform (DWT). Both approaches are applied to three different industrial motors ranging from 1.1 to 450 kW. A detailed explanation of the physical basis of the method and comments related to the application scope of the approach are also given. The results show the robustness of both approaches for the reliable diagnosis of the fault and suggest a clear potentiality for extending the methodology to the detection of other types of faults introducing components dependant on the slip.

A New Pattern for Detecting Broken Rotor Bars in Induction Motors During Start-Up

This paper introduces a novel frequency pattern for diagnosis of broken rotor bars in induction motors during the start-up period. This is important in the case of start-up of large induction motors with long starting time and also motors with frequent start-up. The amplitude of the side-band components of the introduced frequency pattern is a suitable index for diagnosing the broken bars and determining the number of faulty bars precisely during start-up. The paper investigates the performance of a faulty motor. Because the number of broken rotor bars and the load are two major parameters affecting the performance of a faulty motor, the frequency spectrum of torque and speed in a motor with different numbers of broken rotor bars and different loads is analyzed. The time-stepping finite-element method (TSFEM) is used to model the motor. This model takes into account the spatial distribution of the stator windings, nonuniform magnetic permeance of the air gap, nonlinear characteristic of the cores, and continuous rotation of the rotor. The paper compares simulation results in steady-state mode with experimental results and shows that the results agree well.

Development of a signal-extraction scheme for resonant sideband extraction

As a future plan, an advanced gravitational-wave detector will employ an optical configuration of resonant sideband extraction (RSE), achieved with an additional mirror at the signal-detection port of the power-recycled Fabry–Perot Michelson interferometer. To control the complex coupled cavity system, one of the most important design issues is how to extract the longitudinal control signals of the cavities. We have developed a new signal-extraction scheme which provides an appropriate sensing matrix. The new method uses two sets of sidebands: one of the sideband components satisfies the critical coupling condition for the RSE interferometer and reaches the signal-extraction port, and the other sideband is completely reflected by the Michelson interferometer. They provide a diagonalized sensing matrix and enable the RSE control to be robust.

Trichromatic Manipulation of Kerr Nonlinearity in a Three-Level A Atomic System

Trichromatic manipulation of Kerr nonlinearity in a three-level A atomic configuration is investigated theoretically. It is shown that for a weak monochromatic probe Held, the enhanced Kerr nonlinearity can be achieved in multiple separate transparent windows due to interference effect of multiple two-photon Raman channels. Furthermore, the property of Kerr nonlinearity can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump Geld compared to the central component.

Broken rotor bars detection by a new non-invasive diagnostic procedure

A new technique of diagnosing data for broken rotor bars in induction motors derived from two of the three stator currents, the Beirut diagnostic procedure (BDP) is presented in this paper. The theoretical principles directly related to the application of this diagnostic technique are described, emphasizing the use of a severity factor in order to evaluate the extension of the fault. Defining the severity factor as the normalized amplitude of the fault characteristic frequency enables us to draw up a table of comparison of several usual electric diagnostic methods. Besides the traditional one-phase current spectrum analysis, values of the severity factor related to electrical signals like the instantaneous powers, the current space vector modulus and finally related to the new Beirut diagnostic method are analyzed with respect to the variation of the power factor angle and of the sum of the two current side-band angular displacement. The BDP offers several advantages over the usual motor current signature analyses (MCSA) methods: it is shown how the proposed severity factor applied to the new diagnostic technique is not dependent on motor parameters such as the power factor angle and the fault type which is not the case of the instantaneous powers. In addition, the BDP has the advantage of detecting easily fault characteristic frequencies, which is not possible via diagnostic methods that use the detection of two side-band components as in the simple current spectrum. By theoretical analysis, computer simulations, and laboratory experiments, it is shown that the new method enhances the reliability of diagnostics of broken rotor bars in induction motor.

Trichromatic phase dependence of squeezing in resonance fluorescence

We investigate the quantum noise in phase quadratures of resonance fluorescence from a two-level atom driven by a trichromatic exciting field. It is shown that the noise spectra are crucially dependent on the sum of relative phases of the sideband components compared to the central component although the sideband exciting components are much weaker than the central component. When we tune the exciting sidebands on two-photon resonance with the Mollow sideband transitions and set the phase sum to , sideband squeezing in the in-phase quadrature remains almost the same as in the monochromatic case. Once the phase sum is set to zero, the squeezing is destroyed. The responsible mechanism is explained in terms of two-photon emission processes induced by the trichromatic components and the interference between these processes. DOI: 10.1103/PhysRevA.77.063809

Single-to-dual channel NRZ-to-RZ format conversion by four-wave mixing in single semiconductor optical amplifier

All-optical single-to-dual channel format conversion from non-return- to-zero (NRZ) to return-to-zero (RZ) using four-wave mixing (FWM) in a single semiconductor optical amplifier (SOA) is demonstrated. The original NRZ format is converted to RZ format by injecting a synchronised clock signal into the SOA. The FWM effect generates two sideband components, which contain the same data stream as the original NRZ signal with RZ format. The format conversion is successfully implemented both at 20 and at 40 Gbit/s, and all converted RZ signals have a Q-factor larger than 6.

Sideband manipulation of population inversion in a three-level Λ atomic system

Sideband manipulation of population inversion in a three-level A atomic configuration is investigated theoretically. Compared with the case of a nearly monochromatic field, a population inversion between an excited state and a ground state has been found in a wide sideband intensity range by increasing the difference in frequency between three components. Furthermore, the population inversion can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field with respective to the phase of the central component. Changing the sum phase from 0 to π, the population inversion between the excited state and the ground state can increase within nearly half of the sideband intensity range. At the same time, the sideband intensity range that corresponds to the system exhibiting inversion ρ00 > ρ11 also becomes wider evidently.

Reciprocating Optical Modulation on Erbium-Doped LiNbO$_{3}$ for Harmonic Generation

We demonstrated reciprocating optical modulation using erbium-doped LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> crystal for high-order sideband generation and selective amplification. A Ti-diffused waveguide, formed on the crystal, had a gain of 2.1 dB/cm for 1531.4-nm signal light pumped at 1480 nm with a pump power of 200 mW/port. A sideband component of 40 GHz was successfully enhanced and a gain of 12 dB was realized.

A Generic High-Frequency Model for the Nonlinearities in Buck Converters

To investigate the high-frequency behaviors for the switching converters, the modeling and analysis should include the influences from the sideband components, which are generated by the converter's nonlinearities. With a buck converter, two non- linearities are identified in this paper: the pulse-width modulator and the switches. Based on the harmonic-balance approach, the multifrequency model is proposed to address these nonlinearities and to predict the high-frequency performances. With the derived model, different modulation schemes are compared based on their influence on the sideband effect and the control bandwidth limitations. The possible benefit from the double-edge modulation and its limitations are clarified. In addition, the audio-susceptibility is studied considering the nonlinearity of the switches. With the combination of the two nonlinearities, a generic high-frequency model is achieved. Simulation and experimental results are presented to verify the achievements of the proposed models.

Gyrokinetic simulation of zonal flows and ion temperature gradient turbulence in helical systems

The gyrokinetic-Vlasov simulation code (GKV code) is applied to zonal flows and the ion temperature gradient (ITG) turbulence in helical systems with L = 2 and M = 10 like the Large Helical Device (where L and M denote poloidal and toroidal periodicities of the main helical component of the confinement field, respectively) for the standard and inward-shifted model configurations. Because of the slower radial drift motion of helical-ripple-trapped particles, the inward-shifted case provides a higher zonal-flow response than that in the standard model with smaller side-band helical field components. The nonlinear GKV simulations show that the ITG turbulent transport in the inward-shifted model, which has larger growth rates of the ITG stability, is regulated by the zonal flows to a level comparable to the standard case.