Sideband Family Research Articles

Automatic Fault Diagnosis in Wind Turbine Condition Monitoring

Automatic Diagnosis is a novel algorithm developed by Brüel & Kjær Vibro to monitor various failure modes in wind turbines continuously. The algorithm aims at reducing false positives and false negatives, and most importantly, at eliminating the burden of diagnosis by human. Vibration analysis in the order domain using angular resampling helps to deal with speed variation in the vibration signal. The algorithm subsequently identifies prominent peaks in the order powerspectrum, labels these peaks, and then monitor the trends of any families of sidebands and harmonics. In this paper, we compare the results of Automatic Diagnosis with physical inspections using data from wind turbines monitored by Brüel & Kjær Vibro. Results show that Automatic Diagnosis can accurately detect the faults, as confirmed by physical inspections on the turbines. Diagnosing machine condition using high-performance computational infrastructure, instead of using a human, could hugely cut the cost of simultaneously monitoring many wind turbines.

Measurement of Instantaneous Angular Displacement Fluctuation and its applications on gearbox fault detection

Recently, Instantaneous Angular Speed (IAS) measurement is successfully established and prevalently applied to a wide variety of machines due to the hypothesis that the speed fluctuation of rotating machinery carries plentiful dynamic responses. Nevertheless, exploration and application based on angular signal are still insufficient. Under the same hypothesis, in this paper, we introduced an extended algorithm named Instantaneous Angular Phase Demodulation (IAPD), together with the selection of optimal sideband family to extract the Instantaneous Angular Displacement Fluctuation (IADF) signal. In order to evaluate the performance of IADF signal, an effective approach was demonstrated using IADF signal to address the fault detection and diagnosis issue. After extracting the IADF signal, a much effective method was developed to deal with the large amount of data generated during the signal collection process. Then, we used the well-developed techniques, i.e., empirical mode decomposition (EMD) and envelope analysis, to undertake the signal de-noising and feature extraction task. The effectiveness and capability of the IADF signal were evaluated by two kinds of gearboxes under differentconditions in practice. In particular, the prevalent IAS signal and vibration signal were also involved and testified by the proposed procedure. Experimental results demonstrated that by means of the IADF signal, the combination of EMD and envelope analysis not only provided accurate identification results with a higher signal-to-noise ratio, but was also capable of revealing the fault characteristics significantly and effectively. In contrast, although the IAS signal had the potential ability to diagnose the serious fault, it failed for the slight crack case. Moreover, the same procedure even its improvements, i.e., ensemble empirical mode decomposition and local mean decomposition, all failed to recognize the faults in terms of vibration signals.

Dynamic characteristics of rotor system and rub-impact fault feature research based on casing acceleration

Aimed at the vibration of whole aero-engine, a coupled dynamic model of rotor-ball bearing-stator of aero-engine is built. By means of the lumped mass method, taking into account the nonlinear rub-impact, bearing failure force and deformation of the casing, the dynamic equation of the system containing typical rub-impact is derived. The response of the system under different conditions is obtained by using the fourth order Runge-Kutta numerical integration algorithm. By adopting the finite element analysis software ANSYS, the finite element model of the rotor shaft is established and the first six-order natural frequencies of the rotor system are acquired. Taking advantage of the parameters of the signal in time domain and frequency domain, frequency characteristics are extracted as the fault features. The single-point rubbing experiment is carried out in the test rig, and the working speed is higher than the first critical speed, so the rotor shaft is flexible rotor. By the methods of spectrum and cepstrum analysis, the rub-impact characteristics of the casing vibration acceleration time series data are analyzed. The results show that the casing vibration acceleration has obvious impact characteristics; the impact frequency is equal to the product of rotating frequency and number of the blades; the impact frequency component and its multiple-frequencies are demonstrated in the frequency spectrum; the strength of impact is modulated by the rotating frequency, so that there are families of side bands on impact frequency and both sides of frequency doubling, and the interval of sideband equals the rotating frequency. The frequency components of the rotating frequency and its frequency doubling are clearly shown in the cepstrum. By comparing the simulation and experiment, the rubbing characteristics found out in this paper has enough accuracy.

Characteristics analysis of blade-casing rubbing based on casing vibration acceleration

Blade-casing rubbing experiments, which include single-point rubbing and partial rubbing, are carried out on an aero engine rotor experimental rig with casings. Casing vibration acceleration signals are analyzed for extracting the rubbing faults’ characteristics. The results show that under rubbing, casing signals have obvious impact characteristics: impact frequency is the frequency of blades passing the casing, and it equals the product of rotating frequency and the number of blades; the frequency spectrum shows the blade-passage frequency and its multiple-frequencies; impact strength is modulated by the rotating frequency so that there are families of side bands on both sides of the blade-passage frequency and its multiple frequencies, and the side bands’ interval equals the rotating frequency. There are obvious quefrency components of the rotating frequency and its multiple frequencies in the cepstrum, and there is also a distinct rotating frequency and its multiple frequencies in the wavelet envelope spectrum. Finally, the rubbing characteristics determined in this study are verified by using test data from an actual aero engine.

Study on the recognition of aero-engine blade-casing rubbing fault based on the casing vibration acceleration

By mean of the aero-engine rotor experiment rig with casings, the blade-casing rubbing experiments, which include the single-point rubbing and the partial rubbing, are carried out. The casing vibration acceleration signals are analyzed in order to extract the rubbing faults’ characteristics. The results show that: the casing signals under rubbing have obvious impact characteristics; the impact frequency is the frequency of blades passing the casing, and it equals the product of rotating frequency and the number of blades; in the frequency spectrum, there is the blades-passing frequency and its multiple-frequencies; the strength of impact is modulated by rotating frequency, so that there are families of side bands on both sides of the blades-passing frequency and its multiple frequencies, and the side bands’ interval equals the rotating frequency. There are obvious quefrency components of the rotating frequency and its multiple frequencies in the cepstrum. Finally, the rubbing characteristics found out in this paper are verified by using an actual aero-engines’ test data.

Application of power spectrum, cepstrum, higher order spectrum and neural network analyses for induction motor fault diagnosis

The power spectrum is defined as the square of the magnitude of the Fourier transform (FT) of a signal. The advantage of FT analysis is that it allows the decomposition of a signal into individual periodic frequency components and establishes the relative intensity of each component. It is the most commonly used signal processing technique today. If the same principle is applied for the detection of periodicity components in a Fourier spectrum, the process is called the cepstrum analysis. Cepstrum analysis is a very useful tool for detection families of harmonics with uniform spacing or the families of sidebands commonly found in gearbox, bearing and engine vibration fault spectra. Higher order spectra (HOS) (also known as polyspectra) consist of higher order moment of spectra which are able to detect non-linear interactions between frequency components. For HOS, the most commonly used is the bispectrum. The bispectrum is the third-order frequency domain measure, which contains information that standard power spectral analysis techniques cannot provide. It is well known that neural networks can represent complex non-linear relationships, and therefore they are extremely useful for fault identification and classification. This paper presents an application of power spectrum, cepstrum, bispectrum and neural network for fault pattern extraction of induction motors. The potential for using the power spectrum, cepstrum, bispectrum and neural network as a means for differentiating between healthy and faulty induction motor operation is examined. A series of experiments is done and the advantages and disadvantages between them are discussed. It has been found that a combination of power spectrum, cepstrum and bispectrum plus neural network analyses could be a very useful tool for condition monitoring and fault diagnosis of induction motors.

Broadband inversion for MAS NMR with single-sideband-selective adiabatic pulses

We explain how and under which conditions it is possible to obtain an efficient inversion of an entire sideband family of several hundred kHz using low-power, sideband-selective adiabatic pulses, and we illustrate with some experimental results how this framework opens new avenues in solid-state NMR for manipulating spin systems with wide spinning-sideband (SSB) manifolds. This is achieved through the definition of the criteria of phase and amplitude modulation for designing an adiabatic inversion pulse for rotating solids. In turn, this is based on a framework for representing the Hamiltonian of the spin system in an NMR experiment under magic angle spinning (MAS). Following earlier ideas from Caravatti et al. [J. Magn. Reson. 55, 88 (1983)], the so-called "jolting frame" is used, which is the interaction frame of the anisotropic interaction giving rise to the SSB manifold. In the jolting frame, the shift modulation affecting the nuclear spin is removed, while the Hamiltonian corresponding to the RF field is frequency modulated and acquires a spinning-sideband pattern, specific for each crystallite orientation.

On the effects of bearing settings on the dynamic performance of a three-bearing machine tool spindle assembly

An analytical investigation of the response characteristics of a spindle unit supported by three angular contact ball bearings is presented in this paper. A general system of equations is presented utilizing the Hertzian equation for representing the non-linear elastic deformation of the rolling elements. The system of non-linear ordinary differential equations is integrated using the Runge-Kutta Fehlberg technique in Matlab. The model is used to study the effects of bearing settings and preload on the variable-compliance vibrations. The study shows that a three-bearing spindle is characterized by a beat-type mode of response with families of sidebands around the main frequency components. The modulations of the carrier and the spacing of the sidebands are shown to be affected by change in the bearing settings. This type of response is not evident in the conventional two- or four-bearing spindle units.

Time-Reverse ODESSA. A 1D Exchange Experiment for Rotating Solids with Several Groups of Equivalent Nuclei

A one-dimensional exchange experiment is proposed for magic-angle-spinning samples with several groups of equivalent nuclei undergoing internal exchange, such as pure reorientation, as opposed to mutual exchange. The method, which we term time-reverse ODESSA, is an extension of the recently proposed 1D ODESSA experiment for a single group of exchanging nuclei. When several different groups of spins are present, as is usually the case for carbon-13 in polymers and molecular crystals, the normal ODESSA spectrum yields phase-twisted spectra which are difficult to analyze quantitatively. This problem is solved in the time-reverse ODESSA experiment which yields pure absorption spectra for all families of side bands, as long as only internal exchange need be considered. The experiment consists of the usual three pulse sequence of 2D exchange,P1—t1—P2—τm—P3—t2(acquisition), except that the evolution time is fixed at half a rotation period,t1= TR/2, the mixing time is set to an odd number of half rotation periods, τm= (2G− 1)TR/2, and the acquisition starts att2= TR/2 after the detection pulse,P3. The method is demonstrated using the carbon-13 spectra of dimethyl sulfone and an enriched sample of tropolone, and is applied to the study of the π flip of the inner benzene ring of 1,4-diphenoxybenzene. The scope and limitations of the method are discussed.

The necessity for synchronization in DANTE experiments with rotating samples. Reclamation of the asynchronous DANTE pulse train by combination with the TOSS sequence

In recent NMR spectroscopic studies, frequency-selective excitation techniques have become increasingly important. One of their roles is the simplification of spectra by eliminating unwanted resonance lines (1, 2). Another is extracting specific slices of full multidimensional spectra such as two-dimensional exchange/spin diffusion spectra (3), 2D separation spectra (4), and imaging (5). Among such techniques, the DANTE pulse train (6) prevails widely because one can compose the pulse sequence with hard pulses which are more stable in amplitude, and more easily available, than soft pulses, and, moreover, one can readily adjust the effective field strength by altering the pulse spacing. In solid-state NMR, the DANTE pulse train is usually applied to powdered samples under magic-angle spinning (MAS) as well as to single crystals, so that it can operate on specific well-resolved lines ( I). In the MAS experiment, each pulse of the DANTE train should be irradiated synchronously with the spinning period: all the transverse magnetizations due to crystallites are individually modulated by MAS and only become in-phase after every spinning period (7). However, not only is this synchronization difficult in practice but also there are some disadvantages which ensue following a long pulse interval fixed at the spinning period. typically 250400 ps: such a long interval often renders the selective band narrower than the linewidth. Also, the magnetizations decay, in compounds with short T2 values, during the pulse train. Sample heating may occur in the cases where a heteronuclear decoupling field is applied simultaneously. Caravatti et al. ( I ) showed experimentally that synchronization is not necessary for selective saturation with the DANTE-90” pulse train. In addition, Bork and Schaefer (8) recently pointed out that the asynchronous DANTE-180” pulse train inverts an entire spinning sideband family and attempted to explain this observation qualitatively. In fact, we can confirm that the asynchronous DANTE pulse train works properly as long as the spinning frequency, UR, is large compared with chemical-shift anisotropy, AU. Figures 1 a1 c show the ‘%I spectra for polycrystalline glycine observed at vR = 4.0 kHz using the CP (cross-polarization)MAS-DANTE saturation/inversion sequence which consists of the pulse train CP-90”-DANTE-delay-90°-acquisition. ln Figs. 1 a1 C, one can see that the asynchronous pulse train almost completely saturates

Measuring 13C- 13C connectivity in spinning solids by selective excitation

In 1983, Ernst and co-workers (I) used DANTE: pulse trains (2) in CPMAS NMR experiments to irradiate selectively a single spinning sideband, as well as to saturate an entire sideband family (I). They also described the selective inversion of a sideband family by DANTE irradiation which was synchronous with the magic-angle spinning (that is, irradiation sidebands were matched to spinning sidebands). More recently, VanderHart has used DANTE pulse trains in natural-abundance CPMAS 13C NMR experiments on semicrystalline polymers to study crystalline polymorphy by measuring 13C-13C spin exchange (3). These experiments were not complicated by spinning sidebands of significant intensity. In this note, we report how DANTE pulse trains in CPMAS experiments can be used to measure specific 13C-l ‘C connectivity in complex, multiple 13C-labeled solids such as intact bacterial cells, even though the 13C NMR spectra are complicated by sizable spinning sidebands arising both from 13C-l 3C dipolar coupling and from chemical-shift anisotropy. We show that entire spinning sideband families can be inverted by asynchronous DANTE pulse trains whose irradiation sidebands are outside the spectrum of interest. The DANTE pulse trains we use typically consist of 65 0.7 ~LS pulses generated by a 20 kHz RF field. The spacing between pulses is 75 ps. The resulting irradiation sidebands are always outside the carbon spectrum being examined. A 3 ms interval immediately preceding the DANTE pulse train is used to switch the 13C carrier frequency to the selected irradiation frequency, and to permit the decay of residual transverse magnetization arising from pulse imperfections during the 38 kHz matched spin-lock cross-polarization and z-restoration parts of the experiment (Fig. 1). Polarization imbalances created by selective DANTE irradiation are equilibrated during the delay period, T. The CPMAS-delay and CPMAS-DANTE sequences (Fig. 1, top and bottom) differ only in the DANTE pulse train of the latter. The difference of spectra obtained with and without the DANTE pulse train (which we sometimes call the DANTE difference spectrum) therefore reveals directly the selectively irradiated resonance. If this resonance arises from one of the carbons of a covalently bonded pair of 13C-labeled nuclei, the other carbon of the pair can be identified by magnetization transfer during, say, a T = 10 ms period immediately following DANTE irradiation. This time is too short to allow spin diffusion between nonbonded carbons (2). Differences of spectra, obtained

Selective pulse experiments in high-resolution solid state NMR

Applications of selective pulse experiments in high-resolution solid state NMR are explored. It is demonstrated that selective experiments are useful for setting initial conditions for exchange-type experiments and for the simplification of spectra by selective excitation or saturation. A careful analysis of sideband-selective excitation in magic angle spinning experiments is presented. It is demonstrated that excitation of an entire sideband family via a single sideband is not possible. However, saturation of a complete family via selective excitation can be used to simplify overlapping spectra.