An Integrated Dimension Theory and Modulation Signal Bispectrum Technique for Analyzing Bearing Fault in Industrial Fibrizer

Salunkhe V.G., Desavale R., Khot S.M., Yelve N.

Abstract Bearing fatigue life is significantly influenced by bearing clearance. Vibration monitoring of bearing clearance deviations can efficiently reveal bearing wear and give sufficient lead time for maintenance. This study investigates the dynamics of roller bearings utilizing the dimension theory with the support vector machine (SVM) technique for diagnosing the bearing clearance faults of revolving machines. The generation of local defects in rotating machines is closely related to the clearance behavior of the rotor-bearing system. A dynamic model of bearing with dimension theory by matrix method with SVM is developed for characteristics of bearing clearance considering the influence of local defects on the inner and outer bearings races. The characteristics of bearing internal radial clearance considering the impact of the defect on the bearing are analyzed. An experimental study has been performed to capture the vibration signature of radial clearance for different speeds and radial loads of the rotor. The rotor-bearing system equations are numerically integrated, and the results are validated with experimental findings. The collective effects among the four parameters (radial load, speed, defect size, radial clearance) are investigated in detail for the rotor-bearing system. The noisy signal is subsequently eliminated using the modulation signal bispectrum (MSB), and the peaks of the MSB results are represented by the bearing clearance indicator. The efficiency and reliability of the stated approach are evaluated using a specialized bearing test and a run-to-failure sugar centrifuge test. The results suggest that the proposed approach can detect a change in bearing clearance up to 40 µm.

Rathore M.S., Harsha S.P.

Abstract In this article, vibration-based fault diagnostics and response classification have been done for defective high-speed cylindrical bearing operating under unbalance rotor conditions. An experimental study has been performed to capture the vibration signature of faulty bearings in the time domain and for different speeds of the unbalanced rotor. Two-dimensional phase trajectories are generated by estimating the time delay and embedding dimension corresponding to vibration signatures. Qualitative analysis involves the implementation of a deep convolutional neural network (DCNN) utilizing the phase portraits as input to classify the nonlinear vibration responses. Comparison with the state-of-art classifiers such as artificial neural network (ANN), deep neural network (DNN), and k-nearest neighbor (KNN) is presented based on classification accuracy values. Thus, the values obtained are 61%, 67%, 72%, and 99% for ANN, DNN, KNN, and DCNN, respectively. Hence, the proposed intelligent classification model accurately identifies the dynamic behavior of bearing under unbalanced rotor conditions.

Dawoud M., Beitler S., Schwarze H.

Abstract The set and roller slip of an NU215 cylindrical roller bearing with medium clearance (MC) and tight clearance (TC) classes have been tested and compared to those of extensive clearance (EC) presented in Parts I and II of this publication. A total of two cages were tested in this part presenting the brass and polyamide single-part cages. The normal TC clearance under the tight fitting of the inner and outer rings resulted in preloading of all the rollers and hence no set slip. Under low oil flowrates, the roller experienced no slip even in the load free zone. For the MC clearance, the polyamide cage showed better behavior (less roller and rolling set slip tendency) than the brass cage contrasting the results obtained earlier under the EC clearance. It is concluded that the polyamide cage deforms under the unsymmetrical loading of the EC clearance resulting in this elevated slip however, under a more even loading in the MC clearance, its lightweight was reflected in a reduced slip behavior.

Yu K., Lin T.R., Ma H., Li H., Zeng J.

Time-frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with signals having a strong nonstationary characteristic or multicomponent signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this paper. It is shown that the energy concentration of the time-frequency representation (TFR) of a strong frequency-modulated signal from a PCT transform can be further enhanced by an SET transform. The technique can also be employed to accurately extract the signal components of a multicomponent nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR, which demonstrates the superiority of the current technique in dealing with nonstationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with nonstationary signals from practical sources.

Wang J., Xu M., Zhang C., Huang B., Gu F.

Accurate diagnosis of incipient faults in wind turbine (WT) assets will provide sufficient lead time to apply an optimal maintenance for the expensive WT assets which often are located in a remote and harsh environment and their maintenance usually needs heavy equipment and highly skilled engineers. This paper presents an online bearing clearance monitoring approach to diagnose the change of bearing clearance, providing an early and interpretable indication of bearing health conditions. A novel dynamic load distribution method is developed to efficiently gain the general characteristics of vibration response of bearings without local defects but with small geometric errors. It shows that the ball pass frequency of outer race (BPFO) is the primary exciting source due to biased load distribution relating to bearing clearance. The geometric errors, including various orders of runouts on different bearing parts, can be the secondary excitation source. Both sources lead to compound modulation responses with very low amplitudes, being more than 20 dB lower than that of a small local defect on raceways and often buried by background noise. Then, Modulation Signal Bispectrum (MSB) is identified to purify the noisy signal and Gini index is introduced to represent the peakness of MSB results, thereby an interpretable indicator bounded between 0 and 1 is established to show bearing clearance status. Datasets from both a dedicated bearing test and a run-to-failure gearbox test are employed to verify the performance and reliability of the proposed approach. Results show that the proposed method is capable to indicate a change of about 20 µm in bearing clearance online, which provides a significantly long lead time compared to the diagnosis method that focuses only on local defects. Therefore, this method provides a big opportunity to implement more cost-effective maintenance works or carry out timely remedial actions to prolong the lifespan of bearings. Obviously, it is applicable to not only WT assets, but also most rotating machines.

Fingerle A., Hochrein J., Otto M., Stahl K.

Abstract Planetary gearboxes are becoming more popular due to their high-power density and potentially high efficiency. When the planet bearings are internally mounted, the body of the planet gear has to be hollow. The demand for large outer diameters due to high-load requirements might result in a small planet rim thickness. Depending on the rim thickness, its rigidity may become very low. Due to the low stiffness and the special load conditions caused by the double meshing, the deformation of the planet and its bearings are unique. In this paper, the influence of rim thickness on bearing load and lifetime is examined. The analysis is performed with a finite element method (FEM) model of a planet rim with a built-in cylindrical roller bearing. With the resulting planet deformation from the FEM calculation, the load distribution on the rolling elements in the bearing and the bearing lifetime according to ISO/TS 16281:2008 has been evaluated.

Guo J., Zhen D., Li H., Shi Z., Gu F., Ball A.D.

To extract impulsive feature from vibration signals with strong background noise and interference components for accurate bearing diagnostics. A multi-stage noise reduction method is proposed based on ensemble empirical mode decomposition (EEMD), wavelet thresholding (WT) and modulation signal bispectrum (MSB). Firstly, noisy vibration signals are applied with EEMD to obtain a list of intrinsic mode functions (IMFs) that leverage the desired modulation components to different degrees. Then, a number of initial IMFs in the high frequency range, which are separated by using the mean of the standardized accumulated modes (MSAM) to have more modulation contents, are further denoised by a wavelet thresholding approach. These cleaned IMFs in the high frequency are combined with the low frequency IMFs to construct a pre-denoised signal that maintains the modulation properties of the raw signal. Finally, modulation signal bispectrum (MSB) is used to extract the modulation signature by suppressing further the residual random noise and deterministic interference components. This multi-stage noise reduction method was validated through a simulation study and two experimental fault cases studies of rolling element bearing. The results were more accurate and reliable in diagnosing the bearing inner and outer race defects in comparison with the individual use of the state-of-the-art EEMD and MSB.

Huang B., Feng G., Tang X., Gu J.X., Xu G., Cattley R., Gu F., Ball A.D.

This paper investigates the performance of the conventional bispectrum (CB) method and its new variant, the modulation signal bispectrum (MSB) method, in analysing the electrical current signals of induction machines for the condition monitoring of rotor systems driven by electrical motors. Current signal models which include the phases of the various electrical and magnetic quantities are explained first to show the theoretical relationships of spectral sidebands and their associated phases due to rotor faults. It then discusses the inefficiency of CB and the proficiency of MSB in characterising the sidebands based on simulated signals. Finally, these two methods are applied to analyse current signals measured from different rotor faults, including broken rotor bar (BRB), downstream gearbox wear progressions and various compressor faults, and the diagnostic results show that the MSB outperforms the CB method significantly in that it provides more accurate and sparse diagnostics, thanks to its unique capability of nonlinear modulation detection and random noise suppression.

Cui L., Huang J., Zhang F., Chu F.

The angle position of the outer ring fault has a significant influence on the residual life and the operation performance of ball bearing. Therefore, the realization of the localization diagnosis of the outer ring fault is of great importance to the bearing performance degradation assessment and the life prediction. In this paper, a novel localization diagnosis method, named horizontal–vertical synchronized root mean square (HVSRMS) localization law and localization formula, is developed to diagnose the angle position of outer ring fault accurately. Firstly, based on the established nonlinear contact model of the bearing system, the detailed change law of static contact force when the angle position of the outer ring fault is on both sides of 270° is studied, which lays a theoretical foundation for the discovery of localization law. Subsequently, the vibration acceleration signal and dynamic contact force of the outer ring fault are synchronously analyzed through theoretical research, and the new feature for localization diagnosis is presented as: the prime impact direction of horizontal vibration acceleration (IPDoHVA). Therefore, the outer ring fault localization law of ball bearing is proposed. On this basis, the HVSRMS localization formula is improved by combining it with the localization law. Thus the one-to-one mapping relationship between HVSRMS and outer ring fault angle position is determined. Finally, experiments are carried out to validate the accuracy and feasibility of the proposed localization law and localization formula. The research results provide a new approach and method for localization diagnosis and the residual life prediction of a defective bearing.

Tian X., Xi Gu J., Rehab I., Abdalla G.M., Gu F., Ball A.D.

Envelope analysis is a widely used method for rolling element bearing fault detection. To obtain high detection accuracy, it is critical to determine an optimal frequency narrowband for the envelope demodulation. However, many of the schemes which are used for the narrowband selection, such as the Kurtogram, can produce poor detection results because they are sensitive to random noise and aperiodic impulses which normally occur in practical applications. To achieve the purposes of denoising and frequency band optimisation, this paper proposes a novel modulation signal bispectrum (MSB) based robust detector for bearing fault detection. Because of its inherent noise suppression capability, the MSB allows effective suppression of both stationary random noise and discrete aperiodic noise. The high magnitude features that result from the use of the MSB also enhance the modulation effects of a bearing fault and can be used to provide optimal frequency bands for fault detection. The Kurtogram is generally accepted as a powerful means of selecting the most appropriate frequency band for envelope analysis, and as such it has been used as the benchmark comparator for performance evaluation in this paper. Both simulated and experimental data analysis results show that the proposed method produces more accurate and robust detection results than Kurtogram based approaches for common bearing faults under a range of representative scenarios.

Wilkes J.C., Wade J., Rimpel A., Moore J., Swanson E., Grieco J., Brady J.

High-speed foil bearings are currently used in increasingly demanding, high performance applications. The application under consideration is a 120 krpm natural gas turboexpander-compressor, which requires 38 mm (1.5 in.) foil journal bearings with high stiffness and load capacity to help enhance rotordynamic stability. This paper describes the development of the foil bearing for this application and includes measured stiffness and damping coefficients recorded on a high-speed dynamic bearing test rig. The dynamic test data were taken for several different foil bearing configurations with varying spring-element foil thicknesses, number of spring-element foils, and bearing shim thickness. All three parameters have a direct impact on bearing clearance. The influence of these different parameters on measured stiffness and damping coefficients and thermal performance of the bearings are presented and discussed.

Miao Y., Zhao M., Lin J.

Yang R., Jin Y., Hou L., Chen Y.

The characteristic defect frequencies are widely used for diagnosing the local defect of the ball bearing. The varying compliance (VC) frequency of a fault-free rotor–bearing system equals to the BPFO (ball bearing outer race defect frequency) due to the internal kinematic relationship of a bearing assembly. In order to indicate this issue, a semi-analytical method—the harmonic balance method with alternating frequency/time domain technique—is exploited to obtain the solutions of rotor–ball bearing systems with /without an outer race defect. The solutions and the features of a rotor–ball bearing system with essentially nonlinear parametric excitation are analyzed. We prove the VC frequency equals the BPFO and explain the reasons that the harmonics of the characteristic defect frequency generally appear in the frequency domain. The VC, BPFO as well as their harmonics affected by the primary and super-harmonic resonance of the system are found out. Finally, a test rig of a rigid rotor–bearing system is established to verify the theoretical analysis qualitatively by presenting the performance of VC, BPFO and their harmonics in the frequency domain. In addition, the tests are accomplished in a cycle of running up and down to reveal the primary and super-harmonic resonance characteristics. On the basis of the theoretical and experimental results, the basic BPFO is not enough to judge an outer race defect. The discussion on frequency spectrum, the primary and super-harmonic resonance provides a more reliable way to elucidate the characteristic defect frequencies.

Smolík L., Hajžman M., Byrtus M.

Turbochargers are modern and very interesting dynamical systems used in various engines in order to increase their power. They are operated at hundreds of thousands revolutions per minute and tend to be fatigue and stability prone. For this reason, a turbocharger rotor has to be designed carefully with respect to its dynamic properties. The following article deals with effects of radial bearing clearances on the dynamical response of the turbocharger rotor. The influence of a bearing clearance on stiffness and damping of a single-film journal bearing is well known and documented. Turbochargers, however, are often supported by floating ring bearings. Such bearings have two bearing clearances—between a journal and a floating ring and between a floating ring and a housing—which are determined by different temperatures of oil films. Turbocharger analysed in the article is modelled by means of flexible multibody dynamics approaches. Bearings’ behaviour is described using Reynolds equation, which is solved numerically. It is shown, but not mathematically proved, how the outer clearance and the ratio between the inner and the outer clearance affect amplitudes of sub-synchronous components in rotor's response.

You K., Noh G., Shin H.

We propose indices that describe the depth of consciousness (DOC) based on electroencephalograms (EEGs) acquired during anesthesia. The spectral Gini index (SpG) is a novel index utilizing the inequality in the powers of the EEG spectral components; a similar index is the binarized spectral Gini index (BSpG), which has low computational complexity. A set of EEG data from 15 subjects was obtained during the induction and recovery periods of general anesthesia with propofol. The efficacy of the indices as indicators of the DOC was demonstrated by examining Spearman’s correlation coefficients between the indices and the effect-site concentration of propofol. A higher correlation was observed for SpG and BSpG (0.633 and 0.770, resp.,p<0.001) compared to the conventional indices. These results show that the proposed indices can achieve a reliable quantification of the DOC with simplified calculations.

Liu W., Xu Z., Wang J., Tian J., Jin D., Gong Y.

Zhu H., Sui Z., Xu J., Lan Y.

Rolling bearings are vital components in rotating machinery, and their reliable operation is crucial for maintaining the stability and efficiency of mechanical systems. However, fault detection in rolling bearings is often hindered by noise interference in complex industrial environments. To overcome this challenge, this paper presents a novel fault diagnosis method for rolling bearings, combining Convolutional Neural Networks (CNNs) and Gated Recurrent Units (GRUs), integrated with the envelope analysis and adaptive mean filtering techniques. Initially, envelope analysis and adaptive mean filtering are applied to suppress random noise in the bearing signals, thereby enhancing the visibility of fault features. Subsequently, a deep learning model that combines a CNN and a GRU is developed: the CNN extracts spatial features, while the GRU captures the temporal dependencies between these features. The integration of the CNN and GRU significantly improves the accuracy and robustness of fault diagnosis. The proposed method is validated using the CWRU dataset, with the experimental results achieving an average accuracy of 99.25%. Additionally, the method is compared to four classical fault diagnosis models, demonstrating superior performance in terms of both diagnostic accuracy and generalization ability. The results, supported by various visualization techniques, show that the proposed approach effectively addresses the challenges of fault detection in rolling bearings under complex industrial conditions.

Mali A., Shinde P.V., Patil A., Salunkhe V.G., Desavale R.G., Jadhav P.S.

Abstract Bearings often experience small and medium raceway damage due to operating and loading conditions, which induces abnormal dynamic behavior. In this study, a dynamic model of the bearing system with various conditions and bearing faults is developed based on experimental investigations, Extreme Machine Learning (EML), and supervised machine learning K-Nearest Neighbors (KNN). The effects of defects on system dynamic response and the damage vibration of the bearing are investigated through simulation. Experiments verify the typical dynamic characteristics. The fundamental bearing characteristics frequencies and statistical features withdrawn from a vibration response are utilized for fault identification using a machine learning algorithm. Bearing characteristics, frequencies, and statistical features were applied to both proposed approaches and compared regarding their prediction quality. The result shows that the EML performs better than the KNN in terms of precision of fault recognition by up to 99%. This work provides valuable insights for operation, maintenance, and early fault warning related to bearings.