Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

Fractional Envelope Analysis for Rolling Element Bearing Weak Fault Feature Extraction

The bearing weak fault feature extraction is crucial to mechanical fault diagnosis and machine condition monitoring.Envelope analysis based on Hilbert transform has been widely used in bearing fault feature extraction. A generalization of the Hilbert transform, the fractional Hilbert transform is defined in the frequency domain, it is based upon the modification of spatial filter with a fractional parameter, and it can be used to construct a new kind of fractional analytic signal. By performing spectrum analysis on the fractional envelope signal, the fractional envelope spectrum can be obtained. When weak faults occur in a bearing, some of the characteristic frequencies will clearly appear in the fractional envelope spectrum. These characteristic frequencies can be used for bearing weak fault feature extraction.The effectiveness of the proposed method is verified through simulation signal and experiment data.

Investigation on Skidding of Rolling Element Bearing in Loaded Zone

Skidding which occurs when rolling element entering into the loaded zone is prone to cause wear and incipient failure to the raceways and rolling elements. This paper presents a dynamic model to investigate the skidding of a rolling element bearing under radial load when the rolling element is entering into the load zone. In this dynamic model, the effects of the contact forces, friction forces on the rolling element-race and rolling element-cage interfaces, gravity, and the centrifugal forces of rolling elements are taken into consideration. The Hertzian contact theory is applied to calculate the non-linear contact forces. The Coulomb friction law is used to calculate the friction forces. The differential equations of rotational motion of the rolling element with regard to its central axis and the central axis of the outer ring are established respectively. The dynamic equations are then solved by using a fourth-order Runge-Kutta algorithm. The skidding characteristics of rolling element at the entry into the loaded zone are exposed, and the effects of the operating parameters on skidding behavior are carefully investigated.

Rolling Element Bearing Diagnostics by Combination of Envelope Analysis and Wavelet Transform

Rolling element-bearing diagnostics has been studied over the last thirty years, and envelope analysis is widely recognized as being the best approach for detection and diagnosis of rolling element bearing incipient failure. But one of the on-going difficulties with envelope technique is to determine the best frequency band to envelop. Here, wavelet transform technique is introduced into envelope analysis to solve the problem by capturing bearing defects-sensory scales (i.e. frequency bands). A modulated Gaussian function is chosen to be the analytical wavelet because it coincides well with bearing defect-induced vibration signal patterns. Vibration signals measured from railway bearing tests were studied by the proposed method. Cases of bearings with single and multiple defects on inner and outer race under different testing conditions are presented. Experimental results showed that the proposed method allowed a more accurate local description and separation of transient signal part, which were caused by impacts between defects and the mating surfaces in the bearing. The combination method provides an effective signal detection technique for rolling element-bearing diagnostics.

INVESTIGATION ON THE APPLICATION OF THE BOUNDARY ELEMENT METHOD TO THE SPILL GROOVED THRUST BEARING

An application of the boundary element method (BEM) is presented to calculate the behaviors of a spiral grooved thrust bearing (SGTB). The basic reason is that the SGTB has very complex boundary conditions that can hinder the effective or sufficient applications of the finite difference method (FDM) and the finite element method (FEM), despite some existing work based on the FDM and the FEM. In other to apply the BEM, the pressure control equation, i. e., Reynolds' equation, is first transformed into Laplace's and Poisson's form of the equations. Discretization of the SGTB with a set of boundary elements is thus explained in detail, which also includes the handling of boundary conditions. The Archimedean SGTB is chosen as an example of the application Of BEM, and the relationship between the behaviors and structure parameters of the bearing are found and discussed through this calculation. The obtained results lay a solid foundation for a further work of the design of the SGTB.

RMA-CNN:A Residual Mixed Domain Attention CNN for Bearings Fault Diagnosis and Its Time-Frequency Domain Interpretability

Early fault diagnosis of bearings is crucial for ensuring safe and reliable operations.Convolutional neural networks(CNNs)have achieved significant breakthroughs in machinery fault diagnosis.However,complex and varying working conditions can lead to inter-class similarity and intra-class variability in datasets,making it more challenging for CNNs to learn discriminative features.Furthermore,CNNs are often considered“black boxes”and lack sufficient interpretability in the fault diagnosis field.To address these issues,this paper introduces a residual mixed domain attention CNN method,referred to as RMA-CNN.This method comprises multiple residual mixed domain attention modules(RMAMs),each employing one attention mechanism to emphasize meaningful features in both time and channel domains.This significantly enhances the network’s ability to learn fault-related features.Moreover,we conduct an in-depth analysis of the inherent feature learning mechanism of the attention module RMAM to improve the interpretability of CNNs in fault diagnosis applications.Experiments conducted on two datasets—a high-speed aeronautical bearing dataset and a motor bearing dataset—demonstrate that the RMA-CNN achieves remarkable results in diagnostic tasks.

Detection of Bearing Faults Using a Novel Adaptive Morphological Update Lifting Wavelet

The current morphological wavelet technologies utilize a fixed filter or a linear decomposition algorithm, which cannot cope with the sudden changes, such as impulses or edges in a signal effectively. This paper pre- sents a novel signal processing scheme, adaptive morpho- logical update lifting wavelet （AMULW）, for rolling element bearing fault detection. In contrast with the widely used morphological wavelet, the filters in AMULW are no longer fixed. Instead, the AMULW adaptively uses a morphological dilation-erosion filter or an average filter as the update lifting filter to modify the approximation signal. Moreover, the nonlinear morphological filter is utilized to substitute the traditional linear filter in AMULW. The effectiveness of the proposed AMULW is evaluated using a simulated vibration signal and experimental vibration sig- nals collected from a bearing test rig. Results show that the proposed method has a superior performance in extracting fault features of defective roiling element bearings.

An Overview of Bearing Candidates for the Next Generation of Reusable Liquid Rocket Turbopumps

There is a consensus in the aerospace field that the development of reusable liquid rockets can effectively reduce the launch expense.The pursuit of a long service life and reutilization highly depends on the bearing components.However,the rolling element bearings(REBs)used in the existing rocket turbopumps present obvious and increasing limitations due to their mechanical contacting mode.For REBs,high rotational speed and long service life are two performance indexes that mutually restrict each other.To go beyond the DN value(the product of the bearing bore and rotational speed)limit of REBs,the major space powers have conducted substantial explorations on the use of new types of bearings to replace the REB.This review discusses,first,the crucial role of bearings in rocket turbopumps and the related structural improvements of REBs.Then,with the prospect of application to the next generation of reusable liquid rocket turbopumps,the bearing candidates investigated by major space powers are summarized comprehensively.These promising alternatives to REBs include fluid-film,foil,and magnetic bearings,together with the novel superconducting compound bearings recently proposed by our team.Our more than ten years of relevant research on fluid-film and magnetic bearings are also introduced.This review is meaningful for the development of long-life and highly reliable bearings to be used in future reusable rocket turbopumps.

PRINCIPLES AND PARAMETER DESIGN FOR AC-DC THREE-DEGREE FREEDOM HYBRID MAGNETIC BEARINGS

To simplify the mechanical structure, decrease the overall system size of the 3-degree freedom axial-radial magnetic bearings and reduce the manufacturing costs as well as operating costs, an innovated AC-DC 3-degree freedom hybrid magnetic bearing is proposed, which is driven by a DC amplifier in axial direction and a 3-phase power converter in radial directions respectively, and the axial and radial bias magnetic fluxes are provided with a common radial polarized permanent magnet ring. The principle producing magnetic suspension forces is introduced. By using equivalent magnetic circuit method, the calculation formulas of magnetic suspension forces and the mathematics models of the system are deduced. Nonlinearities of suspension forces and cross coupling between different degree freedoms are studied further by calculating the suspension forces at different displacements and control currents to validate the feasibility of the mathematics model. Then based on the mathematics models of the bearing, a control method of this novel bearing is designed. Lastly, the methods on parameter design and calculations of the bearing are presented, and an applicable prototype is simulated to analyze the magnetic path by using finite element analysis. The theory analysis and simulation results have shown that this magnetic bearing incorporates the merits of 3-phase AC drive, permanent magnet flux biased and axial-radial combined control, and reduces overall system size and has higher efficiency and lower cost, This innovated magnetic bearing has a wide application in super-speed and super-precision numerical control machine tools, bearingless motors, high-speed flywheels, satellites, etc.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

NANO-BEARING:THE DESIGN OF A NEW TYPE OF AIR BEARING WITH FLEXURE STRUCTURE

A new type of air bearing with flexure structure is introduced. The new bearing is designed for precision mechanical engineering devices such as mechanical watch movement. The new design uses the flexure structure to provide 3D damping to absorb shocks from all directions. Two designs are presented： one has 12 T-shape slots in the radian direction while the other has 8 spiral slots in the radian direction. Both designs have flexure mountings on the axial directions. Based on the finite element analysis （FEA）, the new bearing can reduce the vibration （displacement） by as much as 8.37% and hence, can better protect the shafts.

An Improved Dynamic Modelling for Exploring Ball Bearing Vibrations from Time-Varying Oil Film

Bearings are key components in rotating machinery,which is widely used in many fields,such as CNC machines,wind turbines and induction machines.The increasingly harsh operation environment can lead to wear and tear on raceways and reduce the precision and reliability of bearing or even machinery.Lubrication could relieve the wear to some degree,which is benefit to prolong the bearing’s life.Thus,investigation on the vibration responses under the influence of oil film is of great significance.However,for mechanism analysis,how to include the oil film into the bearing dynamic model affects the result and efficiency of solution.To address this problem,this study proposed a fast algorithm through load distribution and interpolation when calculating oil film stiffness and thickness during the solution of bearing vibration model.Analysis of oil film on vibration is carried out and a bearing test rig is designed to verify the proposed model.Numerical simulation result shows that rotational speed and load have vital effect on oil film and vibration.The experimental result is consistent with the simulation,which shows that the proposed model has a better performance on modeling bearing vibration and the method of considering oil film is reasonable.

Rolling Bearing Condition Monitoring Technique Based on Cage Rotation Analysis and Acoustic Emission

In this paper,we present an alternative technique for detecting changes in the operating conditions of rolling element bearings(REBs)that can lead to premature failure.The developed technique is based on measuring the kinematics of the bearing cage.The rotational motion of the cage is driven by traction forces generated in the contacts of the rolling elements with the races.It is known that the cage angular frequency relative to shaft angular frequency depends on the bearing load,the bearing speed,and the lubrication condition since these factors determine the lubricant film thickness and the associated traction forces.Since a large percentage of REB failures are due to misalignment or lubrication problems,any evidence of these conditions should be interpreted as an incipient fault.In this paper,a novel method for the measurement of the instantaneous angular speed(IAS)of the cage is developed.The method is evaluated in a deep groove ball bearing test rig equipped with a cage IAS sensor,as well as a custom acoustic emission(AE)transducer and a piezoelectric accelerometer.The IAS of the cage is analyzed under different bearing loads and shaft speeds,showing the dependence of the cage angular speed with the calculated lubricant film thickness.Typical bearing faulty operating conditions(mixed lubrication regime,lubricant depletion,and misalignment)are recreated.It is shown that the cage IAS is dependent on the lubrication regime and is sensitive to misalignment.The AE signal is also used to evaluate the lubrication regime.Experimental results suggest that the proposed technique can be used as a condition monitoring tool in industrial environments to detect abnormal REB conditions that may lead to premature failure.

Fault Diagnosis for Rolling Element Bearing in Dataset Bias Scenario

Recently, data-driven methods, especially deep learning, outperform other methods for rolling elementbearing (REB) fault diagnosis. Nevertheless, most research work assumes that REB dataset is unbiased. Inthe real industry applications, the dataset bias exists with REB owing to varying REB working conditions andnoise interference. Recently proposed adversarial discriminative domain adaptation (ADDA) is an increasinglypopular incarnation to solve dataset bias problem. However, it mainly devotes to realizing domain alignments, andignores class-level alignments;it can cause degradation of classification performance. In this study, we proposea new REB fault diagnosis model based on improved ADDA to address dataset bias. The proposed diagnosismodel realizes domain- and class-level alignments in dataset bias scenario;it consists of two feature extractors,a domain discriminator, and two label classifiers. The feature extractors and domain discriminator are trainedin an adversarial manner to minimize the domain difference in feature extractors. The domain discrepancy inlabel classifier is reduced by minimizing correlation alignment (CORAL) loss. We evaluate the proposed model onthe Case Western Reserve University (CWRU) bearing dataset and Paderborn University bearing dataset. Theproposed method yields better results than other methods and has good prospects for industrial applications.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

Synchronous chirp mode extraction: A promising tool for fault diagnosis of rolling element bearings under varying speed conditions

As critical components in modern aerospace productions,rolling element bearings(REBs)generally work under varying speed conditions,which brings great challenges to their operating health monitoring.Some novel time–frequency decomposition(TFD)algorithms are established recently to extract nonlinear features from the non-stationary signals effectively,which are promising for realizing fault diagnosis of REBs under varying speed conditions.However,numerous personal experiences must be incorporated and the anti-noise performance of these methods needs to be further enhanced.Given these issues,a synchronous chirp mode extraction(SCME)-based REB fault diagnosis method is proposed for the health monitoring of REBs under varying speed conditions in this study.It mainly consists of following two parts.(a)The shaft rotational frequency(SRF)is initially estimated from the low-frequency band of the vibration signal.Simultaneously,an adaptive refining strategy is incorporated to obtain a suitable bandwidth parameter.(b)A cycle-one-step estimation frame is constructed to extract synchronous modes from the envelope waveform of the vibration signal.Meanwhile,a synchronous mode spectrum(SMS)is generated using the information of the extracted synchronous modes,which is a novel REBs fault diagnosis technique with tacholess and resampling-free.In contrast to the current TFD algorithms,the proposed method needs fewer input parameters and owns a well anti-noise performance because there is no iterative optimization in the procedure of construction of SMS.As a result,the health conditions of REBs are evaluated by detecting the exhibited features in the SMS.Simulations and experiments are conducted to validate the effectiveness of the proposed method in terms of REB fault diagnosis.Analysis results demonstrate that the proposed method outperforms the current TFD algorithm and the conventional order tracking technique for fault diagnosis of REB under varying speed conditions.

A Fuzzy Neural Network for Fault Pattern Recognition

This paper combines fuzzy set theory with ART neural net-work , and demonstrates some important properties of the fuzzy ART neural net-work algorithm. The results from application on a ball bearing diagnosis indicate that a fuzzy ART neural net-work has an effect of fast stable recognition for fuzzy patterns.

Iterative HOEO fusion strategy:a promising tool for enhancing bearing fault feature

As parameter independent yet simple techniques,the energy operator(EO)and its variants have received considerable attention in the field of bearing fault feature detection.However,the performances of these improved EO techniques are subjected to the limited number of EOs,and they cannot reflect the non-linearity of the machinery dynamic systems and affect the noise reduction.As a result,the fault-related transients strengthened by these improved EO techniques are still subject to contamination of strong noises.To address these issues,this paper presents a novel EO fusion strategy for enhancing the bearing fault feature nonlinearly and effectively.Specifically,the proposed strategy is conducted through the following three steps.First,a multi-dimensional information matrix(MDIM)is constructed by performing the higher order energy operator(HOEO)on the analysis signal iteratively.MDIM is regarded as the fusion source of the proposed strategy with the properties of improving the signal-to-interference ratio and suppressing the noise in the low-frequency region.Second,an enhanced manifold learning algorithm is performed on the normalized MDIM to extract the intrinsic manifolds correlated with the fault-related impulses.Third,the intrinsic manifolds are weighted to recover the fault-related transients.Simulation studies and experimental verifications confirm that the proposed strategy is more effective for enhancing the bearing fault feature than the existing methods,including HOEOs,the weighting HOEO fusion,the fast Kurtogram,and the empirical mode decomposition.

Characteristics of motorized spindle supported by active magnetic bearings

A motorized spindle supported by active magnetic bearings（AMBs） is generally used for ultra-high-speed machining. Iron loss of radial AMB is very great owing to high rotation speed, and it will cause severe thermal deformation. The problem is particularly serious on the occasion of large power application, such as all electric aero-engine. In this study, a prototype motorized spindle supported by five degree-of-freedom AMBs is developed. Homopolar and heteropolar AMBs are independently adopted as radial bearings. The influences of the two types of radial AMBs on the dynamic characteristics of the motorized spindle are comparatively investigated by theoretical analysis, test modal analysis and actual operation of the system. The iron loss of the two types of radial AMBs is analyzed by finite element software and verified through run-down experiments of the system. The results show that the structures of AMB have less influence on the dynamic characteristics of the motorized spindle. However, the homopolar structure can effectively reduce the iron loss of the radial AMB and it is useful for improving the overall performance of the motorized spindle.

New analysis model for rotor-bearing systems based on plate theory

The purpose of this work is to develop a new analysis model for angular-contact,ball-bearing systems on the basis of plate theory instead of commonly known approaches that utilize spring elements.Axial and radial stiffness on an annular plate are developed based on plate,Timoshenko beam,and plasticity theories.The model is developed using theoretical and inductive methods and validated through a numerical simulation with the finite element method.The new analysis model is suitable for static and modal analyses of rotor-bearing systems.Numerical examples are presented to reveal the effectiveness and applicability of the proposed approach.