THE 3-D BOUNDARY ELEMENT METHOD OF ROLLER BEARING BY PLATE ELEMENT ANALOGUE

The mill roller bearing is made up of an internal ring, middlerolls and an external ring, the analysis of which is a multi-bodiescontact problem. In this paper, based on the three-dimensionalelastic contact BEM without friction, and using the structuralcharacteristics of roller bearings, middle rolls are de- scribed byelastic plate units of different shapes, which is placed on theinternal ring.

A research on the contact stress of roller bearing based on crowning analysis

According to elastic contact theory, contact model between roller and race is established. Compared with the Hertz results, the results are proved, based on which contact stress distribution of different crowning and initial contact length is given, then the appropriate value is derived. On the basis, inertia force and different radial force is given into consideration. Via analysis, it con- cludes that under balanced pure radial load condition the largest contact stress between roller and race increases along with crowning value increasing. With the same crowning value, the largest contact stress between roller and race decreases in the first and increases at the end along with initial contact length increasing. Contact stress between roller and outer race increases along with revolution speed increasing.

Bending stress of rolling element in elastic composite cylindrical roller bearing

A new structure design method of elastic composite cylindrical roller bearing is proposed, in which PTFE is embedded into a hollow cylindrical rolling element, according to the principle of creative combinations and through innovation research on cylindrical roller bearing structure. In order to systematically investigate the inner wall bending stress of the rolling element in elastic composite cylindrical roller bearing, finite element analysis on different elastic composite cylindrical rolling elements was conducted. The results show that, the bending stress of the elastic composite cylindrical rolling increases along with the increase of hollowness with the same filling material. The bending stress of the elastic composite cylindrical rolling element decreases along with the increase of the elasticity modulus of the material under the same physical dimension. Under the same load, on hollow cylindrical rolling element, the maximum bending tensile stress values of the elastic composite cylindrical rolling element after material filling at 0° and 180° are 8.2% and 9.5%, respectively, lower than those of the deep cavity hollow cylindrical rolling element. In addition, the maximum bending-compressive stress value at 90° is decreased by 6.1%.

Finite element analysis of deformation characteristics in cold helical rolling of bearing steel-balls

Due to the complexity of investigating deformation mechanisms in helical rolling(HR) process with traditional analytical method, it is significant to develop a 3D finite element(FE) model of HR process. The key forming conditions of cold HR of bearing steel-balls were detailedly described. Then, by taking steel-ball rolling elements of the B7008 C angular contact ball bearing as an example, a completed 3D elastic-plastic FE model of cold HR forming process was established under SIMUFACT software environment. Furthermore, the deformation characteristics in HR process were discovered, including the forming process, evolution and distribution laws of strain, stress and damage based on Lemaitre relative damage model. The results reveal that the central loosening and cavity defects in HR process may have a combined effect of large negative hydrostatic pressure(positive mean stress)caused by multi-dimensional tensile stresses, high level transverse tensile stress, and circular-alternating shear stress in cross section.

Influence of the Number of Rollers on a Tapered Roller Bearing

In roller bearings, the outer ring is usually fixed and the inner ring has the rolling motion. Concerning TRB （tapered roller bearings）, this motion generates forces that are transmitted to the outer ring by the tapered rollers. Thus, contact stresses occur and the number of rollers plays a major role with respect to the load distribution. This influence is analyzed in this study by the FEM （finite element method） with commercial code ABAQUS, where two models were evaluated： a common TRB and the same one but with fewer rollers. As an application, a manual automotive transmission was considered for the input loads.

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.

Frequency Loss and Recovery in Rolling Bearing Fault Detection

Rolling element bearings are key components of mechanical equipment. The bearing fault characteristics are a ected by the interaction in the vibration signals. The low harmonics of the bearing characteristic frequencies cannot be usually observed in the Fourier spectrum. The frequency loss in the bearing vibration signal is presented through two independent experiments in this paper. The existence of frequency loss phenomenon in the low frequencies, side band frequencies and resonant frequencies and revealed. It is demonstrated that the lost frequencies are actually suppressed by the internal action in the bearing fault signal rather than the external interference. The amplitude and distribution of the spectrum are changed due to the interaction of the bearing fault signal. The interaction mechanism of bearing fault signal is revealed through theoretical and practical analysis. Based on mathematical morphology, a new method is provided to recover the lost frequencies. The multi-resonant response signal of the defective bearing are decomposed into low frequency and high frequency response, and the lost frequencies are recovered by the combination morphological filter(CMF). The e ectiveness of the proposed method is validated on simulated and experimental data.

An improved resampling algorithm for rolling element bearing fault diagnosis under variable rotational speeds

In order to address the issues of traditional resampling algorithms involving computational accuracy and efficiency in rolling element bearing fault diagnosis, an equal division impulse-based（EDI-based） resampling algorithm is proposed. First, the time marks of every rising edge of the rotating speed pulse and the corresponding amplitudes of faulty bearing vibration signal are determined. Then, every adjacent the rotating pulse is divided equally, and the time marks in every adjacent rotating speed pulses and the corresponding amplitudes of vibration signal are obtained by the interpolation algorithm. Finally, all the time marks and the corresponding amplitudes of vibration signal are arranged and the time marks are transformed into the angle domain to obtain the resampling signal. Speed-up and speed-down faulty bearing signals are employed to verify the validity of the proposed method, and experimental results show that the proposed method is effective for diagnosing faulty bearings. Furthermore, the traditional order tracking techniques are applied to the experimental bearing signals, and the results show that the proposed method produces higher accurate outcomes in less computation time.

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 instantaneous rotational frequency estimation based on EMD soft-thresholding denoising and instantaneous fault characteristic frequency

The accurate estimation of the rolling element bearing instantaneous rotational frequency(IRF) is the key capability of the order tracking method based on time-frequency analysis. The rolling element bearing IRF can be accurately estimated according to the instantaneous fault characteristic frequency(IFCF). However, in an environment with a low signal-to-noise ratio(SNR), e.g., an incipient fault or function at a low speed, the signal contains strong background noise that seriously affects the effectiveness of the aforementioned method. An algorithm of signal preprocessing based on empirical mode decomposition(EMD) and wavelet shrinkage was proposed in this work. Compared with EMD denoising by the cross-correlation coefficient and kurtosis(CCK) criterion, the method of EMD soft-thresholding(ST) denoising can ensure the integrity of the signal, improve the SNR, and highlight fault features. The effectiveness of the algorithm for rolling element bearing IRF estimation by EMD ST denoising and the IFCF was validated by both simulated and experimental bearing vibration signals at a low SNR.

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. © 2017 Chinese Association of Automation.

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.

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.

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.

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.

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.

Mechanical performance analysis of hollow cylindrical roller bearing of cone bit by FEM

Bearings are key components of cone bit,thus its rapid failure is a major cause of leading to lower life of the bit.To improve the bearing performance and prolong working life,contact mechanics of hollow cylindrical roller bearing of cone bit was simulated.Effects of hollow size,drilling pressure,friction coefficient and fitting clearance on mechanics performance of the bearing were studied.The results show that the maximum equivalent stress of the hollow cylindrical roller bearing appears on the claw journal,and the maximum contact stress appears on the contact pair of the hollow roller.Besides,hollow sizes have a greater impact on the equivalent stress and contact stress of the cylindrical roller,while the influence on the stress of the cone and claw journal is relatively small.With the increasing of the drilling pressure and fitting clearance,equivalent stress and contact stress of bearing parts increase.The friction coefficient has little impact on mechanical performance of the bearing.As the 121/4SWPI517 type hollow cylindrical roller bearing of cone bit an example,the optimal hollow size is 55%,the drilling pressure is 140 kN and the fitting clearance is 0e0.02 mm.

The Evolution of Reliability and Efficiency of Aerospace Bearing Systems

The worldwide air traffic underwent a rapid development in recent decades.?Between the early 70s and the late 90s of the last century civil air traffic?doubled every 15 years. The civil aviation market will continue to grow with 4% - 5%?each year within the next 20 years. This enormous growth represents major?challenges for airframers, engine makers, suppliers, airlines, air traffic management?and ground infrastructure. In addition, the public debate on the worldwide?civil air traffic is dominated by environmental and climate issues, even though only 2% of the man-made carbon dioxide (CO2) emissions are due to air transportation. Therefore the aerospace industry will have to focus on a low-emission and quite air traffic, and on the conservation of natural resources and our environment. The end-use consumer and environmental policy requirements?for aircrafts of the next generation translate into components with improved efficiency and reliability. Rolling bearings are one of these components which?significantly determine the reliability and mechanical efficiency of aerospace applications such as aircraft and rotorcraft engines and transmission systems.?They have to withstand very demanding operating conditions. Especially main shaft?bearings in modern aircraft engines experience high rotational speeds andtemperatures. Furthermore aerospace bearings have to meet the highest reliability?standards and require low-weight design solutions. These operating conditions?and requirements present a continuous challenge for improvements in all?fields of bearing technology. This article presents solutions in aspects of materials, design, analysis, and surface technologies in order to meet the environmental, reliability, and economical requirements of advanced aerospace bearing systems. State of the art bearing analysis and advanced bearing design solutions?contributing to lower friction power losses and increased systems efficiency?are discussed. Weight, functional, and maintenance benefits are presented with the example of highly integrated aircraft engine main shaft bearings. It is also shown that the progress in bearing materials and surface technology development is the basis for weight and friction energy reduction in aerospace?bearing systems.

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.

Time-varying stiffness analysis of double-row tapered roller bearing based on the mapping structure of bearing stiffness matrix

Time-varying stiffness is one of the most important dynamic characteristics of rolling element bearings.The method of analyzing the elements in the bearing stiffness matrix is usually adopted to investigate the characteristics of bearing stiffness.Linear mapping structure of the bearing stiffness matrix is helpful to understand the varying compliance excitation and its influence on vibration transmission.In this study,a method to analyze the mapping structure of bearing stiffness matrix is proposed based on the singular value decomposition of block matrices in the stiffness matrix.Not only does this method have the advantages of coordinate transformation independence and unit independence,but also the analysis procedure involved is geometrically intuitive.The time-varying stiffness matrix of double-row tapered bearing is calculated and analyzed using the proposed method under two representative load cases.The principal stiffnesses and principal axes defined in the method together indicate the dominant and insignificant stiffness properties with the corresponding directions,and the vibration transmission properties are also revealed.Besides,the coupling behaviors between different shaft motions are found during the analysis of mapping structure.The mechanism of the generation of varying compliance excitation is also revealed.