Simulating gear and bearing interactions in the presence of faults: Part I. The combined gear bearing dynamic model and the simulation of localised bearing faults

This paper presents a simulation model for a gearbox test rig, in which a range of bearing faults can be implemented. Bearing faults sometimes manifest themselves by their interaction with meshing gears, and to simulate this it is necessary to model a whole system of gears and shafts supported in bearings. This has now been done for an experimental test rig through the incorporation of a time-varying, non-linear stiffness bearing model into a previously developed gear model. The incorporated bearing model is based on Hertzian contact theory, which relates the raceway displacement to the bearing load, and also accounts for the slippage between the elements. It has the capacity to model localised spalls (inner race, outer race and rolling elements), which are discussed in this part of the paper and extended inner and outer race faults (rough surfaces), which are discussed in part II. Even though the whole gearbox has not been modelled in detail, the non-linear time-varying gear-meshing operation is modelled in some detail. Both simulated and experimental localised fault signals (acceleration signals) were subjected to the same diagnostic techniques; namely spectrum comparisons, Spectral Kurtosis (SK) analysis and envelope analysis. The processed simulated signals showed a similar pattern to that observed in their measured counterparts and were found to have a characteristic, referred to in the literature as double pulses, corresponding to entry into and exit from the localised fault. The simulation model will be useful for producing typical fault signals from gearboxes to test new diagnostic algorithms, and possibly prognostic algorithms.     

Simulation and analysis of vibration signals generated by rolling element bearing with defects

Dynamic loading of a rolling element bearing structure is modeled by a computer program developed in Visual Basic programming language. The vibration response of the structure to the dynamic loading is obtained using a standard finite element package I-DEAS. A force model is proposed to model the localized rolling element bearing defects. Time and frequency domain analyses are performed for diagnostics of rolling element bearing structures. Statistical properties of the vibration signals for healthy and defected structures are compared. The envelope (HFRT) method is employed in the frequency domain analysis. The effect of the rotational speed on the diagnostics of rolling element bearing defects is investigated. An optimum sensor location on the structure is sought. Effect of the structure geometry on the monitoring techniques is studied. An optimum monitoring method can be employed by analyzing the rolling element bearing structure following the procedure proposed in this study. The present commercial computer aided engineering packages can be used in special engineering applications such as condition monitoring of rolling element bearings.     

Mechanism of dent initiated flaking and bearing life enhancement technology under contaminated lubrication condition: Part I: Effect of tangential force on dent initiated flaking

In this paper, we have clarified experimentally the mechanism of dent initiated flaking as observed in rolling element bearings operating under contaminated lubrication conditions. A characteristic of dent initiated flaking is the initiation of cracks on the trailing edge of dents relative to the rolling direction. Based on the results of twin-disk testing and ball-on-rod rolling contact fatigue (RCF) testing conducted, we have confirmed that the crack initiation at the edge of a dent is strong influenced by the tangential force. The tangential force leads to the generation of a large tensile stress at the trailing edge of dents, which in turn leads to crack initiation.     

Mechanism of dent initiated flaking and bearing life enhancement technology under contaminated lubrication condition: Part I: Effect of tangential force on dent initiated flaking

In this paper, we have clarified experimentally the mechanism of dent initiated flaking as observed in rolling element bearings operating under contaminated lubrication conditions. A characteristic of dent initiated flaking is the initiation of cracks on the trailing edge of dents relative to the rolling direction. Based on the results of twin-disk testing and ball-on-rod rolling contact fatigue (RCF) testing conducted, we have confirmed that the crack initiation at the edge of a dent is strong influenced by the tangential force. The tangential force leads to the generation of a large tensile stress at the trailing edge of dents, which in turn leads to crack initiation.     

Application of EEMD and improved frequency band entropy in bearing fault feature extraction

Ensemble empirical mode decomposition (EEMD) is widely used in condition monitoring of modern machine for its unique advantages. However, when the signal-to-noise ratio is low, the de-noising function of it is often not ideal. Thus, a new fault feature extraction method for rolling bearing combining EEMD and improved frequency band entropy (IFBE) is proposed, i.e., EEMD–IFBE. According to the problem of multiple intrinsic mode functions (IMFs) generated by EEMD, how to select the sensitive IMF(s) that can better reflect fault characteristics, a novel method based on FBE for sensitive IMF is proposed. In addition, since the bandwidth parameter is set empirically when the band-pass filter is designed based on the original FBE, a novel bandwidth parameter optimization method based on the principle of maximum envelope kurtosis is proposed. First, the original vibration signal is subjected to EEMD to obtain a series of IMFs; Then, the FBE values are obtained for the original signal and each IMF component, and the bandwidth of the band-pass filter (empirically) is designed as the characteristic frequency band at the minimum entropy value, and the affiliation between the characteristic frequency band of each IMF and the characteristic frequency band of the original signal is compared, and then selecting the sensitive IMF(s) that reflects the characteristics of the fault; Third, due to the influence of background noise, it is difficult to accurately obtain the fault frequency from the selected IMF(s). Therefore, the band-pass filter designed based on FBE is used, and the bandwidth parameter is optimized based on the principle of envelope kurtosis maximum, and then the selected sensitive IMF is band-pass filtered. Finally, the envelope power spectrum analysis is performed on the filtered signal to extract the fault characteristic frequency, and then the fault diagnosis of the bearing is realized. The method is successfully applied to simulated data and actual data of rolling bearing, which can accurately diagnose fault characteristics of bearing and prove the effectiveness and advantages of the method.     

A multi-step progressive fault diagnosis method for rolling element bearing based on energy entropy theory and hybrid ensemble auto-encoder

It is meaningful to efficiently identify the health status of bearing and automatically learn the effective features from the original vibration signals. In this paper, a multi-step progressive method based on energy entropy (EE) theory and hybrid ensemble auto-encoder (HEAE), systematically blending the statistical analysis approach with the deep learning technology, is proposed for rolling element bearing (REB) fault diagnosis. Firstly, a preliminary detection about the REB health status is performed by the statistical analysis technique integrated with the EE theory. Secondly, if fault exists in REB, a new HEAE is constructed based on denoising auto-encoder and contractive auto-encoder to strengthen the feature learning ability and automatically extract the deep state features from the raw data. Subsequently, a modified t-distributed stochastic neighbor embedding (M-tSNE) algorithm is developed to achieve the features reduction to further improve the diagnosis efficiency. Finally, the low-dimensional representations after features reduction are as the inputs of softmax classifier to recognize the fault conditions. The proposed method is applied to the fault diagnosis of REB. The results confirm the effectiveness and superiority of the proposed method, and it is more suitable for the actual engineering applications compared with other existing methods.     

A subspace method for the blind extraction of a cyclostationary source: Application to rolling element bearing diagnostics

The need for blindly separating mixtures of signals arises in many signal processing applications. A class of solutions to this problem was recently proposed by the so-called blind source separation (BSS) techniques which rely on the sole knowledge of the number of independent sources present in the mixture. This paper deals with the case where the number of sources is unknown and statistical independence may not apply, but where there is only one signal of interest (SOI) to be separated, which is cyclostationary. It proposes a blind extraction method using a subspace decomposition of the observations via their cyclic statistics. This method is first developed for instantaneous mixtures and is then extended to the convolutive case in the frequency-domain where it does not suffer from the permutation problem as does classical BSS. Experiments on industrial data are finally performed and illustrate the high performance of the proposed method.     

钢丝滚道球轴承的点接触问题有限元仿真

以某型飞行器三轴仿真转台主轴轴系中的钢丝滚道球轴承为例,通过ANSYS对该滚珠．滚道间的非协调性接触问题进行有限元建模与仿真,发现最大接触应力发生在钢丝滚道的表面,而滚珠的最大接触应力发生在其接触面正下方短距离内。有限元分析结果有力地阐明了点蚀易在钢丝滚道接触表面形成并逐渐扩展的机理。本文的工作为进一步开展钢丝滚道的点蚀及磨损的实验研究提供了理论依据。     

Defect detection in deep groove ball bearing in presence of external vibration using envelope analysis and Duffing oscillator

This paper deals with detection of local defects existing on races of deep groove ball bearing in the presence of external vibrations using envelope analysis and Duffing oscillator. Experiments have been carried out using a test rig for capturing the vibration signals of test bearing. The external vibration has been imparted to the housing of the test bearing through electromechanical shaker. In envelope analysis the centre frequency has been selected using the spectral kurtosis for the filters length of 32 and 64 for different bandwidths. Through this study, it has been revisited and confirmed that the defect detection in envelope analysis mainly depends on the selection of centre frequency and bandwidth. The spectra of selected centre frequency with several bandwidths have been studied and compared for identification of defective frequency. The system defined by the Duffing equation entered into the periodical state from the chaotic state at the critical value of disturbing periodic force in the presence of defective bearing signal. The state change has been identified using the phase plane trajectories and Lyapunov exponents of Duffing equation. It is worth to mention here that envelope spectrum reveals the information about the defect frequencies and their harmonics. However, the Duffing oscillator only confirms the presence of defect frequencies by indicating closed phase plane trajectories and negative Lyapunov exponents. Authors believe that for speedy assessment about the presence of defects on races of rolling element bearings, the use of Duffing oscillator may be preferred.     

空心球轴承接触状态和承载性能理论研究初探

用有限元法对空心球轴承的接触面形状和尺寸、接触应力进行了模拟计算,研究了空心球轴承的承栽性能,不同空心度对球轴承承栽性能的影响进行了分析,为空心球轴承的设计与应用提供指导。     

A novel approach integrating dimensional analysis and neural networks for the detection of localized faults in roller bearings

The detection of the defective/worn out bearing components used in rotating machines is one of the main concerns in various applications. To improve the computational efficiency in the nonlinear dynamic analysis for the rolling contact bearings, a new methodology based on dimensional analysis (DA) theory is proposed in this paper. The developed model is used to predict the vibration responses due to artificially spalled bearing components to quantify the level of structural damages into these components. The use of a back propagation neural network (BPNN) has been made that also predicted responses from the network trained by developed algorithm using the experimental data obtained from the defective bearing components on the developed test rig. A comparison between the responses predicted by proposed DA method and the BPNN showed a fair amount of the agreement between the two approaches and validated the proposed model and proved outstanding tool for identification of spalled/damaged bearing components.     

Evolution of matt surface topography in aluminium pack rolling. Part II: effect of material properties

A model has been presented in a companion paper [1] to predict the generation of roughness on the matt surface in pack rolling of aluminium foil. The model is based on the finite element method using isotropic plasticity. This model is used in the current paper to investigate the effect of material properties on the generation of surface roughness. There is a large inhomogeneity of strain during deformation, with harder grains generally deforming less than softer ones. It is found that the roughness amplitude is roughly proportional to the standard deviation of the initial grain yield stress distribution, normalised by the initial mean yield stress, so that a wider distribution of the initial yield stress results in greater surface roughness. It is shown that a suitable linear hardening law can be used to approximate the roughening behaviour for real material flow stress curves.     

The development of pivot bearing with multiple degrees of freedom: 3rd report: Examination for specification to improve bearing stiffness by finite element method analysis and its inspection by experiment

This paper deals with the examination of specifications to improve the performance of a pivot bearing with two degrees of freedom by finite element method (FEM). As the target of estimation for performance of the bearing, we evaluated the contact pressure and the stiffness. As the results of FEM considering the number of grooves and the contact angle of the planetary ball, a large effect was obtained in the case that the number of rows of planetary balls was 2. The effect was confirmed by measuring axial displacement.     

Pressure distribution in a curvilinear hydrostatic bearing lubricated by a micropolar fluid in the presence of a cross magnetic field

The flow of a micropolar fluid in the clearance of a curvilinear hydrostatic thrust bearing in the presence of a cross magnetic field was considered. By solving the equations of motion for the orthogonal curvilinear coordinate system, a formula describing the pressure distribution was obtained. Plane and spherical thrust bearings were considered as examples.     

Rolling cylinder on an elastic half-plane with harmonic oscillations in normal force and rotational speed. Part I: Solution of the partial slip contact problem

We study the effect of harmonic oscillations during the steady rolling of a cylinder on a plane in partial slip contact conditions in the limit of small oscillations. The solution is an extension of that given in Barber et al. [1] for infinitely large coefficient of friction. Here, the effect of varying normal load and hence contact area is investigated in detail by analyzing the first order variation of the tangential force and the corresponding relative displacements.In particular, the solution is given in terms of an explicit length scale d in the Flamant solution used as a Green function. Appropriate choice of values of d allows to treat both two-dimensional problems and three-dimensional ones having elliptical contact area sufficiently elongated in the direction of the rotation axis.Also, this analysis can be used as starting point for corrugation calculations in railway tracks, where oscillations in time of the normal forces can result in non-uniform wear and hence in amplification of the corrugation.     

扫描电子束铝合金表面处理应力场仿真与试验验证

研究扫描电子束铝合金表面处理应力场的分布规律,对了解残余应力的形成机理具有十分重要的理论及实际意义。在热弹塑性理论的基础上建立电子束表面处理应力场的有限元模型,分析高温热力学参数对电子束表面处理应力场的影响;通过仿真与试验验证相结合的方法确定材料的高温热力学参数,得到铝合金电子束表面扫描后的应力分布规律。随着弹性模量和切变模量的增加,ADC12铝合金材料表面的变形量和最大应力均成非线性增加。经电子束表面处理后试样表面扫描带附近为拉应力,而在其他位置为压应力;最大拉应力出现在扫描带的内侧边缘处,外侧边缘次之,而扫描带中间的拉应力最小;最大表面应力为127.6 MPa,变形量为1.8 mm。     

Numerical analysis and experimental investigation of modal properties for the gearbox in wind turbine

Wind turbine gearbox (WTG), which functions as an accelerator, ensures the performance and service life of wind turbine systems. This paper examines the distinctive modal properties of WTGs through finite element (FE) and experimental modal analyses. The study is performed in two parts. First, a whole system model is developed to investigate the first 10 modal frequencies and mode shapes of WTG using flexible multi-body modeling techniques. Given the complex structure and operating conditions of WTG, this study applies spring elements to the model and quantifies how the bearings and gear pair interactions affect the dynamic characteristics of WTGs. Second, the FE modal results are validated through experimental modal analyses of a 1.5 WM WTG using the frequency response function method of single point excitation and multi-point response. The natural frequencies from the FE and experimental modal analyses show favorable agreement and reveal that the characteristic frequency of the studied gearbox avoids its eigen-frequency very well.     

The lubricated wear of ceramics : Part II: The wear and friction of silicon nitride and steel in the presence of mineral oil or an ester based lubricant

The friction and wear characteristics of combinations of silicon nitride, alumina and AISI 52100 steel in the presence of mineral oil containing anti-wear, dispersant and detergent additives have been investigated in a tri-pin-on-disc machine. The tests were carried out at a nominal temperature of 100°C for a range of sliding speeds, loads and total sliding distances. In Part II of this two-part paper a comparison will be made between the tribological performance of these sliding pairs of materials in mineral oil and ester based lubricant environments. The results of the investigation showed that the alumina performed relatively poorly under these test conditions, whereas silicon nitride showed good potential as an improved wear resisting material compared with 52100 steel. Wear factors of the order of 10⁻¹⁰ mm³/Nm were deduced for the alumina, while values as low as 10⁻¹¹ mm³/Nm were typical of the silicon nitride sliding against 52100 steel discs. The alumina pins wore by a process of brittle fracture at the surface, whereas the silicon nitride pins wore primarily by a tribochemical polishing mechanism. The rate of tribo-chemical wear was found to be proportional to the nominal contact area.     

ZK60镁合金棒材ECAP过程有限元模拟分析

采用刚黏塑性有限元理论,在挤压温度为200℃、挤压速度为2 mm/s、背压强度为40 MPa时,对ZK60镁合金棒材进行四道次ECAP过程的数值模拟,观察棒材在四道次ECAP过程中金属流动情况,并分析棒材在四道次ECAP过程中应力场和温度场的分布和变化规律.