滚动轴承非线性时变参数动力学模型与故障机理研究

基于滚动轴承故障动力学模型研究其振动特性及故障机理是实现轴承故障准确诊断的基础。为描述滚动轴承缺陷对其振动响应特性的影响,考虑滚动体与缺陷的相对几何关系,提出了时变接触变形与时变刚度耦合的滚动轴承故障非线性动力学模型。以NSK6205深沟球轴承为对象,通过建立6+N_b自由度非线性时变参数动力学模型,分析了滚动体通过外圈缺陷区域时接触变形、接触刚度以及振动响应的变化过程,得到了不同缺陷尺寸下滚动轴承故障冲击振动响应特征变化规律。理论分析和实验研究结果表明,随着缺陷尺寸的增加,滚动轴承故障振动响应产生由双冲击到多冲击的变化特征,不同缺陷尺寸下,滚动体进入和离开缺陷过程中产生的冲击响应明显不同。研究成果为基于振动信号实现滚动轴承故障尺寸判断提供了理论依据。     

Application of an envelope technique in the detection of ball bearing defects in a laboratory experiment

To judge the diagnostic capabilities of an envelope technique, based on enveloping the resonance frequency of a transducer,

1 Bearcon Signature™, Carl Schenck AG, Germany

artificially damaged ball bearings (SKF 6207) were run under oil lubrication at different radial loads and speeds in a laboratory experiment. Damage to the outer race, inner race and ball of different magnitudes was introduced by spark erosion and the response of the measurement system was analysed. The results showed that vibration spectrum components of outer race defects showed up in the envelope spectra of undamaged bearings, and that the detectability of defects was primarily limited by the speed of the bearing; on occasion the automatic scaling facility of the analyser was a limiting factor. Inner race and ball defects showed the well-known effects of load modulation in the defect contact zone, which can become dominant in the envelope spectra at high loads and speeds. This phenomenon could be confirmed by computer simulation. The detection of ball damage was hampered by the fact that overrolling of the defect in purely radially loaded bearings takes place incidentally. This drawback could be mitigated by applying a trigger technique to the envelope signal.     

考虑局部故障边缘形态的球轴承振动特征

在分析球与不同边缘形态的局部故障之间接触关系的基础上,根据赫兹接触理论建立了球与局部故障光滑圆柱型边缘之间的接触刚度模型,以及球进入故障区域时的时变位移激励模型。考虑弹性流体动力润滑油膜的影响,提出时变冲击激励耦合的球轴承圆弧边缘型局部故障动力学模型。该模型考虑了故障边缘形态特征变化引起的球进入故障时的时变额外位移激励,以及球与故障边缘之间的时变接触刚度。研究滚道表面圆弧型边缘型局部故障激励下的球轴承振动响应特征,并分析故障边缘形态变化对球轴承振动响应特征的影响规律,解决了尖锐边缘型局部故障模型无法描述其边缘形态变化的问题,为获得可靠的局部故障球轴承的动力学响应特征提供新的手段和方法,也为球轴承局部故障的准确识别与定量诊断提供一定的理论依据。     

考虑三维运动和相对滑动的滚动球轴承局部表面损伤动力学建模研究

滚动体通过局部表面损伤时轴承的运动参数及动力学响应是轴承疲劳损伤分析和故障诊断的有效输入和重要依据。基于GUPTA轴承模型构建具有局部表面损伤的滚动球轴承的完整动力学模型。该模型中每个轴承元件(滚球、内圈及外圈)具有6个自由度,并且考虑了元件之间的相对滑动和润滑牵引特性。在对局部表面损伤进行建模时,完整考虑了损伤出现后由于材料缺失而引入的额外间隙,以及损伤对赫兹接触刚度及接触载荷作用方向的影响。研究滚球在通过局部表面损伤时轴承的加速度与滚球/损伤之间冲击力的对应关系,以及轴承转速和损伤宽度对轴承振动响应的影响规律。仿真结果表明,由于考虑了相对滑动和滚球/损伤之间冲击力的影响,本模型能够对具有局部表面损伤的球轴承进行更为合理的动力学特性分析,可为滚动球轴承的疲劳损伤分析和故障定量诊断提供一定的理论依据。     

Vibration analysis of rolling element bearings with various defects under the action of an unbalanced force

In this paper, a method based on the finite element vibration analysis is presented for defect detection in rolling element bearings with single or multiple defects on different components of the bearing structure using the time and frequency domain parameters. A dynamic loading model is proposed in order to create the nodal excitation functions used in the finite element vibration analysis as external loading. A computer code written in Visual Basic programming language with a graphical user interface is developed to create the nodal excitations for different cases including the outer ring, inner ring or rolling element defects. Forced vibration analysis of a bearing structure is performed using the commercial finite element package I-DEAS under the action of an unbalanced force transferred to the structure via a ball bearing. Time and frequency domain parameters such as rms, crest factor, kurtosis and band energy ratio for the frequency spectrum of the enveloped signals are used to analyse the effect of the defect location and the number of defects on the time and frequency domain parameters. The role of the receiving point for vibration measurements is also investigated. The vibration data for various defect cases including the housing structure effect can be obtained using the finite element vibration analysis in order to develop an optimum monitoring method in condition monitoring studies.     

Nonlinear Dynamic Response of Cylindrical Roller Bearing–Rotor System with 9 Degree of Freedom Model Having a Combined Localized Defect at Inner–Outer Races of Bearing

This article presents a nonlinear dynamic model for a cylindrical roller bearing–rotor system with interaction forces between the inner race, outer race, and roller. Roller–race contacts are modeled predicting nonlinear stiffness (Hertz contact theory) and nonlinear damping for a rotor–cylindrical roller bearing system. Here a shaft–rotor bearing system is modeled with 9 degrees of freedom with one defect on the inner race and one defect on the outer race for a case of combined localized defects. In the mathematical formulation, contacts between rolling elements and inner and outer races are considered as nonlinear springs and nonlinear damping is taken into consideration. Contact force calculations with nonlinearity are solved using the Newton-Raphson method for n unknown nonlinear simultaneous equation. The Newmark-β implicit integration technique coupled with the Newton-Raphson method is used to solve the differential equations. The results are obtained in the form of a time domain plot, frequency domain plot, and phase plot/Poincare map. The validity of the proposed model is compared with experimental results. A bifurcation graph of speed versus peak amplitude predicts the behavior of the system.     

Predicting polygonal-shaped defects during hot ring rolling using a rigid-viscoplastic finite element method

We applied a rigid-viscoplastic finite element method to investigate polygonal-shaped defects that occur during ring rolling and developed an improved analysis model with relatively fine finite elements near the roll gap to reduce the computational time, along with a scheme to minimize the volume change. We also simulated the formation of a polygonal-shaped defect during hot ring rolling of a ball bearing outer race. The results were in good qualitative agreement with actual experimental phenomena.     

波纹度波数对深沟球轴承振动特性的影响

建立了三自由度轴承动力学模型和波纹度模型,以6201深沟球轴承为研究对象,基于定步长四阶龙格-库塔法得到轴承振动频率和振动加速度,分别通过与文献和试验结果的对比,验证了模型的正确性.并分析了内外圈波纹度波数对轴承加速度峰峰值和有效值的影响,结果表明:轴承振动加速度响应的峰峰值和有效值随内外圈波纹度波数增大而增大,波纹度...     

轴承间隙及柔性特征对机构动态误差的影响分析

为能够准确、有效地揭示轴承间隙与柔性特征对机构动态误差的影响规律,基于多体动力学理论与Hertz接触理论,提出一种计及轴承间隙与柔性特征影响的多体系统建模方法。该方法采用力约束替代运动约束,构建多体系统环境下的轴承精细化模型。基于该方法,可深入揭示轴承微观动力特性与多体系统宏观动态性能及运动精度之间的映射关系。在此基础上,以含深沟球轴承的曲柄滑块机构为仿真算例,分析轴承间隙与柔性特征对该机构运动位置与速度误差的影响规律。研究表明,轴承内外圈中心形成的相对偏心轨迹的变化特征是由多体系统动态环境下的轴承受载特性决定的;在轴承偏心影响下的机构运动位置与速度误差大小会随曲柄转角位置不同而变化。     

A comparative experimental study on the use of acoustic emission and vibration analysis for bearing defect identification and estimation of defect size

Vibration monitoring of rolling element bearings is probably the most established diagnostic technique for rotating machinery. The application of acoustic emission (AE) for bearing diagnosis is gaining ground as a complementary diagnostic tool, however, limitations in the successful application of the AE technique have been partly due to the difficulty in processing, interpreting and classifying the acquired data. Furthermore, the extent of bearing damage has eluded the diagnostician. The experimental investigation reported in this paper was centred on the application of the AE technique for identifying the presence and size of a defect on a radially loaded bearing. An experimental test rig was designed such that defects of varying sizes could be seeded onto the outer race of a test bearing. Comparisons between AE and vibration analysis over a range of speed and load conditions are presented. In addition, the primary source of AE activity from seeded defects is investigated. It is concluded that AE offers earlier fault detection and improved identification capabilities than vibration analysis. Furthermore, the AE technique also provided an indication of the defect size, allowing the user to monitor the rate of degradation on the bearing; unachievable with vibration analysis.     

具有局部表面损伤的滚动球轴承动力学建模

提出了一种滚动球轴承局部表面损伤故障的动力学分析方法。模型中每个轴承元件具有6个运动自由度,并完整地考虑了陀螺效应、离心力及润滑牵引等动力学因素。通过几何特征的变化对局部表面损伤进行了建模。采用四阶变步长Runge-Kutta-Fehlberg积分法对动力学方程进行了数值求解,并在时域和频域中对动力学响应进行了分析。研究结果表明,由于考虑了润滑剂的牵引效果,计算得到的故障特征频率较纯滚动假设下的计算结果有一定的差异。文中综合考虑了轴承元件的三维运动、相对滑动、润滑效应以及局部表面损伤等因素,因此所提出的模型更为全面、有效和实用。     

Thrust bearing groove race defect measurement by wavelet decomposition of pre-processed vibration signal

Nature of vibration signal from a ball bearing system reveals location of fault and its severity. A proper signal processing technique is required to extract relevant information from a vibration signal. In this work measurement of groove race defect width in thrust bearing is presented by processing vibration signal using wavelet based technique. In the first step, pre-processing of vibration signal is done by multiplying the signal amplitude with its own absolute values. It helps to overcome the problem of detection of weak burst in normal vibration signal retaining sign of the original signal. In the second step, Symlet5 wavelet based decomposition is applied to the pre-processed signal to measure the size of seeded defect in outer groove race of thrust bearing. The decomposition based on Symlet wavelet is preferred because it reduces the ambiguity in detecting the entry point and exit point of the defect as it is having linear phase in nature. Measurement has been done for the groove defect width over the range of 0.4399–1.4854 mm. Measurement of defect has been also verified using image examination. Maximum deviation in result has been found in the cases which have minimum axial load (48 N) for every size of defect. With increase in axial load to 73 N and further to 98 N the bearing system gets properly stressed, which increases the accuracy of measurement. With further increase in axial load to 126 N and above, it has been observed that the burst disappears due to prevailing over-stressed condition of the loading disk and additional stiffness and damping of the flexible shaft at increased load.     

基于小波包的滚动轴承故障特征提取

在深入分析离散小波包变换快速算法的基础上，给出了离散小波包变换快速算法中产生频率混淆的原因，即由正交镜像滤波器的非理想截止特必, 隔点采样和隔点插零的特性共同作用产生的，提出了一种消除频率混淆的算法，利用该算法和原算法，分别对某型滚动轴承内环剥落故障的振动信号进行处理，提取其故障特征，结果表明，原算法由于存在频率混淆，可能掩盖故障特征，提出的新算法，由于很好地消除了频率混淆，能有效地提取滚动轴承局部故障的特征。     

A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing

The paper presents an analytical model for predicting the effect of a localized defect on the ball bearing vibrations. In the analytical formulation, the contacts between the ball and the races are considered as non-linear springs. The contact force is calculated using the Hertzian contact deformation theory. A computer program is developed to simulate the defect on the raceways with the results presented in the time domain and frequency domain. The model yields both the frequency and the acceleration of vibration components of the bearing. The effect of the defect size and its location has been investigated. Numerical results for 6305 deep groove ball bearing have been obtained and discussed. The results obtained from the experiments have also been presented.     

Effect of the raceway defects on the nonlinear dynamic behavior of rolling bearing

The defects on raceways would aggravate the vibration of bearing and greatly influence the bearing performance, in order to monitor the running state of the bearing and detect the early defect, the characteristics induced by the defect must be explored. This paper establishes a bearing dynamic model to explore the effect of raceway defects on the nonlinear dynamic behavior of rolling element bearing. The interaction between ball and races is modeled based on Hertz theory, while the presence of defects changes the ball-race interaction. The effects of defect size, position and number on bearing dynamic behaviors are investigated with the aid of phase trajectories, shaft center orbits, FFT spectra, etc. The results indicate that the defects can make the motion of the system more complicated and induce vibration at some characteristic frequencies, which can be used to recognize the bearing failure at early stage. The proposed research provides useful information for the design and status monitoring of mechanical systems.

     

滚动轴承故障特征的时间—小波能量谱提取方法

振动信号中的周期性冲击现象是诊断滚动轴承各元件故障的重要依据之一,针对滚动轴承故障特征,在小波变换理论基础上提出一种时间—小波能量谱信号处理方法,它能够有效地提取出振动信号中冲击成分的时域和频域特征。利用时间—小波能量谱方法分析正常、外圈故障、内圈故障、滚珠故障等四种状态下滚动轴承的振动信号,并与传统的包络解调分析方法进行对比分析。时间—小波能量谱不仅可以有效提取出冲击特征明显的滚动轴承外圈故障,还能提取出内圈、滚珠等信号特征微弱的滚动轴承故障,而包络解调分析方法只能提取出外圈故障特征而不能提取出滚珠故障、内圈故障特征。结果表明,时间—小波能量普比包络解调分析方法更能有效地提取出振动信号中的冲击信号成分。     

中介轴承故障动力学建模与振动特征分析

中介轴承是航空发动机转子的关键支承部件之一,工作转速高,润滑条件差,易发生故障。基于动力学模型的故障机理研究可以为中介轴承故障诊断提供依据。以Gupta圆柱滚子轴承复杂动力学建模方法为基础,考虑外圈的运动建立了中介轴承动力学模型,通过试验对模型进行验证。在此基础上,分别考虑滚道表面形貌和轴承间隙的变化,建立中介轴承磨损故障动力学模型;针对中介轴承滚道表面剥落等局部损伤故障,考虑滚动体通过损伤区域时趋近量和接触载荷方向的改变,建立中介轴承局部损伤故障动力学模型。利用所建故障动力学模型对不同磨损状态下中介轴承外圈径向振动响应进行研究。研究表明,出现磨损后,振动响应频率中出现若干随机成分;对于局部损伤和磨损的复合故障,随着磨损加剧,振动幅值随之增大,随机成分所占比重增加,损伤的故障特征不明显。     

Active magnetic bearings used as exciters for rolling element bearing outer race defect diagnosis

The active health monitoring of rotordynamic systems in the presence of bearing outer race defect is considered in this paper. The shaft is assumed to be supported by conventional mechanical bearings and an active magnetic bearing (AMB) is used in the mid of the shaft location as an exciter to apply electromagnetic force to the system. We investigate a nonlinear bearing-pedestal system model with the outer race defect under the electromagnetic force. The nonlinear differential equations are integrated using the fourth-order Runge–Kutta algorithm. The simulation and experimental results show that the characteristic signal of outer race incipient defect is significantly amplified under the electromagnetic force through the AMBs, which is helpful to improve the diagnosis accuracy of rolling element bearing׳s incipient outer race defect.     

Characteristics analysis of aero-engine whole vibration response with rolling bearing radial clearance

For the influence of rolling bearing radial clearance on the whole vibration in the aero-engine whole system, a real engine rotorbearing- casing whole model is established. The rotor and casing systems are modeled by means of FEM; the support systems are modeled by lumped-mass model; rolling bearing radial clearance and strong-nonlinearity of Hertz contact force at four different supports are considered. The coupled system response is obtained by the numerical integral method. The characteristics of the whole vibration response are analyzed. For rolling bearing at a typical support, the rotor, outer ring of rolling bearing and casing response characteristics at different rotating speeds are analyzed. The changing law of contact forces for each ball and the global contact forces at different speeds are analyzed. The influence of the radical clearance on the contact forces on the whole vibration is analyzed. The results show that the contact forces will be larger and the acceleration amplitude jumps obviously when the radial clearance is increased, and due to the variable stiffness of the rolling bearing, the natural frequency will appear when the stiffness changes fiercely, that is frequency-locked phenomenon. When the radical clearance is larger and the rotating speed is between two critical speeds, the rotor squeezes the outer ring now and then. Reducing the radical clearance can reduce the whole vibration and increase the rotor’s stability.     

不同轴向载荷下氮化硅全陶瓷轴承润滑特性

全陶瓷球轴承广泛应用在航天航空领域、燃气发动机和极端工况下,然而针对全陶瓷轴承油润滑特性的研究比较少见。以氮化硅6206全陶瓷深沟球轴承作为研究对象,在轴承测振仪上开展陶瓷轴承润滑特性实验研究,采用拟静力学和最小油膜厚度理论通过MatLab的牛顿迭代法得到比较精确的数值解,分析陶瓷轴承的接触载荷、轴向载荷、离心力、最小油膜厚度之间的关系,并通过改变供油量和轴向载荷得到陶瓷轴承在不同工况下的振动规律。实验结果表明：在轴向载荷相同条件下球与外圈之间的接触载荷比球与内圈之间的接触载荷大,轴向位移随着轴向载荷增加呈递增趋势;在轴向载荷一定时,存在一个最佳供油量使轴承振动最小,在干摩擦条件下轴承振动随着轴向载荷增加呈先减少后增大的趋势。