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.     

Determination of magnetic flux density on the surfaces of rolling-element bearings as an indication of the current that has passed through them—an investigation

This paper introduces a theoretical model to determine the developed magnetic flux density on the inner and outer surfaces of the inner race and outer race, and on the surface of rolling-elements of a rolling bearing operating under the influence of an electric current. The flux density, analytically determined, is compared with that of the flux density developed on the surfaces of races and rolling-elements of bearings tested on the bearing test-up under the influence of an electric current. The magnetic flux density on the surfaces of damaged bearings of motors and alternators has also been measured and the theoretical model is used to determine the amount of current flow through the damaged bearings. The current flow through the bearings, thus established, has been compared with that of the current evaluated by the measurement of shaft voltage and bearing resistance. The model has the potential to ascertain the cause of failure by current passage and to establish the amount of flow of leakage current through the bearings by determining the magnetic flux density on the surfaces of rolling-element bearings. The current flow, thus established, together with the measurement of the shaft voltage, allow the bearing impedance to be established.     

A dynamic model of ball bearing for simulating localized defects on outer race using cubic hermite spline

In this paper a dynamic model is presented for predicting the vibration behavior of a ball bearing under the influence of localized defects on the outer race. The calculation of contact force is based on Hertzian contact deformation theory. The pulse generated by the ball striking the defect on outer race is modeled by using the blending functions of the cubic hermite spline. The effect of change in the angular position of the defect, size of the defect on outer race, multiple defects on outer race and the variation of load on the vibration amplitude is predicted by this model. A computer program in MATLAB is developed and the governing equation of motion is solved by Euler’s method. The numerical results are presented as a function of variation of the geometry of the outer race due to the impact at the defect and normal race contact w.r.t. time and the conclusion about the health of the bearing is determined by the spectral analysis. To validate the results, experimentation has also been performed.     

A Wireless Sensor Telemeter for in situ Cage Vibration Measurement and Corroboration with Analytical Results

ABSTRACT

This article presents both experimental and analytical investigations on the dynamic behavior of the cage in a ball bearing. For the experimental investigation, a wireless sensor telemeter system was designed and developed to monitor the cage motions. The sensor, which was integrated on the bearing cage, is composed of a commercially available capacitor–inductor (LC) circuit. The LC circuit on the rotating cage was coupled to a transceiver that was stationary and positioned in close proximity to the cage. In order to achieve the objective of the analytical investigation, the explicit finite element method (EFEM) was used to simulate the bearing cage. The EFEM cage model was then combined with the dynamic bearing model to simulate the cage motion during operation. The results from the experimental measurement using the telemeter were then compared with the analytical modeling. The developed telemeter demonstrated the capability of the cage telemeter in detecting various bearing frequencies. These include the cage frequency, shaft frequency, and ball pass frequency on the outer race (BPFO), which was introduced by creating a spall on the bearing outer race. Compared to standard accelerometers that are commonly used to measure vibrations on the bearing housing, the cage telemeter has shown advantages in sensing cage motions and detecting bearing defects regardless of the location of the damage. Analytical simulation using the EFEM cage model correlated well with the experimental results and provided more insight into the bearing cage dynamics.     

电磁轴承-无轴承电机系统在转子主动控制的应用研究

主动磁轴承借助电磁力来控制转子的振动,无轴承电机在实现转矩控制的同时实现电机的悬浮控制。本文在对永磁偏置三自由度电磁轴承和两自由度无轴承电机的磁悬浮机理一般性描述的基础上,分析了其产生的悬浮控制力。并以转子电磁振动为研究对象,结合电磁轴承和无轴承电机的特点,提出利用一种新型的五自由度磁悬浮异步电机作为执行机构对转子电磁振动进行主动控制,实现了转子系统稳定工作。此系统可以有两方面的应用,既可以用做转子的支承,也可以用做转子振动主动控制的增稳。     

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.     

径向磁悬浮轴承参数不确定控制的研究

研究了基于状态空间算法的径向磁悬浮轴承参数不确定H∞ 控制 ,将磁悬浮轴承的位移和速度变量直接反馈 ,设计了H∞ 状态反馈控制器 ,解决了轴向重载磁悬浮轴承系统中的关联不确定性问题。仿真结果表明 ,在所考虑的参数不确定范围内控制系统具有鲁棒稳定性。     

Defect diagnostics of roller bearing using instantaneous frequency normalization under fluctuant rotating speed

We investigated the feasibility of utilizing the normalized characteristic frequencies for diagnosing the defective roller bearings in case of fluctuant rotating speeds. The time-frequency distributions of the envelope signals of the vibration data were constructed through the Empirical mode decomposition (EMD) as well as the instantaneous frequency calculation. The bearing defect-related frequencies were then normalized with respect to the instantaneous rotation frequency of the shaft so that the factor of the rotating speed fluctuation was removed; thus the characteristic frequencies of bearing malfunctions could be observed in terms of constant values. The magnitude distributions of the marginal envelope spectra at the corresponding normalized bearing defect-related frequencies were extracted as the feature vectors. The Support vector machine (SVM) was used to classify the extracted feature vectors of different bearing fault classes. A test rig of roller bearing system was performed to illustrate the different bearing faults, including different levels of inner race defect, outer race defect and roller defect. The analysis results demonstrate the capability and effectiveness of the proposed approach for accurately identifying the bearing defects in case of fluctuant rotating speed.     

液体动静压球轴承轴心运动轨迹研究

为研究外载荷对轴承转子系统稳定性的影响,以小孔节流的液体动静压球轴承转子系统为研究对象,建立液体动静压球轴承转子系统动力学模型。通过求解轴承润滑数学模型获得非线性油膜力,分析转子所受到的外载荷,采用欧拉算法预测出轴心下一个时刻位移、速度和加速度,并分析转子系统质量、不平衡载荷和阶跃载荷对转子回转精度的影响。结果表明：随着转子系统质量的增加,所需平衡的油膜力增加,轴心振动幅度增加,从而导致转子回转精度降低;相对于不考虑不平衡载荷,考虑不平衡载荷后其振动形态为椭圆且振动幅值增大,减小不平衡值将减小振幅并提高旋转精度;随着阶跃载荷的增加,达到平衡所需的时间也增加。     

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.     

三点接触球轴承打滑动力学分析与验证

三点接触球轴承是航空发动机中的关键基础件。目前对三点接触球轴承的仿真分析多基于拟静力学模型,对于打滑、擦伤等特殊行为缺乏解释,而滚球打滑易引起滚道磨损、蹭伤等故障。在对轴承元件进行受力分析的基础上,引入滚球与左右半内圈的接触状态判断条件,采用动力学方法对三点接触球轴承进行了打滑分析。然后,分析了设计接触角及运行参数对轴承打滑率的影响。最后,通过实验研究了滚球通过内圈频率及滚球公转转速随轴向载荷及内圈转速的变化规律,并与动力学模型仿真值进行对比验证了方法的有效性。研究结果表明：轴向载荷越小或转速越高,打滑率越大;在转速和载荷工况条件相同的情况下,轴承打滑率随着设计接触角的增加而增加;而在不同转速工况下,轴承发生打滑的轴向载荷临界值不同,其数值随转速的升高而增加。     

Auto-Eliminating Clearance Auxiliary Bearing Device for Active Magnetic Bearing Systems

An auto-eliminating clearance auxiliary bearing device (ACABD) for active magnetic bearings (AMBs) has recently been designed and a prototype system was tested in this study. ACABD mainly consists of a series of connected tilting supports. In this design, a ball bearing is directly mounted on a rotor as the auxiliary bearing in an AMB system. The outer race of this ball bearing is surrounded by these supports. In the open position, there exists an initial protective clearance between the outer race of the ball bearing and the tilting supports. When the bearing-mounted rotor drops on these supports due to an AMB failure, the friction between the outer race of the ball bearing and the tilting support rotates these supports to eliminate the clearance and recenter the rotor. Due to elimination of the clearance, the possibility of backward whirl of the rotor is eliminated. The movement mechanism of this device is analyzed kinematically. The rotation of these supports, elimination of the protective clearance, as well as the rotor rotating stability after the clearance elimination are discussed from the perspective of statics. Furthermore, a preliminary prototype experimental rig was developed to demonstrate the feasibility of the ACABD after AMB system failure. Experimental results show that, after the AMB system failed, the ACABD immediately eliminated the clearance between the outer race of the ball bearing and the supports and pushed the rotor center close to the initial position.     

基于旋滚比的电主轴轴承预紧力优化研究

为研究不同工况下轴承预紧力对电主轴轴承动力学的影响规律,基于外轨道控制理论,建立了一种以旋滚比可优化的轴承预紧力动力学模型。通过分析高速状态下滚动体载荷和特征参数动态变化过程,构建综合考虑滚动体滚动、自旋转、陀螺运动和离心力的轴承动力学分析模型,在此基础上,计算旋滚比动态变化结果;研究Jones发现的阈值与旋滚比之间的动态定量映射关系;以轴承滚动体打滑状态为优化目标,使用MATLAB仿真分析不同工况下轴承最佳预紧力。建模分析表明,轴承旋滚比大小可以反映轴承预紧效果,也可实现轴承预紧力动态定量优化。     

Rotordynamic Analysis of a Shaft Using Magnetorheological and Nanomagnetorheological Fluid Journal Bearings

The rotordynamic behavior of a system supported by journal bearings is critical to its reliability. A suitable method of control of the orbital motion of a shaft in a journal bearing is the use of smart lubricants, in effect fluids with controllable physical properties. There are various categories of smart lubricants. One class of smart lubricants, magnetorheological fluids, are produced as a dispersion of magnetic particles in a carrier fluid, which is usually a conventional lubricant. These particles form chains under the influence of a magnetic field, which hinder the lubricant flow, thus changing its apparent viscosity. Magnetorheological fluids (MRFs) exhibit high yield stress, low delay of response, and relatively low friction while not in their active state. A subcategory of MRFs, nanomagnetorheological fluids (NMRFs) with particle size on the nanometer scale, exhibits lower yield stress than MRFs but display high viscosity. The effect of the MRFs and NMRFs on the rotordynamic behavior of a shaft is calculated through a combined finite element and computational fluid dynamics analysis. Though the MRF with the specific geometrical configuration of the bearing is not sufficiently activated and therefore does not improve the performance of the magnetorheological journal bearing, the NMRF has the ability of limiting up to 82% the amplitude of the vibrations of the shaft.     

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.     

Comparison of Power Losses and Temperatures between an All-Steel and a Direct Outer Ring–Cooled,Hybrid 133-mm-Bore Ball Bearing at Very High Speeds

Next-generation aircraft engines will have to face more stringent requirements for reliability, thrust to weight, efficiency, environment protection, and profitability. These requirements affect all engine modules and components, including rolling element bearings. To cope with the above-mentioned requirements, next-generation aircraft engine main shaft bearings will operate under higher loads, speeds, and temperatures and increased reliability. In addition, lighter weight components are desirable. Hence, new material and cooling technologies including weight- and stress-optimized designs need to be developed.

In this article, the experimental investigation results of a novel main shaft ball bearing featuring ceramic balls, direct outer ring cooling, squeeze film damping, as well as surface-nitrided raceways are presented. Bearing rig testing under typical aircraft engine flight conditions has been performed. Savings for oil flow quantity of more than 45% and for power loss of more than 15% were identified. Outer ring temperature reductions of more than 20 K were achieved due to the use of ceramic ball material and the direct outer ring cooling concept. The ultra-high-speed capability of the bearing was demonstrated. Rotational speeds of 24,000 rpm were achieved at bearing temperatures below 200°C. The fundamental experimental results including oil and bearing temperature distribution, power dissipation, and bearing efficiency are presented. In addition, experimental power loss and temperature results are compared with data for a conventional all-steel bearing.     

浮环轴向长度对高速轻载涡轮增压器转子系统振动特性影响研究

浮环轴承内外轴向长度结构参数会影响油膜压力分布与偏心率,产生显著分频振动而引发高速轻载涡轮增压器转子非线性振动故障。基于流体润滑理论和浮环力矩平衡方程,推导了含浮环轴承的涡轮增压器转子系统动力学方程,揭示浮环轴承轴向长度与转子系统振动响应之间的关系。以某型汽油机用涡轮增压器转子系统为例,分析浮环内、外轴向长度对轴承油膜压力、偏心率等动力特性的影响,构建转子系统动力学有限元模型,通过三维振动瀑布图研究不同浮环轴向长度下转子系统频域瞬态振动响应,结果表明：浮环内轴向长度从2.6增加到4.6 mm,导致浮环转速升高,最大内油膜压力减小,轴颈偏心率降低,分频幅值增加且出现分频的轴颈转速由142 kr/min降至76 kr/min,更易产生明显的非线性涡动现象;浮环外轴向长度从3.6增加到6.15 mm,使浮环转速降低,最大外油膜压力变小,浮环偏心率及轴颈相对浮环的偏心率减小,低转速下分频幅值减少且出现分频的轴颈转速由10 kr/min升至22 kr/min,可抑制转子系统过早发生非线性涡动,为浮环轴承结构参数设计与试验提供理论支撑。     

Simulation and Control of an Active Tilting-Pad Journal Bearing

This study developed an active tilting-pad journal bearing with a feedback control system to regulate the orbit of a rotating shaft. The control is implemented by means of linear actuators installed behind the pivot of each pad, which allow the radial motion of the pads in real time. The control design uses the linear feedback of the state variables of the bearing-rotor system, with the feedback gains determined by the optimization of a quadratic performance index. The optimization is based on a linear spring-mass model that incorporates the direct stiffness and damping elements associated with each of the bearing pads. This linear model is found by the simulation of the system under small perturbations using a nonlinear Reynolds equation model. The nonlinear model is capable of simulating the radial motions of the pads by the actuators and is used to verify the effectiveness of the feedback control. It is shown that certain design parameters in the quadratic performance index may be used to determine both the stiffness and the damping of the closed-loop bearing system and that the shaft orbit can be thereby suitably regulated.     

动车组转向架轴承局部损伤振动特性分析

针对动车组转向架轴承,根据轴承故障产生机理建立了轴承故障动力学工程模型。模型充分考虑了车轴弯曲刚度、轴承间隙及滚动体和滚道间的非线性接触力等因素,并包含内圈、外圈以及滚动体故障轴承动力学模型,使用龙格库塔数值积分方法进行了动力学仿真分析。针对实际轴承搭建实验台,对不同故障类型及不同程度故障进行了实际测试。仿真分析与实验结果吻合度较高,最大误差不超过5%,证明了该动力学模型的有效性。     

Computational and analytical studies of the processes in electromagnetic bearings in adjustment of the rotor of a turbine engine

The stability of an electromagnetic bearing control system-rotor system with a nonlinear dependence of the magnetic force on the control current is studied by analytical and experimental methods. The possibility of implementing an electromagnetic suspension of a rotor in the absence of currents of initial magnetic biasing is demonstrated. The advantages and disadvantages of such an implementation of the control system are determined. A program for calculating the time evolution of the motion of a rotor on electromagnetic bearings is developed and implemented in practice. A technique for verifying the program under conditions where initial data for calculations are not known accurately is proposed.