Relative comparison of stiffness and damping properties of double decker high precision and conventional rolling-element bearings

This paper reports the relative comparison of stiffness and damping properties of Double Decker High Precision Bearing (DDHPB) and conventional rolling-element bearings. It has been determined that under different load and speed conditions, DDHPB and the conventional bearings have identical critical speed, comparable net deflection and stiffness. On the contrary, relative damping of the DDHPB, evaluated by rotating speed component of vibrations, at different operating conditions is approximately three times more than that of the conventional bearing. Excitation tests at different speeds have also indicated better damping characteristics of DDHPB as compared to the conventional bearing. This potential of DDHPB permits its use in typical industrial applications where damping is a significant requirement.     

Adaptive combined HOEO based fault feature extraction method for rolling element bearing under variable speed condition

It is still a challenge for condition monitoring and fault diagnosis for rolling element bearings working under variable speed, while some conventional diagnostic methods are useless. Order tracking is commonly used as an effective tool of the non-stationary vibration analysis for rotating machinery and tacho-less order tracking may be more applicable for practical situations, while the key point is to obtain more accurate instantaneous rotating speed. What’s more, the collected bearing fault vibration signals always contain strong background noise that greatly affects the result of fault feature extraction. To solve these problems, a fault feature extraction method is proposed in this study. The Chirplet-based approach was used to estimate some obvious harmonics of instantaneous rotating speed and the average value of these components was regarded as the final instantaneous rotating speed to reduce the estimation error. Since the higher order energy operator (HOEO) can not only improve the signal-to-noise ratio and signal-to-interference ratio, but is also easily applied, an adaptive combined HOEO method based on hybrid particle swarm optimizer with sine cosine acceleration coefficients (H-PSO-SCAC) was constructed to enhance the impulse components, and then, the fault features were extracted by the order spectrum analysis. Simulation and experimental results indicate that the proposed algorithm is effective for rolling element bearings’ fault diagnosis under variable speed condition.     

配对角接触球轴承静态力学特性

根据角接触球轴承实际的工作状态,建立背靠背配对安装形式的角接触球轴承接触模型,计算配对轴承在径向、轴向和力矩载荷联合作用下的载荷分布以及接触应力,并将理论值与Ansys有限元法得出的结果进行对比,验证计算结果的准确性。详细研究了在联合载荷的作用下,配对轴承静态载荷分布以及接触特性的变化规律。研究结果表明:配对角接触球轴承的内圈在联合载荷作用下发生位移,使载荷分布不均匀,接触应力主要集中在载荷对称线附近的部分钢球上,改变联合载荷会使两列轴承载荷分布规律以及接触特性发生变化。     

角接触球轴承组配与凸出量测量方法

生产企业制造组配角接触球轴承时,对不同组合方式和载荷要求的角接触球轴承的组配,可通过不同的凸出量测量方法来实现。     

基于角域AR模型滤波的滚动轴承故障诊断

在齿轮噪源存在的变转速滚动轴承故障诊断过程中,因混合信号中转频分量相对较小,使得基于时频表达的阶比跟踪技术受到限制。虽然基于故障特征频率的角域重采样能提取轴承的故障特征,但这种算法不能确定故障位置,而且可能会出现误判。针对这一问题,提出了基于角域自回归(auto regressive,简称AR)模型滤波的处理方法。该方法利用线调频小波路径追踪算法从降采样处理的混合信号中提取齿轮瞬时啮合频率趋势线并估计转速,根据估计转速信息对原混合信号进行等角度重采样,获得了角域信号。利用角域信号中齿轮啮合振动成分具有周期性的特点,使用AR模型对其滤波,并且对滤波后信号进行包络阶比分析,完成故障判断。通过处理仿真信号和实验信号,验证了该方法不仅能有效地去除齿轮噪声,并且可以判断轴承故障位置。     

评价箔片径向空气轴承载荷性能的一种经验方法

介绍一种简单的“经验法则”来评价箔片空气轴承的载荷性能,它是一种可挠面的动压气体轴承,正在研究其在无油透平机械中的应用。经验法则是基于基本原理和文献中报道的可靠实验数据得出的,通过一个经验值——载荷系数D,将轴承的载荷性能和轴承的尺寸、速度联系起来。在经验法则中,轴承承载力是轴承转速和轴承设计面积的线性函数。轴承载荷系数D和轴承弹性支承结构的设计特点和轴承运行工况(温度、速度)有关。     

On the design and development of hybrid journal bearings: a review

This paper presents a comprehensive review of developments in the design and application of hydrostatic and hybrid journal bearing systems during the last few decades. Revolutionary changes have taken place in the applications of hydrostatic and hybrid journal bearings, from very low‐speed radar to very high‐speed turbo‐machinery and ultra‐precision machine tools requiring high stiffness to improve accuracy. Hydrostatic and hybrid bearings are of interest because of their potential at very high operating speed and heavy load‐carrying capacity. This paper also outlines the analyses done of these types of journal bearings in practical application, which has led to improved bearing design. This review critically discusses the parameters that significantly affect the static and dynamic performance of a journal bearing. This review includes coverage of recent publications in the literature pertaining to hydrostatic and hybrid journal bearings focusing on the influence of parameters such as bearing geometry, supply pressure, flow control devices, fluid compressibility, fluid inertia, journal misalignment, bearing flexibility, surface roughness, and thermal effects. Copyright © 2006 John Wiley & Sons, Ltd.     

Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown that load capacity is a linear function of bearing surface velocity and bearing projected area. Furthermore, it was found that the load capacity coefficient, D, is related to the design features of the bearing compliant members and operating conditions (speed and ambient temperature). Early bearing designs with basic or “first generation” compliant support elements have relatively low load capacity. More advanced bearings, in which the compliance of the support structure is tailored, have load capacities up to five times those of simpler designs. The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new Oil-Free turbomachinery systems.     

Prediction of the friction torque in grease lubricated angular contact ball bearings using grey system theory

The development of special grease makes it possible for angular contact ball bearings to operate at high speed and temperature; however, as an important performance parameter, friction torque of bearings lubricated with grease is much greater than that of bearings lubricated with oil-air, and heat generation due to frictional loss is also greater, so it is necessary to predict the friction torque occurring in grease lubricated angular contact ball bearings. Based on grey system theory, a new prediction methodology for bearing friction torque is proposed which capitalizes on the notion that the information about friction torque of angular contact ball bearing is generally poor, incomplete and uncertain. A grey prediction model, GM (1, N) model, is presented to predict the friction torque in grease lubricated angular contact ball bearings. Several experiments on the friction torque of grease lubricated angular contact ball bearings were conducted to model and validate the effectiveness of the GM (1, N) model through on-line and off-line approaches. Experimental results show that about 90% of bearing friction torque under varying speed can be predicted in the on-line prediction; above 85% of bearing friction torque under varying speed and different loads can be predicted in the off-line prediction. Comprehensive analysis shows that, the GM (1, N) model performs very well for both modeling data and model validation data under different loads, varying bearing speed and work cycles, the proposed methodology can be used to predict bearing friction torque with good accuracy and robustness.

     

A new fault diagnosis algorithm for helical gears rotating at low speed using an optical encoder

Helical gears are widely used in gearboxes due to its low noise and high load carrying capacity, but it is difficult to diagnose their early faults based on the signals produced by condition monitoring systems, particularly when the gears rotate at low speed. In this paper, a new concept of Root Mean Square (RMS) value calculation using angle domain signals within small angular ranges is proposed. With this concept, a new diagnosis algorithm based on the time pulses of an encoder is developed to overcome the difficulty of fault diagnosis for helical gears at low rotational speeds. In this proposed algorithm, both acceleration signals and encoder impulse signal are acquired at the same time. The sampling rate and data length in angular domain are determined based on the rotational speed and size of the gear. The vibration signals in angular domain are obtained by re-sampling the vibration signal of the gear in the time domain according to the encoder pulse signal. The fault features of the helical gear at low rotational speed are then obtained with reference to the RMS values in small angular ranges and the order tracking spectrum following the Angular Domain Synchronous Average processing (ADSA). The new algorithm is not only able to reduce the noise and improves the signal to noise ratio by the ADSA method, but also extracts the features of helical gear fault from the meshing position of the faulty gear teeth, hence overcoming the difficulty of fault diagnosis of helical gears rotating at low speed. The experimental results have shown that the new algorithm is more effective than traditional diagnosis methods. The paper concludes that the proposed helical gear fault diagnosis method based on time pulses of encoder algorithm provides a new means of helical gear fault detection and diagnosis.     

An investigation of the effects of measurement noise in the use of instantaneous angular speed for machine diagnosis

In order to discriminate small changes for early fault diagnosis of rotating machines, condition monitoring demands that the measurement of instantaneous angular speed (IAS) of the machines be as accurate as possible. This paper develops the theoretical basis and practical implementation of IAS data acquisition and IAS estimation when noise influence is included. IAS data is modelled as a frequency modulated signal of which the signal-to-noise ratio can be improved by using a high-resolution encoder. From this signal model and analysis, optimal configurations for IAS data collection are addressed for high accuracy IAS measurement. Simultaneously, a method based on analytic signal concept and fast Fourier transform is also developed for efficient and accurate estimation of IAS. Finally, a fault diagnosis is carried out on an electric induction motor driving system using IAS measurement. The diagnosis results show that using a high-resolution encoder and a long data stream can achieve noise reduction by more than 10 dB in the frequency range of interest, validating the model and algorithm developed. Moreover, the results demonstrate that IAS measurement outperforms conventional vibration in diagnosis of incipient faults of motor rotor bar defects and shaft misalignment.     

高速角接触球轴承中的冲击滑动研究

高速角接触球轴承中,球与保持架的碰撞会导致球与滚道的冲击滑动,从而引起滚道划伤和轴承早期失效。为探究球与保持架的冲击碰撞导致的瞬时滑动,以某高速角接触球轴承为研究对象,通过对联合载荷下角接触球轴承的动力学仿真,分析了变速工况及保持架结构参数对球与保持架的冲击碰撞、球与滚道的冲击滑动以及零件磨损率的影响。结果发现,加减速及恒定转速下,球与保持架的运动呈现周期性变化;由于球进入和离开径向载荷区域时公转角速度的变化,球与保持架碰撞并导致球相对内、外圈滚道发生冲击滑动;为适应球公转角速度的变化,适当增大兜孔间隙,可以减小球与保持架兜孔碰撞力的大小和频率,从而减小球与滚道的冲击滑动以及保持架的磨损率。     

Application of Instantaneous Rotational Speed to Detect Gearbox Faults Based on Double Encoders

Considerable studies have been carried out on fault diagnosis of gears, with most of them concentrated on conventional vibration analysis. However, besides the complexity of gear dynamics, the diagnosis results in terms of vibration signal are easily misjudged owing to the interference of sensor position or other components. In this paper, an alternative gearbox fault detection method based on the instantaneous rotational speed is proposed because of its advantages over vibration analysis. Depending on the timer/counter-based method for the pulse signal of the optical encoder, the varying rotational speed can be obtained e ectively. Owing to the coupling and meshing of gears in transmission, the excitations are the same for the instantaneous rotational speed of the input and output shafts. Thus, the di erential signal of instantaneous rotational speeds can be adopted to eliminate the e ect of the interference excitations and extract the associated feature of the localized fault e ectively. With the experiments on multistage gearbox test system, the di erential signal of instantaneous speeds is compared with other signals. It is proved that localized faults in the gearbox generate small angular speed fluctuations, which are measurable with an optical encoder. Using the di erential signal of instantaneous speeds, the fault characteristics are extracted in the spectrum where the deterministic frequency component and its harmonics corresponding to crack fault characteristics are displayed clearly.     

Effect of Silicon Nitride Balls and Rollers on Rolling Bearing Life

Three decades have passed since the introduction of silicon nitride rollers and balls into conventional rolling-element bearings. For a given applied load, the contact (Hertz) stress in a hybrid bearing will be higher than that of an all-steel rolling element bearing. The silicon nitride rolling-element life as well as the lives of the steel races were used to determine the resultant bearing life of both hybrid and all-steel bearings. Life factors were determined and reported for hybrid bearings. Under nominal operating speeds, the resultant calculated lives of the deep-groove, angular-contact, and cylindrical roller hybrid bearings with races made of post-1960 bearing steel increased by factors of 3.7, 3.2, and 5.5, respectively, from those calculated using the Lundberg-Palmgren equations. An all-steel bearing under the same load will have a longer life than the equivalent hybrid bearing under the same conditions. Under these conditions, hybrid bearings are predicted to have a lower fatigue life than all-steel bearings by 58% for deep-groove bearings, 41% for angular contact bearings, and 28% for cylindrical roller bearings.     

Doppler Effect removal based on instantaneous frequency estimation and time domain re-sampling for wayside acoustic defective bearing detector system

The phenomenon of Doppler Effect in the acoustic signal recorded by the wayside acoustic defective bearing detector (ADBD) leads to the difficulty for fault diagnosis of train bearings with a high moving speed, which is a barrier that would badly reduce the effectiveness of online defect detection. In order to improve the performance of condition monitoring of the bearings on a passing train with microphones amounted besides the railway, the elimination of the Doppler Effect should be solved firstly. An effective method for removing the Doppler Effect embedded in the source signal is presented in this paper. The Short Time Fourier Transform-Viterbi Algorithm (STFT-VA) is applied to obtain instantaneous frequency estimation of the distorted signal. According to the acoustic theory of Morse, the non-linear data fitting is then carried out to get the fitting instantaneous frequencies. The necessary parameters for time domain interpolation re-sampling, which is totally based on the kinematic analysis, are acquired from the fitting curve and the re-sampling sequence could be established in the time domain. As a result of the preceding steps, the fault diagnosis for the train bearings could be implemented with the restored signal. The effectiveness of this proposed method is verified by means of a simulation with three adjacent frequencies and an experiment with practical acoustic signals of train bearings with a crack on the outer race and the inner race. The results of the simulation and the experiment indicate that the proposed method has an excellent performance in removing Doppler Effect, and could be well employed to the condition monitoring and fault diagnosis of train bearings with a high moving speed.     

随机风载作用下风力发电机齿轮传动系统动态可靠性分析

运用最小二乘支持向量机(Sparse least squares support vector machines,SLS-SVM)机器学习方法建立风场随机风速模型,根据随机风速模型和空气动力学理论得到随机风引起的系统外部载荷激励,建立考虑齿轮时变啮合刚度和滚动轴承时变刚度的风力发电机行星齿轮传动系统齿轮—轴承耦合动力学模型,并对动力学模型进行仿真计算,分别得到各齿轮副的动态啮合力和滚动轴承动态接触力。以此为基础,将载荷作用过程视为随机过程,推导出随机载荷作用下的等效载荷累计分布函数。根据应力—强度干涉理论建立风力发电机齿轮传动系统各齿轮和轴承的动态可靠性模型,利用二阶矩和摄动方法求出各齿轮、轴承的动态可靠性指标,并计算出动态可靠度,研究各齿轮、轴承和传动系统的动态可靠度随时间的变化规律,为风力发电机齿轮传动系统动态可靠性设计奠定了基础。     

Thermo-mechanical analysis of angular contact ball bearing

The thermal-mechanical character, which is difficult to ensure because of the lack of a corresponding theory and tool, has a significant effect on the dynamics of bearings. It even leads to a sudden failure of bearings in a working situation. In this research, a thermal deformation model was established, based on the analysis of temperature effect on the basic size of angular contact ball bearing. And the transmission from rolling size to bearing axial stiffness was explicit. On the basis of the variation of Hertz contact stiffness and the change of initial contact angle of angular contact ball bearing caused by temperature rise, a “Thermo- mechanical” model of bearing was proposed. According to this model, using the corresponding calculation procedure programmed by MATLAB, the effect of bearing temperature on the axial stiffness has been studied. And the correctness of this model was verified with experiments. Some design suggestions have been made for the decision of bearing preload: to prevent the bearing failure caused by overheating.     

滚动轴承内圈温度无线监测技术

温度是反映滚动轴承运行状态的重要指标之一,高速运行中轴承旋转套圈的温度远高于静止套圈温度,实现轴承旋转套圈（通常为内圈）的实时温升监测对保证运行安全尤为重要。基于电气和机械设计技术的协同,提出一种滚动轴承内圈温度无线监测方案,将测试系统嵌入轴承锁紧螺母中,利用锁紧螺母与轴承接触配合实现对轴承内圈温度采集。设计研究集成温度测试、无线数据传输及无线电能供给电路。重点实现电能无线供给以满足轴承旋转套圈温度持续监测的电能需求。最后通过对32008圆锥滚子轴承温度采集,验证该方案的可行性。该方法在保障轴承完整性的条件下能实现轴承旋转套圈温度的监测,为轴承状态监测和热特性试验研究提供了新的技术手段,解决了实际工况下轴承旋转套圈测温难题。     

An analysis of axial deflection of double‐decker high‐precision bearings vis‐à‐vis conventional ball bearings

Axial deflection of double‐decker high‐precision bearings (DDHPBs) under the influence of axial loads has been theoretically analyzed and has been compared with conventional angular contact and deep‐groove ball bearings of the same bore and outer diameter. The analysis, in general, indicates that the ratio of the axial deflection of DDHPBs to that of the conventional angular contact and deep‐groove ball bearings under the influence of identical axial loads is less than unity. The analysis also indicates that angular contact ball bearings mounted back to back for taking the axial load from both directions can be replaced by DDHPBs, which have less axial deflection and longer life under identical applied loads than angular contact and deep‐groove ball bearings. The better dynamic response characteristics, energy efficiency, uniform stress distribution, lower indentation and deflection on the elements of DDHPBs indicate that DDHPBs have relatively better performance characteristics, higher fatigue life and may have higher potential in various industrial applications as compared to that of the conventional bearings under identical operating conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

Quantitative diagnosis of fault severity trend of rolling element bearings

The condition monitoring and fault diagnosis of rolling element bearings are particularly crucial in rotating mechanical applications in industry. A bearing fault signal contains information not only about fault condition and fault type but also the severity of the fault. This means fault severity quantitative analysis is one of most active and valid ways to realize proper maintenance decision. Aiming at the deficiency of the research in bearing single point pitting fault quantitative diagnosis, a new back-propagation neural network method based on wavelet packet decomposition coefficient entropy is proposed. The three levels of wavelet packet coefficient entropy(WPCE) is introduced as a characteristic input vector to the BPNN. Compared with the wavelet packet decomposition energy ratio input vector, WPCE shows more sensitive in distinguishing from the different fault severity degree of the measured signal. The engineering application results show that the quantitative trend fault diagnosis is realized in the different fault degree of the single point bearing pitting fault. The breakthrough attempt from quantitative to qualitative on the pattern recognition of rolling element bearings fault diagnosis is realized.