倾覆力矩对推力球轴承疲劳寿命的影响

由于滚动轴承标准中推力球轴承基本额定寿命的计算没有考虑倾覆力矩的影响,造成其误差较大,针对此问题,考虑了推力球轴承在轴向力和倾覆力矩作用下钢球的实际载荷分布,用Lundberg和Palmgren方法计算了轴承的疲劳寿命,并在此基础上拟合出了倾覆力矩与增量当量载荷之间的关系,对滚动轴承标准中推力球轴承基本额定寿命的计算公式进行了修正,计入了倾覆力矩的影响。修正后的寿命计算方法不仅简便,而且准确。     

Rolling Bearing Service Life Based on Probable Cause for Removal—A Tutorial

In 1947 and 1952 G. Lundberg and A. Palmgren developed what is now referred to as the Lundberg-Palmgren model for rolling bearing life prediction based on classical rolling-element fatigue. Today, bearing fatigue probably accounts for less than 5% of bearings removed from service for cause. A bearing service life prediction methodology and tutorial indexed to eight probable causes for bearing removal, including fatigue, are presented that incorporate strict series reliability; Weibull statistical analysis; available published field data from the Naval Air Rework Facility; and ～224,000 rolling-element bearings removed for rework from commercial aircraft engines. Bearing service life L_serv can be benchmarked and calculated to the bearing L₁₀ fatigue life as follows: L_serv = X^1/m L₁₀, where X is the number of bearings removed from service because of fatigue divided by the total of all bearings removed from service regardless of cause and m is the Weibull modulus of the bearings removed from service. The most conservative bearing L₁₀ service life calculation is obtained assuming an exponential distribution where m = 1.1. Of the ～224,000 commercial engine bearings removed from service for rework, 1,977 or 0.88% were rejected because of fatigue. From the Naval Air Rework Facility bearing data, eliminating rolling–element fatigue as a cause for removal, the L₁₀ service life of these bearings would increase by approximately 3%.     

A finite element model for rolling contact fatigue of refurbished bearings

Bearing refurbishing has become a popular method of extending the life of rolling element bearings. In the refurbishing process the raceways of the bearing may be ground to remove any surface damage prior to repolishing and reassembly with larger sized rolling elements. In the current study a continuum damage mechanics finite element model was developed to quantify the damage in original and refurbished bearings. After calculating the damage accumulation for a set number of contact cycles with the original bearing geometry, refurbishing is simulated by removing a layer of the original surface. The refurbished microstructural model is then subjected to additional computational contact cycles until a fatigue crack reaches the surface, signifying failure. This model preserves the fatigue damage accumulated prior to refurbishing and evaluates its influence on the refurbished bearing fatigue life. All refurbished bearing surfaces showed a significant amount of life after refurbishing with L₁₀ lives from the point of refurbishment, varying from 20% to 94% of the original L₁₀ life. The results indicate that the remaining life of the refurbished bearing population is inversely related to the time before refurbishing and is proportional to the depth of the regrinding. Results obtained from this investigation are in good agreement when compared to the Lundberg-Palmgren bearing life equation modified for analyzing the life of a refurbished bearing.     

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.     

滚动轴承疲劳寿命数值仿真技术的研究

建立了滚动轴承疲劳寿命计算的数学模型,运用Monte-Carlo方法对其实验数据进行模拟,编制出相应的计算程序并建立了滚动轴承疲劳寿命预测系统.在计算机上完成滚动轴承寿命计算、数值模拟和滚动轴承的疲劳寿命的预测.     

A new approach to detection of defects in rolling element bearings based on statistical pattern recognition

The paper presents a new approach to the classification of rolling element bearing faults by implementing statistical pattern recognition. Diagnostics of rolling element bearing faults actually represents the problem of pattern classification and recognition, where the key step is feature extraction from the vibration signal. Characterization of each recorded vibration signal is performed by a combination of signal's time-varying statistical parameters and characteristic rolling element bearing fault frequency components obtained through the envelope analysis method. In this way, an 18-dimensional vector of the vibration signal feature is obtained. Dimension reduction of the 18-dimensional feature vectors was performed afterward into two-dimensional vectors representing the training set for the design of parameter classifiers. The classification was performed in two classes, into defective and functional rolling element bearings. Main trait of parameter classifiers is simplicity in their design process, as opposed to classifiers based on neural networks, which employ complex training algorithms.     

Vibration response of rigid rotor in unloaded rolling element bearing

Rolling element bearings appear in nearly 90% of all rotating machinery. Their dynamic performance is often the limiting factor in the performance of the machines that use them. The specific construction of a bearing has a decisive influence on its dynamic behaviour. The paper defines a new vibration model of a rigid rotor supported by rolling element bearings. By application of the defined model, the parametric analysis of the influence of internal radial clearance value and number of rolling elements influence on rigid rotor vibrations in unloaded rolling element bearing was performed. The defined vibration model and parametric analysis were verified experimentally. The results of experimental analysis are also presented in this paper.     

Reevaluation of Rolling Element Bearing Load-Life Equation Based on Fatigue Endurance Data

The load-life exponents used in the modified life rating equation for rolling element bearings were determined by statistical analysis of the experimental data generated in the 1940s, following Lundberg and Palmgren's seminal work. Based on fracture mechanics arguments, the fatigue life is known to be inversely proportional to the square root of the size of the nonmetallic inclusions. However, modern high-performance vacuum induction melt–vacuum arc remelt (VIMVAR) bearing steels are clean and nonmetallic inclusions are no longer the weak link. Fatigue life predictions (L₁₀ life) for modern bearings using the modified load-life relations greatly underpredict observed life. Hence, there is a need to update parameters of these equations using more recent life data. Based on the endurance data reported in Harris and McCool (1), validation analysis of the modified life rating equation was performed to reevaluate the values of load-life exponent for both ball and cylindrical roller bearings. The results from this study indicate that the load-life exponent for ball bearings should be 4.1, instead of 3, and for roller bearings it should be 5.5, instead of 3.33. Bearing L₁₀ life calculated using the corrected load-life exponents values shows better agreement with observed life. Details of the sampling technique used for reducing epistemic uncertainty in experimental data and the process of statistical reevaluation using Bayesian updating are discussed in detail. The accuracy of reevaluated results is presented using logarithmic plots of the ratio of predicted to actual fatigue lives for all data samples.     

滚动轴承动力特性测试方法

轴承的动力特性对转子－轴承系统的动力特性有重要的影响。但至今，滚动轴承的动力特性仍缺乏系统的资料，在许多情况下，将滚动轴承简化为无阻尼的定常弹性元件。本文分析了滚动轴承动力特性的主要影响因素，介绍了滚动轴承动力特性的两种测试方法，并以某航空轴承为例作了具体测试，取得了比较一致的结果。本文提出的方法可作为建立滚动轴承动力特性数据库的基本手段。     

滚动轴承疲劳故障在线诊断的研究

通过对滚动轴承振动信号的在线监测提取出对疲劳故障敏感的参数：峭度、功率谱故障频带能量值、小波包故障频带能量值．选择足够的具有代表性的样本数据训练神经网络,用训练好的神经网络进行在线诊断,可以得出轴承发生疲劳故障的程度,再经过共振解调法诊断出轴承具体损伤的元件,实验表明本方法对滚动轴承的疲劳故障能正确诊断。该监测和诊断方法对其他设备的监测和诊断也有重要的意义。     

New Stress-Based Fatigue Life Models for Ball and Roller Bearings

New stress-based life models are introduced to define “dynamic stress capacity” in rolling bearings for the first time. The generalized stress capacity equations are formulated, for both point and line contacts, in terms of distinct geometrical and materials parameters while the empirical constants are now material independent. Life equations are first developed for individual rolling element to race contacts and then statistically combined to estimate lives of both races, rolling elements, and, finally, the whole bearings for both ball and roller bearings. An estimate of the empirical constant for the ball bearing equation is derived by regression analysis of available experimental data. The applicable constant for roller bearings is then derived by relating the ball and roller bearing constants to the fundamental subsurface fatigue hypothesis applicable to both point and line contacts. For AISI 52100 bearing steel at room temperature, life predictions with the new stress-based equations are in complete agreement with those currently provided by widely used load-based formulations, where the empirical constant contains the elastic properties of AISI 52100 bearing steel. In addition to these life equations based on the magnitude and depth of maximum orthogonal subsurface shear stress and the volume of material stressed, a new model that eliminates life dependence on the depth of maximum orthogonal shear stress and relates life to only the subsurface maximum shear stress and the stressed volume is presented. Though the predicted life estimates with the currently used and newly introduced life models are comparable in the contact stress range of 2 to 3 GPa, the new model provides significantly higher lives at low contact stresses.     

Effect of Roller Geometry on Roller Bearing Load–Life Relation

Cylindrical roller bearings typically employ roller profile modification to equalize the load distribution, minimize the stress concentration at roller ends, and allow for a small amount of misalignment. The 1947 Lundberg-Palmgren analysis reported an inverse fourth-power relation between load and life for roller bearings with line contact. In 1952, Lundberg and Palmgren changed their load–life exponent to 10/3 for roller bearings, assuming mixed line and point contacts. The effect of the roller–crown profile was reanalyzed in this article to determine the actual load–life relation for modified roller profiles. For uncrowned rollers (line contact), the load–life exponent is p = 4, in agreement with the 1947 Lundberg-Palmgren value, but crowning reduces the value of the exponent, p. The lives of modern roller bearings made from vacuum-processed steels significantly exceed those predicted by the Lundberg-Palmgren theory. The Zaretsky rolling-element bearing life model of 1996 produces a load–life exponent of p = 5 for flat rollers, which is more consistent with test data. For the Zaretsky model with fully crowned rollers, p = 4.3. For an aerospace profile and chamfered rollers, p = 4.6. Using the 1952 Lundberg-Palmgren value p = 10/3, the value incorporated in ANSI/ABMA and ISO bearing standards, can create significant life calculation errors for roller bearings.     

基于多重因素的滚动轴承寿命计算新方法

基于L-P轴承寿命理论,对当前滚动轴承主要的寿命预测模型进行了定性分析。通过经验公式整理、试验数据总结和图形数据处理等方法,重点研究失效概率系数、材料系数、润滑系数、负荷系数、温度系数和清洁系数对轴承疲劳寿命的影响,并建立了多重因素作用下轴承寿命预估模型。基于此模型,利用Matlab和VB的混合编程,开发了轴承疲劳寿命图谱软件,实现了轴承寿命与影响因素的四维可视化显示,并分析各修正系数对滚动轴承寿命的影响规律,确保轴承处于最佳工作状态。     

滚动轴承扩展寿命计算方法及影响因素研究

介绍了滚动轴承寿命计算方法及其特点,根据ISO281:2007详细描述了滚动轴承寿命修正系数的计算方法,并结合算例对影响轴承寿命的主要因素进行了分析.     

Comparison of Models for Ball Bearing Dynamic Capacity and Life

Generalized formulations for dynamic capacity and life of ball bearings, based on the models introduced by Lundberg and Palmgren and Zaretsky, have been developed and implemented in the bearing dynamics computer code ADORE. Unlike the original Lundberg-Palmgren dynamic capacity equation, where the elastic properties are part of the life constant, the generalized formulations permit variation of elastic properties of the interacting materials. The newly updated Lundberg-Palmgren model allows prediction of life as a function of elastic properties. For elastic properties similar to those of AISI 52100 bearing steel, both the original and updated Lundberg-Palmgren models provide identical results. A comparison between the Lundberg-Palmgren and the Zaretsky models shows that at relatively light loads the Zaretsky model predicts a much higher life than the Lundberg-Palmgren model. As the load increases, the Zaretsky model provides a much faster drop-off in life. This is because the Zaretsky model is much more sensitive to load than the Lundberg-Palmgren model. The generalized implementation, where all model parameters can be varied, provides an effective tool for future model validation and enhancement in bearing life prediction capabilities.     

Effect of fluid film wave bearings on attenuation of gear mesh noise and vibration

The attenuation of the gear mesh noise/vibration by fluid film wave bearings relative to rolling element bearings was experimentally investigated. Tests were performed on a gearbox that can accommodate both rolling element bearings and wave bearings. It was found that at specific speeds and torques, the wave bearings could significantly reduce the noise/vibration compared to rolling element bearings. Because the gear noise is accompanied by noise from other sources, a method was developed to extract from the original signal only the mesh harmonic components.The wave bearing dynamic coefficients were also predicted. It was found that adjusting the wave bearing parameters could considerably increase the capacity of the wave bearings to attenuate the gear mesh noise and vibration.     

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.     

Particle Damage in Hertzian Contacts and Life Ratings of Rolling Bearings

Particle denting, and contamination marks found on bearing raceways, can induce stress concentrations and facilitate surface initiated fatigue. The lubricant film developed at the dent and related local surface stresses are also significant to the crack initiation mechanism. In this article, a new methodology is presented to link the micro-EHL film and related local stresses to the fatigue life of rolling bearings. The applied methodology is based on Fourier analysis of the harmonic components of the surface microgeometry to predict stresses and induced lubricant film. The application of this method to actual bearing surfaces is discussed and analyzed in relation to some existing microcontact EHL solutions. A global evaluation of the use of the method to rolling bearings dynamic load ratings is also carried out. A comparison between experimentally obtained rolling bearing life and lives predicted using the present theory indicate the global ability of the model to describe the effect of the lubrication quality on the life expectancy of rolling contacts. From this analysis, an assessment of some typical equations used in rolling bearing dynamic ratings is carried out. It is found that the degree of lubrication of the rolling contact and the cleanliness conditions of the oil are indeed significant to the prediction of the life expectancy of the bearing.     

基于LMD能量特征的滚动轴承故障诊断方法

针对滚动轴承故障振动信号的多载波多调制特性,提出一种基于局域均值分解(local mean decomposition,简称LMD)能量特征的特征向量提取方法,并与支持向量机相结合用于滚动轴承的故障诊断。首先,采用LMD方法将复杂调制振动信号分解为若干单分量信号乘积函数(production function,简称PF);然后,对反映信号主要特征的PF基于时间轴积分,得到各PF分量能量矩并构造特征向量;最后,将其输入多分类支持向量机中,用于区分滚动轴承的故障类型与故障程度。对滚动轴承内圈故障、外圈故障及滚动体故障振动信号的分析结果表明,该方法能有效提取滚动轴承各工作状态信号的故障特征,能准确识别故障类型,同时对故障程度的判断表现出较高的识别率。     

Optimization of partially crowned roller profiles for tapered roller bearings

The roller profile plays a key role in the overall performance of roller bearings. In traditional profile design for roller bearings, the roller profile was often analyzed in terms of the bearing performance, particularly the fatigue life. However, the bearing dynamic stiffness and fatigue life were seldom considered simultaneously in the design of Tapered roller bearings (TRBs). Among the available roller profiles, the partially crowned roller profile has been acknowledged as one of the best from the viewpoint of the bearing fatigue life and stiffness characteristics. This paper presented a design optimization for the partially crowned roller profile to improve the performance of TRBs. Two profile parameters of rollers employed for TRBs including the central flat length and crown radius were investigated. The optimal design parameters for the roller profile were obtained in consideration of both bearing fatigue life and stiffness. The proposed design approach was useful and applicable for further geometrical optimization, manufacturing, and engineering application of rolling bearings.