Optimization analysis on assembly interference of cylindrical roller bearings

Experimental data on the wear of rolling elements are used to develop a method developed for determining the fatigue life of rolling bearings taking into account their wear. The results of calculating the fatigue life of a bearing taking into account the wear of rolling elements are given. It is shown that wear of rolling elements reduces the fatigue life of bearings.

During the use of rolling bearings in wind turbines, aero engines, and other equipment, they often operate under variable operating and loading conditions. The practice has shown that the sequence of these loads and their interaction has a significant impact on the fatigue life of rolling bearings. In order to better understand this issue, a modified nonlinear fatigue damage accumulation model, which considers the influences of both load sequence and load interaction, is proposed in this paper and verified using the fatigue testing data for six materials. Then, the verified model was applied to evaluate the fatigue damage accumulation and fatigue life of a rolling bearing. The results have shown that, compared with the existing models, the proposed model can more accurately predict the damage accumulation and fatigue life of the rolling bearing under variable loading conditions.

Rolling-element bearings operated at high speed or high vibration may require a tight interference fit between the bore of the bearing and shaft to prevent rotation of the bearing bore around the shaft and fretting damage at the interfaces. Previous work showed that the hoop stresses resulting from tight interference fits can reduce bearing lives by as much as 65%. Where tight interference fits are required, case-carburized steel such as AISI 9310 or M50 NiL is often used because the compressive residual stresses inhibit subsurface crack formation and the ductile core inhibits inner-ring fracture. The presence of compressive residual stress and its combination with hoop stress also modifies the Hertz stress life relation. This article analyzes the beneficial effect of residual stresses on rolling-element bearing fatigue life in the presence of high hoop stresses for three bearing steels. These additional stresses were superimposed on Hertzian principal stresses to calculate the inner race maximum shearing stress and the resulting fatigue life of the bearing. The load life exponent p and Hertz stress life exponent n increase in the presence of compressive residual stress, which yields increased life, particularly at lower stress levels. The Zaretsky life equation is described and is shown to predict longer bearing lives and greater load and stress life exponents, which better predicts observed life of bearings made from vacuum-processed steel.

Professor Sadeghi and his coworkers have been developing a method to estimate the rolling contact fatigue life of rolling bearings in recent years using a continuum damage mechanics (CDM) approach. Development of the method has involved progression from a defect-free and inclusion-free model to ones incorporating grain boundary cracks and inclusions.The most recent paper on this topic is authored by Walvekar et al. [1]. In Sec. 2.2, the authors stated “It was hypothesised that failure mechanism for torsional fatigue and rolling contact fatigue are equivalent because the mechanism for damage accumulation is similar for both types of fatigue phenomena.” It is necessary to verify whether such a hypothesis is correct or not but this has not been carried out within the paper.This hypothesis was postulated by Raje and Sadeghi in 2009 in a paper published in the IMechE Journal of Engineering Tribology entitled “Statistical Numerical Modelling of Sub-Surface Initiated Spalling in Bearing Contacts” [2]. In Sec. 3, the authors stated “It is hypothesised that since fatigue damage under rolling contact conditions is caused purely by the action of shear stresses, the mechanism of failure is similar to that prevalent in torsional fatigue. Thus, by knowing the stress-life relationship for a material in torsional fatigue, the fatigue damage parameters can be extracted.”Torsional fatigue data on SAE 52100 bearing steel from Styri were used to provide the shear stress to failure [3], but Styri stated that in about 90% of cases, failures start below the surface, presumably at inclusions or other defects that act as stress concentrating features. However, the model being validated by Raje and Sadeghi is for a material free of defects, voids, or inclusions, while the steel used by Styri would be of 1940 s pedigree but with no statement of its cleanliness.Would the authors comment upon this observation, particularly as, intuitively, the torsional fatigue life of a pristine steel would be expected to be much longer than the one containing defects or inclusions while failures would be surface-initiated?Furthermore, results from the CDM model of pristine steel are compared to L10 bearing lives measured by Lundberg and Palmgren for NU 209 cylindrical roller bearings. The authors present a method in Sec. 4.3 for the conversion of L10 life in shaft revolutions to inner race stress cycles. A comparison of the model results and the bearing lives of Lundberg–Palmgren is then presented. The authors stated that “Stress-life results for this bearing are shown in Fig. 7 and are found to be in good agreement with stress-life results from the current model.”Would the authors comment upon this conclusion, taking into account that the results from the CDM model of pristine steel are being compared to bearings of 1940 s pedigree with no statement of cleanliness?In Sec. 4.2, the authors claim that the model is found to fit within the range of experimental data for cylindrical roller bearings reported by Harris and Barnsby [4]. Reference to this data appears to suggest that shaft revolutions have been plotted as opposed to stress cycles in Fig. 7. Would the authors confirm whether this is the case or not?Intuitively, a defect-free and inclusion-free model should predict lives that are much longer than both the experimental data from Harris–Barnsby and Lundberg–Palmgren. Once defects such as inclusions are introduced into the model, comparisons may then be made with the experimental data. It is necessary to model the size, number, shape, and composition of the inclusions (and other defects, such as carbide stringers) within the steels tested by Harris–Barnsby (1980 s/1990 s pedigree) and Lundberg–Palmgren (1940 s pedigree) in order to carry out such a comparison. Only at this point the claims can be made for validation (or otherwise) of the model. Would the authors comment upon this observation?It also appears that the CDM model has not been validated at lower contact stresses. It may be difficult to validate the model at contact stresses below 2200 MPa (the main region of interest for industrial machines) for the following reasons:Would the authors comment upon validation of the model at lower contact stresses?

An external load applied to a rolling bearing is distributed among the rolling elements. The conventional calculation of load distribution among rolling element already established assumes that the bearing races, shaft and housing are rigid except for elastic contact deformations at the individual contacts between rolling elements and raceways. In many applications, the bearing rings as well as the supporting structures can not be considered rigid, so that the load distribution is different from that predicted on the above assumption. It is known that a bearing fatigue life is affected by a load distribution. Thus accurate prediction of the bearing life requires the precise determination of actual load distributions. Several experimental methods to determine the load distribution of rolling bearings have been proposed so far. Their methods, however, can not provide dynamic load distributions while rolling elements make one revolution along the raceway. The objective of this study is to establish a more direct method than the other ones for determining rolling element load distributions not only statically but also dynamically. The method herein proposed provides the measurement of strains of rollers developed under an applied load by using an optical fiber strain sensor mounted on a roller of a measuring cylindrical roller bearing. The obtained strain data provides rolling element load distributions. This paper presents the method for determination of static load distributions.

The calculating method for fatigue life of rolling bearings is based on the theory of Lundberg and Palmgren. The rated life is determined from the ratio of the dynamic load rating of the bearing to the dynamic equivalent load. However, in actual applications, flaking damage may occur earlier than this rated life. For example, surface initiated flaking may occur due to contamination in the lubricant. In addition, differences in the internal clearance of bearings are also thought to influence the occurrence of surface initiated flaking. This study aims to investigate the effect of different internal clearance on surface initiated flaking in tapered roller bearings. First, rotating tests were conducted on combination tapered roller bearings with dented raceways under several axial clearances different from the standard condition. Second, the surface profiles of the bearings before and after the tests were compared to investigate the relationship between the distribution of flaking area and the axial clearance. Furthermore, the effect of axial clearance on the surface initiated flaking life was clarified from the comparison between the results of the rotating tests. Finally, the theoretical and experimental lives were compared. As a result, it has been found that when the axial clearance is excessively large, the distribution of flaking is biased toward the large diameter side of the outer raceway. In addition, it has been demonstrated that the bearing life is substantially affected by the axial clearance, and that the bearing life shortens as the axial clearance increases.

In the process of smelting and manufacturing, bearing steel inevitably have defects such as non-metallic inclusions. Moreover, inclusion geometry (type, quantity, size, distribution, and shape) has a significant effect on the fatigue failure of bearing steel. In order to study effect extent of the size and distribution of inclusion on the fatigue life of bearings, this paper uses the test high-speed rail bearings LY-Z028 to research and analysis. The micro-model of contact between single inclusion and the matrix is established, and then performs ANSYS simulation on stress concentration which caused by size of single inclusion and relative surface depth. Further, multiple linear regression method is used to compare the effect extent of these two factors on the fatigue life. The results show that size of single inclusion has a greater impact on the fatigue life than relative surface depth, which can provide an effective reference for smelting and production requirements.

The statistical size effect is well known but not always interpreted correctly. The present paper shows that a statistical size effect exists only for high failure probabilities, which, however, are not permitted in practical component design. On the other hand, the limit for design and dimensioning is given by the failure-free time (where failure probability equals 0), which is independent of component size. Eliminating the misunderstood statistical size effect and considering failure-free time in standardized calculation of fatigue life of rolling bearings would yield more realistic results.

Non-uniform roller-race contact performance of bearings along width in the rotor-bearing system under dynamic loads

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.

Research and/or Engineering Questions/Objective There are many domestic enterprises that produce auto-hub bearings in China. But the majority of products are only applied in the after-sale market as the unstable quality of the domestic products can’t meet the OEM’s requirements. In order to improve fatigue life and dimensional stability of GCr15 steels, the cryogenic treatment was introduced to control the percentage of retained austenite of GCr15 bearing steel. Methodology The correlation between cryogenic treatment parameters and microstructure of the hub-bearing was studied. The percentage of retained austenite after different cryogenic treatments was measured by X-ray diffraction experimental. The equation was established to reveal the relationship between the percentage of retained austenite and cryogenic temperature. Finally, the fatigue life was performed by strengthen test according to JB/T 50013-2000 test rules of life and reliability of rolling bearings. Results After cryogenically treated in −40, −80, −120, −160, −196 °C chamber for 2 h, the investigation revealed that the retained austenite of the specimen surface is with proportional to the temperature decrease of deep cryogenic treatment. The specimens possess the maximum hardness and the minimum impact toughness during keeping at −80 °C deep cryogenic treatment temperature. Limitations of this study This study work has verified that the cryogenic treatment can improve the fatigue life and dimensional stability of wheel hub bearing. In order to obtain broader application and promotion, it requires further investigation on the characteristic properties of cryogenic treatment to be applied to other automotive bearings and other kinds of parts. What does the paper offer that is new in the field in comparison to other works of the author Since the mechanism of cryogenic treatment is not yet to be understood very well, So in general cryogenic treatment is still in the dormant level at present. In this study, we focus on investigating the mechanism and optimizing parameters of cryogenic treatment to improve the fatigue life of wheel-hub bearing. Conclusion The test results indicate the cryogenic treatment can improve the fatigue life of DAC 4007040 hub bearing, which runs 39.537 million revolutions, Re = 99.22 % by optimizing cryogenic treatment. In the same load conditions, the fatigue life of DAC 4007040 hub bearing subjected to conventional heat treatment is only 21.79 million revolutions in average, Re = 96.7 %.KeywordsWheel-hub bearingCryogenic treatmentRetained austenite fatigue lifeStrengthen test

Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings

A model for determination and analysis of bearing external radial and axial load distributions per individual rolling elements and a model for determination of the resistance to motion of rolling friction, accounting for rolling element locations during the bearing track motion with respect to the direction the bearing radial load resultant vector acts, are presented. A dynamic angle of the rolling element location has been defined as well. The models have been developed to determine values of bearing load distribution parameters, individual rolling element loads, and resistances to rolling motion of bearings and rolling bearing systems, as well as to analyze distributions and values of the radial and axial stiffness of rolling elements, bearings, and kinematic pairs as a function of the bearing rolling element distribution and the direction along which the bearing radial load resultant vector acts. The proposed models have been built to carry out analysis of the resistance to motion of rolling kinematic pairs of industrial robot manipulators. Slow-speed and short-period motions of rolling bearings have been assumed as a characteristic type of motion of rolling kinematic pairs in manipulators. © 2000 John Wiley & Sons, Inc.

Rolling bearings are widely used in aeroengine, machine tool spindles, locomotive wheelset, and so forth. Rolling bearings are usually the weakest components that influence the remaining life of the whole machine. In this paper, a fatigue life prediction method is proposed based on quasistatic modeling of rolling bearings. With consideration of radial centrifugal expansion and thermal deformations on the geometric displacement in the bearings, the Jones’ bearing model is updated, which can predict the contact angle, deformation, and load between rolling elements and bearing raceways more accurately. Based on Hertz contact theory and contact mechanics, the contact stress field between rolling elements and raceways is calculated. A coupling model of fatigue life and damage for rolling bearings is given and verified through accelerated life test. Afterwards, the variation of bearing life is investigated under different working conditions, that is, axial load, radial load, and rotational speed. The results suggested that the working condition had a great influence on fatigue life of bearing parts and the order in which the damage appears on bearing parts.

The endurance of a thrust-loaded, double row radial cylindrical roller bearing