In machines with linear-guideway type recirculating linear ball bearings (linear bearings), to prevent shutdown of machines caused by unexpected-failures of linear bearings, there has been an increasing demand for the development of defect (especially flaking) detection techniques of linear bearings by using vibration or acoustic emission (AE) measurements. Although studies [1–3] on vibrations of linear bearings without defects have been carried out, work on vibrations and AE of defective linear bearings are few [4, 5].

An explicit dynamic model of a deep groove ball bearing under a radial load is proposed. All components are treated as rigid bodies whereas the bearing outer ring flexibility is taken into account using fixed interface component mode synthesis (CMS). The classical lubricated Hertzian contact theory is used to calculate elastic deflections and non-linear contact forces. The dynamic loading of the outer ring interface nodes is ensured using C 2 -continuous rational cubic splines. A Runge-Kutta-Felhberg 4th/5th order integration scheme is used to solve the dynamic equilibrium of all components. Time and frequency domain analyses are then carried out to investigate the dynamic behaviour of the ball bearing. The accuracy of these works is validated by comparison with the results of an analytical model and a model based on finite elements proposed in prior researchs.

Since being originally introduced, cylindrical rolling element bearings have been significantly improved, in terms of their performance and working life. A major objective has been to decrease the Hertz contact stresses at the roller–raceway interfaces, because these are the most heavily stressed areas in a bearing. It has been shown that bearing life is inversely proportional to the stress raised to the ninth power (even higher). Investigators have proposed that under large normal loads a hollow element with a sufficiently thin wall thickness will deflect appreciably more than a solid element of the same size. An improvement in load distribution and thus load capacity may be realized, as well as contact stress is also reduced considerably by using a bearing with hollow rolling elements. Since for hollow rolling element no method is available for the calculation of contact stresses and deformation. The contact stresses in hollow members are often calculated by using the same equations and procedures as for solid specimens. This approach seems to be incorrect. Recently, the Finite Element Analysis (FEA) has been successfully used to evaluate contact problems for the roller bearings. Investigations have been made for hollow rollers in pure normal loading. Different hollowness percentages ranging from 0% to 90% have been analysed in FEA software to find the optimum percentage hollowness which gives minimum stress and finally longest fatigue life.

Modern Wind Turbines adjust their blades orientation at different wind speeds for power control and optimum energy production. A big slewing ring about 2 metres diameter placed at each blade root, allows the blade orientation withstanding highly variable heavy loads, vibrations, continuous rotating oscillations and severe ambient conditions. The blade pitch system design and control strategy in a WTG is strongly conditioned by the load dependant friction of the bearing that shall be accurately defined for cost-effective designs. The pitch system is also the main brake of the rotor requiring high reliability for their components under fatigue loads, and in particular for the slewing rings due to its inherent difficulties for maintenance or replacement. The present methodology allows the fatigue and friction estimation of slewing rings, based on rolling bearing models and classical theories like Hertz, Lundberg-Palmgren, and Miner fatigue cumulative damage. This approach simulates the stress supported by each ball in the contact with the raceways, estimates the bearing friction due to these contact stresses, and the fatigue life of the overall bearing.

A computer program for dynamic analysis of ball bearings, in which a simple mixed lubrication model for the retainer/race and retainer/ball contact is incorporated, is developed and retainer instability in reaction wheel bearings is investigated. Results show that an increase in the amount of oil promotes the instability and that a retainer with rectangular pockets is more stable than one with circular pockets.

This paper reports on a theoretical study on the fluid-assisted surface cracking in lubricated rolling-sliding contact. An analytical 2D model, validated by the CFD simulations, is developed to describe the transient process of lubricant seepage into a surface-breaking crack during the contact loading. The fluid-crack interaction is studied by FE calculations.

A study on the life distribution and reliability for roller guides with cage is carried out with a total number of 90 test samples in two lots ( N s = 38 and 52), and fatigue life distribution functions, such as two and three parameters Weibull distribution, and log-normal distribution are used for analyzing the test data. The basic dynamic load rating formula standardized by ISO in 2004 is also compared with the life test data in relation to the effect of crowning on both ends of the carriage raceway. Weibull slope, compatibility of distribution functions and λb m factor are also examined.

With considering the contact angle variations, the nonlinear systems of equations are utilized to obtain load distributions of automotive wheel bearings with axial preloading under radial and lateral tire loads and analyze the effects of axial preloading and wheel offset on the performances of the bearings. The results show that the axial preloading has much more significant influences on the load distributions, the displacements, the system fatigue life and the moment rigidity than the wheel offset. The relative inclination angle is linearly proportional to the axial preloading. The moment rigidity and the system fatigue life are opposite to an amount of axial clearance. In order to improve the rigidity of the automotive wheel bearings and get longer service life synchronously, the bearings should be kept working at a negative axial clearance.

A dynamic analysis tool for calculating cage stress in needle roller bearings under planetary motions was developed to examine the mechanism of rising cage stress. This analysis considers three degrees of freedom of a cage and rollers and two degrees of freedom of a planetary gear in two-dimensional model. Moreover, the elastic deformation of the cage is implemented to determine the cage stress by using a Component-Mode-Synthesis method. In order to validate this dynamic analysis, two needle roller bearings with different structural cage strengths were tested in a planetary gear system. In cases where the weaker cages were damaged, the analyzed stress of the cages nearly reached or exceeded the material fatigue strength. This high stress was observed when a roller passed the load zone collided with the pocket bar due to the centrifugal force of planetary motion. The maximum cage stress increased with the carrier rotation speed and the stress of the damaged weaker cage only exceeded the fatigue strength in the experimental range of carrier speed. These results indicate that the dynamic model is effective and valid for the current application.

Indents in roller bearings perturb the pressure and stress distribution and increase the failure risk. A numerical study of the pressure perturbation is proposed. An existing dry contact model is extended to account for the indent shoulder influence and the pressure collapse in deeper indents. Moreover, results on pure-rolling lubricated contacts are presented. Finally, the ellipticity influence is studied both for dry and lubricated contacts.

This paper describes a novel design of oil-film monitoring sensor capable of measuring oil-film thickness in concentrated contacts. The approach is to use a thin (approx. 4 μm) sputtered coating of piezoelectric material, such as Aluminium Nitride. When correctly electroded this acts as an ultrasonic sensor with a usable bandwidth from 20–350 MHz. This sensor allows the interrogation of the small lubricated region between the ball and raceway without any special focusing requirements. Typically the dimensions of the contact region is less than a millimeter wide. This sensor system is then demonstrated experimentally on a deep groove ball bearing with the piezoelectric thin film on the external surface of the bearing outer raceway. The interaction of ultrasound with the oil-film is modeled using a quasi-static spring model and this allows properties such as film thickness to be extracted. The measured thicknesses are shown to agree well those obtained from classical elastohydrodynamic lubrication theory for the high bearing loads and low speeds where several data points can be collected from the contact during a ball passage. Measurement of oil film thickness in the region of 0.1–1 μm is demonstrated.

For high-precision mechanical systems such as gas-turbine engines, which operate under extreme conditions, it is particularly important to accurately predict the behavior of the mainshaft rolling bearings. This prediction includes, among others, the load distribution, stiffness and power dissipation. Although shaft speeds tend to increase, rings and shaft walls are becoming thinner due to size and weight constraints. Thus, bearing behavior is no longer independent of the housing and ring stiffness. Furthermore, since forty years, the use of squeeze film damper is largely widespread in gas-turbine engines to significantly reduce the vibratory levels. Due to the flexibility of the ring providing the interface between the roller bearing and the fluid film, it appears an elastic coupling which modifies the behavior of the bearing-squeeze film damper system. This paper presents first a squeeze film damper model with a flexible inner ring (i.e. outer ring of the roller bearing). An analytical stop model is introduced to reproduce the interference between the inner ring of the squeeze film damper and its housing. In a second part, an elastic coupling between the presented squeeze film damper model and an existing roller bearing model is proposed. Finally, the results presented show that this coupling has a first order influence on the behavior of the bearing-squeeze film damper system. It is also shown that the coupling between a roller bearing and a squeeze film damper when linked by a flexible ring introduces a dissymmetry of the load distribution with respect to the applied load direction. Moreover, in certain cases, the position of the bearing in its housing can reach eccentricities larger than the radial clearance of the squeeze film damper.

An analysis of double arched ball bearing which considers centrifugal forces and gyroscopic effects is performed. Based on operating conditions of a 5 DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from 2 to 3 or 4 contact points. The commonly control criterion of ball bearing by the inner or outer raceway is debatable and is known to fit with difficulty with experimental data. In addition when more than two contact points are involved it becomes obsolete. The paper presents a mathematical model to describe the complex ball bearing internal kinematics under the effect of the external working conditions. Lubricant thickness is taken into account in geometrical equations and the non-linear system of this quasi-static model is solved by a Newton-Raphson method. The 3D model is first validated through comparisons with published data for conventional or single arched ball bearings. Results are also compared to those provided by the commercial software RBL4. The analysis of a double arched ball bearing is finally performed and the complex motion of the ball highlighted.

A new type of rolling contact damage was found out in the fatigue tests of the deep groove ball bearings #6206 under pure radial load and grease lubrication. In appearance, the damages had a few cracks at perpendicular to the ball revolution direction, sank about 20 μ m in the surface of rolling raceway, happened only in the raceway of stationary races and surface of balls, and distributed widely within loaded zone. And in the cross section there were a lot of cracks propagated at 60∼80 degrees to the rolling surface at not only damage position but also other parts. The cracks at the damage position just opened to the surface. It is supposed that the damages are caused by rolling contact fatigue and metal to metal contacts due to lubricant starvation under grease lubrication.

The experimental formula based on Lundberg-Palmgren theory has been used for the calculation of basic dynamic load rating of ball screws because its contact state resembles that of angular contact ball bearings. However, the compatibility between the theoretical and the actual rating life of ball screws has not been yet confirmed by life tests and probability theory. The inherent properties of ball screws are also not considered in this formula. In this paper, the authors deal with the development of ball screw life test machine and fatigue life test for ball screws with a total number of 31 test samples. Type and occurrence location of the initial failure of each sample are investigated. The fatigue life test data are analyzed with two and three parameters Weibull distribution functions. The basic dynamic load rating of the ball screws are also estimated from the life test data. The results are summarized as follows: (1) Initial failures are generated at the surface of the balls and the nut raceway as a spalling. (2) The life distribution of the test data fairy well fits three parameters Weibull distribution function. (3) Basic dynamic load rating, which is estimated by the life test, is approximately in agreement with that of manufacturer’s catalog.

Only few studies have been published on EHD contacts that experienced simultaneously rolling, sliding and spinning motions. This paper describes a new test rig especially designed to simulate such operating conditions while imposing normal load and speeds as those found in real life mechanisms. Then, experimental results are presented and discussed.

A dynamic cylindrical bearing model was modified to analyze large bore cylindrical mill bearings with pin cages. A factor-response methodology was coupled to the dynamic modeling input and output variables in order to generate a suitable transfer function for predicting bearing performance. Response optimization of the transfer function indicated that a traction-based parameter was determined to have the greatest effect on reducing roller slip and improving bearing performance.

This paper deals with a design of crowning to reduce the ball passage vibrations of a linear guideway type recirculating linear ball bearing (linear bearing) with the crowning length L C (1.2 s ≤ L C ≤ 1.7 s , where s is the distance between the adjacent balls in the load zone). First, a fundamental condition to reduce the ball passage vibrations is provided. Second, a design method of the crowning by applying an approximate curve (an assumed functional formula) to the control points (satisfying the fundamental condition or being the intersection of straight and crowning areas of a raceway) is presented. Third, the design procedure is explained by giving an example. In the design example the power function crowning fits the control point best. In addition, the calculated amplitude for the power function crowning is lower than those for the circular arc crowning and the crowning of the commercial linear bearing. Finally, the validity of the presented design method is confirmed experimentally.

The effect of raceway curvature on ball bearing contact stress and fatigue life is analyzed with both Hertzian theory and FEM. A numerical program and a 3-D FEM model are developed to calculate the contact stress and deformation at the bearing ball and raceway. The simulation results of the contact stress and deformation are discussed. The accuracy is evaluated by contrasting finite element results with analytical solutions from Hertzian theory. The effect of bearing race curvature on the contact maximum stress and area between ball and races is discussed. The results show that the race curvature is very sensitive factor to affect the bearing contact stress. The raceway curvature effect on the bearing thrust load capability and bearing running temperature is analyzed and discussed as well. For the validation, A. B. Jones’ program has been used to calculate bearing life with different raceway curvatures.

More often then not, the rolling element bearings of rotating machinery are the mechanical components that are first prone to premature failure. Early warning of an impending bearing failure is vital to the safety and reliability of high-speed turbo-machinery. Presently, vibration monitoring is one of the most applied procedures in on-line damage and failure monitoring of rolling element bearings. This paper presents results from an experimental rotor-bearing test rig where quantified damage was induced in the supporting tapered ball bearings. Subsequently the vibration signature due to damage at the inner race of the bearing is examined. Four on-line vibration signature analyzing schemes are used concomitantly: (i) time averaging, (ii) frequency domain analysis, (iii) joint time-frequency analysis (Wigner-Ville and wavelet transforms) and (iv) chaotic vibration analysis (modified Poincare diagrams). The size/level of the damage is corroborated with the vibration amplitude and the resulting relationships are linearized to provide quantification criteria for bearing progressive failure prediction. The results from the above mentioned methodologies are compared for accuracy and redundancy, thus increasing the reliability for early detection of bearing damage and failure. It is shown that the use of the modified Poincare map can provide an effective way for identification and quantification of bearing damage in rolling element bearings.