The objectives of this investigation were to design and develop an experimental turbocharger test rig (TTR) to measure the shaft whirl of the rotating assembly and the axial and frictional loads experienced by the bearings. The TTR contains a ball bearing turbocharger (TC) that was instrumented and operated under various test conditions up to 55,000 rpm. In order to measure the thrust loads on the compressor and turbine sides, customized sensors were integrated into the TC housing. The anti-rotation (AR) pin that normally prevents the bearing cartridge from rotating was replaced with a custom-made load cell adapter system. This sensor was used to measure the frictional losses in the bearing cartridge without altering the operation of the TC. Proximity sensors (probes) were also installed in the compressor housing to monitor shaft whirl. Axial load results indicated that the compressor side bears most of the thrust load. As the backpressure or the speed of the TC was increased, the thrust load also increased. Frictional measurements from the AR pin sensor demonstrated low power losses in the ball bearing cartridge. For certain shaft speed ranges, the data from the sensors illustrated periodic trends in response to the subsynchronous whirl of the shaft.

Hollow cylindrical roller bearings (HCRBs) have obtained much attention from design engineers in bearing industries since they can perform better than solid cylindrical roller bearings (SCRBs) in centrifugal forces, contact stiffness, cooling ability, fatigue life, etc. In this study, an analytical dynamic model of a lubricated HCRB is presented to analyze the influences of the radial load, the shaft speed, and the hollowness percentage of the roller on the bearing vibrations, which cannot be formulated by the methods in the reported literature. Both the support stiffness of the shaft and the roller mass are formulated in the presented dynamic model. The hollow hole in the roller is modeled as a uniform one. Numerical results show that the hollowness percentage of the roller has a great influence on the vibrations of the roller and the inner race of the HCRB. Moreover, the vibrations of the components of the HCRB are not only determined by the hollowness percentage of the roller, but also depended on the external radial load and shaft speed. Therefore, during the design process for the hollowness percentage of the roller, the influences of the radial load and the shaft speed on the vibrations of the bearing components should be considered, except for the fatigue life. The results show that this work can give a new dynamic method for analyzing the vibrations of the HCRBs. Moreover, it can give some guidance for the design method for the HCRBs.

Rolling contact fatigue (RCF) induces a complex subsurface stress state, which produces significant microstructural alterations within bearing steels. A novel modeling approach is presented in this paper, which investigates the effects of microstructural deterioration, phase transformations, and residual stress (RS) formation occurring within bearing steels subject to RCF. The continuum damage mechanics approach was implemented to capture microstructural decay. State and dissipation functions corresponding to the damage mechanics process were used via an energy criterion to predict the phase transformations of retained austenite (RA). Experimental measurements for RA decomposition and corresponding RS were combined to produce a function providing RS formation as a function of RA decomposition and stress history within the material. Microstructural decay, phase transformations, and internal stresses were implemented within a two-dimensional (2D) finite element analysis (FEA) line contact model to investigate variation in microstructural alterations due to RSs present within the material. In order to verify the model developed for this investigation, initial simulations were performed implementing conditions of previously published experimental work and directly comparing to observed RA decomposition and RS formation in 52100 steel deep groove ball bearings. The finite element model developed was then used to implement various RS profiles commonly observed due to manufacturing processes such as laser-shot peening and carburizing. It was found that some RS profiles are beneficial in altering RA decomposition patterns and increasing life while others proved less advantageous.

Lubrication analysis of rolling bearing is often conducted with assumed operating conditions, which does not consider the effect of internal dynamics of rolling bearing. In this paper, the effects of the applied load and bearing rotational speed on the lubrication performance in an angular contact ball bearing are conducted, which combines the bearing dynamic analysis and thermo-elastohydrodynamic lubrication (TEHL) analysis. First, the internal motions and contact forces are obtained from the developed bearing dynamic model, and then were integrated into the TEHL model to investigate the lubrication performance of the bearing. The results show that the rotational speed and external load has significant effects on film thickness, temperature, and power loss; if the improper axial load is applied for certain bearing speed, the lubrication performance will deteriorate and thermal failure may occur; there exists critical load or speed to keep good lubrication performance and avoid thermal failure; the skidding contributes to the thermal failure and bad lubrication performance.

In this study, a new approach has been developed to simulate three-dimensional (3D) experimental rolling contact fatigue (RCF) spalls using a two-dimensional (2D) finite element (FE) model. The model introduces a novel concept of dividing the 3D Hertzian pressure profile into 2D sections and utilizing them in a 2D continuum damage mechanics (CDM) RCF model. The distance between the two sections was determined by the size of the grains in the material microstructure. The 2D RCF model simulates characteristics of case carburized steels by incorporating hardness gradient and residual stress (RS) distribution with depth. The model also accounts for the topological randomness in the material microstructure using Voronoi tessellation. In order to define the failure criterion for the current model, sub-surface stress analysis was conducted for the Hertzian elliptical contact. It was predicted that the high shear stress region near the end of the major axis of the contact is the cause of catastrophic damage and spall formation. This prediction was validated by analyzing the spalls observed during RCF experiments using a surface profilometer. The model was implemented to predict RCF lives for 33 random material domains for different contact geometry and maximum Hertzian pressures. The model results were then compared to the RCF experiments conducted on two different test rigs, a three-ball-on-rod and a thrust bearing test apparatus (TBTA). It was found that the RCF lives obtained from the model are in good agreement with the experimental results. The results also demonstrated that the spalls generated using the analytical results resemble the spalls observed in experiments.

Measuring and verification of contact force in a rolling element bearing is a big problem. In this study, a new measuring method for contact force in a large-scale ball bearing is developed. The idea is to measure the deformation under the ball–race contact by displacement sensor at first, and the displacement of the end face of load bearing ring is also measured to determine the contact angle of ball–race contact. Then, the corresponding theory is developed to calculate the contact angle of ball–race contact by the displacement of the end face of load bearing ring. At last, the ball–race contact force is determined by accurately calculating through finite element method (FEM). Results show that the relation between contact force and deformation of measuring surface which is under ball–race contact is linear. The position of ball greatly affects the contact angle of ball–race contact. The contact angle of the ball which is near the arm of force is larger than that of the ball which is far from the arm of force. On the contrary, the measuring deformation of ball–race contact that is near the arm of force is less than that of ball–race contact that is far from the arm of force. The method developed here is only suitable for large-scale rolling element bearing because of the size constraint of the sensor.

The analytical expressions currently available for Hertzian contact stresses are applicable only for homogeneous materials and not for case-hardened bearing steels, which have inhomogeneous microstructure and graded elastic properties in the subsurface region. Therefore, this article attempts to determine subsurface stress fields in ball bearings for graded materials with different ball and raceway geometries in contact. Finite element models were developed to simulate ball-on-raceway elliptical contact and ball-on-plate axisymmetric contact, to study the effects of elastic modulus variation with depth due to case hardening. Ball bearings with low, moderate, and heavy load conditions are considered. The peak contact pressure for case-hardened steel is always more than that of through-hardened steel under identical geometry and loading conditions. Using equivalent contact pressure approach, effective elastic modulus is determined for case-carburized steels, which will enable the use of Hertz equations for different gradations in elastic modulus of raceway material. Nonlinear regression tools are used to predict effective elastic modulus as a weighted sum of surface and core elastic moduli of raceway material and design parameters of ball–raceway contact area. Mesh convergence study and validation of equivalent contact pressure approach are also provided. Implications of subsurface stress variation due to case hardening on bearing fatigue life are discussed.

Movement analyses of bearings with regard to stable and unstable motion behavior typically investigate the cage whirl. However, some experimental and simulation-based studies exist that analyze the movements of the rolling elements. The majority of these investigations focus on lower shaft speeds. This paper presents an image-based approach for investigating the rolling element motions under high-speed operation condition. A new evaluation algorithm is presented and its suitability is verified first by generic images and afterward by experiments on cylindrical roller bearings.

Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

This paper presents mathematical expressions to identify the existence of localized surface defects on the raceways of the deep groove ball bearings. For the formulation of the mathematical expressions, matrix method of dimensional analysis based on force, length, time, and temperature (FLTϴ) system of unis is used. The model is based on the complete set of physical dimensions and operating parameters of the deep groove ball bearing in that the spall size is directly allied with vibration responses. The formulated governing model equations are solved numerically by applying a scheme of empirical modeling through multiple factorial regression analysis. Experiments are performed on the laboratory test rig to verify the results obtained from the developed model equations. For the experiments, deep groove ball bearings designated as SKF 6307 are used. These bearings are having artificially induced square-shaped surface defects of different sizes on the outer and inner races and are analyzed for different operating speeds. A good similarity between the predicted numerical values and the experimental results is noticed. This study showed that the proposed methodology can be successfully used for the characterization of the localized surface defects on the raceways of the deep groove ball bearings.

In this paper, a model was developed to study the effects of rotor and support flexibilities on the performance of rotor–bearing–housing system. The system is composed of a flexible rotor and two supporting deep-groove ball bearings mounted in flexible bearing housings. The dynamics of the ball bearings were simulated using an existing dynamic bearing model, which was developed using the discrete element method (DEM). The explicit finite element method (EFEM) was used to model the flexibilities of the rotor and bearing support. In order to combine the dynamic bearing model with finite element rotor and support system, new contact algorithms were developed for the interactions between the various components in the system. The total Lagrangian formulation approach was applied to decrease the computational effort needed for modeling the rotor–bearing–housing system. The combined model was then used to investigate the effects of bearing clearances and housing clearances. And it was found that, as the rotor is deformed due to external loading, the clearances have a significant impact on the bearing varying compliance motion and reaction moments. Results also show that deformation of the flexible housing depends on the total force and moment generated within the bearing due to rotor deformation. The first critical speed of rotor was simulated to investigate the unbalance response of the rotor–bearing system. It was demonstrated that rotor critical speed has a significant effect on inner race displacement and reaction moment generated at bearing location.

Movement analyses of bearings focusing on cage motion behavior are often conducted by simulations, typically by investigating the cage whirl. Some experimental studies exist in which a metal cage or a modified one is analyzed with sensors. This paper presents an image-based approach for investigating the cage motion of an injection molded, window-type cage under operation condition. Besides analyses at constant rotational speed, the cage center movement behavior for different accelerations is investigated.

This paper investigates the nonlinear characteristics of varying compliance contact resonance in a rotor–bearing system and takes into consideration the Hertzian contact deformation and internal radial clearance. We created an experimental rig of a rigid rotor supported by rolling element bearings. In the course of the rotational speed run up and down, the frequency–amplitude curves of the varying compliance vibrations were observed during experiments using different radial loads and compared with the results of our numerical simulations. The experimental and numerical results indicate that the varying compliance contact resonance in the vertical direction presents the soft spring characteristic, while the soft and hard spring characteristics coexist for the horizontal resonance.

In this paper, the driving force of a linear-guideway type recirculating ball bearing (linear bearing) is measured and explained as the first step toward an understanding of sticking, which is the significant increase in driving force required to move a linear bearing under back-and-forth operation with a short stroke length. First, the driving force required for operation of a test bearing (which is a linear-guideway type recirculating ball bearing with load balls) and acceleration of a moving body (which consists of a carriage of the test bearing, an arm, and weight) were measured. The measurements showed that the sticking occurred when the test bearing, under a relatively higher rolling moment load, was driven in an offset position for a certain period. Next, the driving force of a test bearing with alternating load balls and spacer balls was measured, and it was clear that the cause of the sticking was the sliding friction between rolling balls. Finally, the ball locations in the load zone of the test bearing with load balls were observed in operation, and the occurrence process of the sticking is explained.

In this paper, investigation on the friction torque of a double row roller slewing bearing which is operated in the azimuth axis of a gun turret is performed. For this purpose, a friction measurement test setup is designed and friction torque measurements are conducted. Tests are performed at low speeds and various loading conditions. Friction sources are decoupled and examined separately in order to fully understand effect of each component on friction torque of the slewing bearing. Therefore, friction caused by rolling motion and friction caused by two different types of lip seals are investigated. In addition, friction identification analyses are performed. In the analysis, load distribution of the bearing is calculated by finite element analysis software and rolling motion is simulated with a multibody-dynamic analysis program. In the end, analyses results are compared and verified with the test results.

This paper deals with the load–displacement relationship of a ball bearing with axial, radial, and angular displacements for both the inner and outer rings. First, the expressions for the load–displacement relationship of ball bearings with any number of balls under the combined axial, radial, and moment loads were presented by using a system in which both the inner and outer rings are allowed to move in the axial, radial, and angular directions. Second, the presented expressions were compared with Jones' expressions (which are typical conventional expressions for the load–displacement relationship), then the range of application of Jones's expressions were elucidated. Third, the relative axial displacement, the relative radial displacement, and the relative angular displacement of a miniature ball bearing type 692 under the combined axial, radial, and moment loads were calculated. Finally, it was shown that the relative angular displacement in the case with no inner ring angular displacement is R i /R o times the relative angular displacement in the case with no outer ring angular displacement, in which R i and R o are the radii of the inner and outer race curvature center loci.

The objectives of this investigation were to develop a coupled dynamic model for turbocharger ball bearing rotor systems, correlate the simulated shaft motion with experimental results, and analyze the corresponding bearing dynamics. A high-speed turbocharger test rig was designed and developed in order to measure the dynamic response of a rotor under various operating conditions. Displacement sensors were used to record shaft motion over a range of operating speeds. To achieve the objectives of the analytical investigation, a discrete element angular contact ball bearing cartridge model was coupled with an explicit finite element shaft to simulate the dynamics of the turbocharger test rig. The bearing cartridge consists of a common outer ring, a pair of split inner races, and a row of balls on each end of the cartridge. The dynamic cartridge model utilizes the discrete element method in which each of the bearing components (i.e., races, balls, and cages) has six degrees-of-freedom. The rotor is modeled using the explicit finite element method. The cartridge and rotor models are coupled such that the motion of the flexible rotor is transmitted to the inner races of the cartridge with the corresponding reaction forces and moments from the bearings being applied to the rotor. The coupled rotor–cartridge model was used to investigate the shaft motion and bearing dynamics as the system traverses critical speeds. A comparison of the analytical and experimental shaft motion results resulted in minimal correlation but showed similarity through the critical speeds. The cartridge model allowed for thorough investigation of bearing component dynamics. Effects of ball material properties were found to have a significant impact on turbocharger rotor and bearing dynamics.

Large bearings employed in wind turbine applications have half-contact widths that are usually greater than 1 mm. Previous numerical models developed to investigate rolling contact fatigue (RCF) require significant computational effort to study large rolling contacts. This work presents a new computationally efficient approach to investigate RCF life scatter and spall formation in large bearings. The modeling approach incorporates damage mechanics constitutive relations in the finite element (FE) model to capture fatigue damage. It utilizes Voronoi tessellation to account for variability occurring due to the randomness in the material microstructure. However, to make the model computationally efficient, a Delaunay triangle mesh was used in the FE model to compute stresses during a rolling contact pass. The stresses were then mapped onto the Voronoi domain to evaluate the fatigue damage that leads to the formation of surface spall. The Delaunay triangle mesh was dynamically refined around the damaged elements to capture the stress concentration accurately. The new approach was validated against previous numerical model for small rolling contacts. The scatter in the RCF lives and the progression of fatigue spalling for large bearings obtained from the model show good agreement with experimental results available in the open literature. The ratio of L 10 lives for different sized bearings computed from the model correlates well with the formula derived from the basic life rating for radial roller bearing as per ISO 281. The model was then extended to study the effect of initial internal voids on RCF life. It was found that for the same initial void density, the L 10 life decreases with the increase in the bearing size.