Showing papers in "Journal of Tribology-transactions of The Asme in 2010"

A Dynamic Model for Vibration Studies of Deep Groove Ball Bearings Considering Single and Multiple Defects in Races

Abstract: A dynamic model is reported herein for the study of vibrations of deep groove ball bearings having single and multiple defects on surfaces of inner and outer races. Masses of shaft, housing, races, and balls are considered in the modeling. The coupled solution of governing equations of motions is obtained using Runge―Kutta method. The model provides the vibrations of shaft, balls, and housing in time and frequency domains. Computed results from the model are validated with experimental results, which are generated using healthy and defective deep groove ball bearings. Characteristic defect frequencies and its harmonics are broadly investigated using both theoretical and experimental results. Comparison of vibration spectra for the cases having single and two defects on races reveals relatively higher velocity amplitudes with two defects. Good correlations between theoretical and experimental results are observed. Authors believe that this dynamic model can be used with confidence for the study and prediction of vibrations of healthy and defective deep groove ball bearings.

A Transient Mixed Elastohydrodynamic Lubrication Model for Spur Gear Pairs

Abstract: In this study, a transient, non-Newtonian, mixed elastohydrodynamic lubrication (EHL) model of involute spur gear tooth contacts is proposed. Unlike the contact between two cylindrical rollers, spur gear contacts experience a number of time-varying contact parameters including the normal load, radii of curvature, surface velocities, and slide-toroll ratio. The proposed EHL model is designed to continuously follow the contact of a tooth pair from the root to the tip to capture the transient characteristics of lubricated spur gear contacts due to these parameter variations, instead of analyzing the contact at discrete positions assuming time-invariant parameters. The normal tooth force along the line of action is predicted by using a gear load distribution formulation and the contact radii and tangential surface velocities are computed from the kinematics and geometry of involute profiles. A unified numerical approach is adapted for handling asperity interaction in mixed EHL conditions. The differences between the transient and discrete EHL analyses are shown for a spur gear pair having smooth surfaces and different tooth profile modifications. The transient behavior predicted by the proposed model is found to be mainly due to the squeezing and pumping effects caused by sudden load changes. The lubrication behavior under rough conditions is also investigated at different operating conditions. DOI: 10.1115/1.4000270

A Contact Stiffness Model of Machined Plane Joint Based on Fractal Theory

Abstract: A general contact stiffness model is proposed in this paper to study the contacts between rough surfaces of machined plane joints. The proposed model uses fractal geometry for surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent contact stiffness of microcontacts, where the contact stiffness is derived from Hertz contact theory. Three cast iron specimens are produced from different machining methods (milling, grinding, and scraping), and their rough surface profiles are extracted. The structure function method was used to calculate each profile's fractal dimension and scale coefficient. Both theoretical analysis and experimental results of contact stiffness are obtained for these specimens under different contact loads. The comparison between the theoretical contact stiffness and the experimental results at the interface indicates that the present fractal model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experimental data.

A Mass-Conserving Complementarity Formulation to Study Lubricant Films in the Presence of Cavitation

Abstract: A new mass-conserving formulation of the Reynolds equation is developed using the concept of complementarity. This new method overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. Validation against a number of analytical and semi-analytical formulations, for a variety of problems including textured bearings and squeeze film dampers, is performed. The current formulation is shown to be in very good agreement with existing analytical and numerical mass-conserving solutions.

Partial Slip Contact Analysis on Three-Dimensional Elastic Layered Half Space

Abstract: An elastic contact model for three-dimensional layered or coated materials under coupled normal and tangential loads, with consideration of partial slip effects, has been developed in this paper. The response functions for calculating the displacements and stresses were determined in the frequency domain by using the Papkovich–Neuber potentials. The partial slip contact problem was solved by a numerical procedure based on the conjugate Gradient method and fast Fourier transform technique. The contact pressure, surface shear tractions, stick ratios, rigid body displacements, and subsurface stresses are analyzed under different conditions with variations in the material properties and coating thickness. Results show that stiffer coatings tend to decrease the stick ratios and the rigid ball tangential displacements in comparison to those with compliant coatings under the same contact conditions. For stiffer coatings, the values of the von Mises stress and compressive surface stress increase and the positions of maximum von Mises stress move up to the surface; meanwhile, the distributions of the compressive stress become asymmetric due to the action of the tangential load. DOI: 10.1115/1.4001011

Revisiting the Cattaneo–Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies

Abstract: The Cattaneo-Mindlin concept of interfacial slip in tangentially loaded compliant bodies is revisited and its basic simplifying assumptions are critically examined. It is shown that these assumptions, which, in the absence of modern numerical techniques, were essential in 1949 to enable an elegant quantitative solution of the basic problem of presliding between contacting bodies, are actually non physical. An alternative approach to the same problem that is based on treating sliding inception as a failure mode involving material plastic yield is discussed. This alternative approach was suggested even before 1949 but for the same lack of modern numerical techniques could only be promoted qualitatively. Some recent theoretical models, that are based on this earlier alternative approach, and in which the simplifying assumptions of the Cattaneo-Mindlin concept were completely relaxed are described along with their experimental verification. It is shown that the pre-sliding problem between contacting bodies can be accurately solved by these models using realistic physical assumptions and failure criterion.Copyright © 2009 by ASME

On the Prediction of Running-In Behavior in Mixed-Lubrication Line Contact

Abstract: A model is presented, which enables one to predict the running-in performance of the rolling/sliding surfaces subjected to mixed-lubrication line contact. The load-sharing concept was used, in which it is assumed that both the fluid film and the asperities contribute in carrying the imposed load. The plastic deformation of asperities during the running-in is taken into consideration. In the application of the load-sharing method, it is often assumed that asperity heights have a Gaussian distribution. This assumption has been relaxed in this model. Prediction results for the variation in the arithmetic average of asperity heights (R a ) during the running-in period for contact of two rollers are compared with published experimental data. Also presented are the results for the variation in wear volume, wear rate, and friction coefficient during the running-in period. The effect of surface pattern, speed, and load on the running-in behavior is studied. The steady-state wear rate for different surface patterns calculated from this model is compared with the wear rate predicted by the thermal desorption model, and the results are in agreement both in trend and magnitude. The effect of running-in on the Stribeck curve for different surface pattern is discussed.

A Voronoi FE Fatigue Damage Model for Life Scatter in Rolling Contacts

Abstract: It has been widely accepted that the microstructure of bearing materials can significantly affect their rolling contact fatigue (RCF) lives. Hence, microlevel topological features of materials will be of significant importance to RCF investigation. In order to estimate the fatigue lives of bearing elements and account for the effects of topological randomness of the bearing materials, in this work, damage mechanics modeling approach is incorporated into a Voronoi finite element method recently developed by the authors. Contrary to most of the life models existing in the literature for estimating the RCF lives, the current model considers microcrack initiation, coalescence, and propagation stages. The proposed model relates the fatigue life to a damage parameter D, which is a measure of the gradual material degradation under cyclic loading. In this investigation, 40 semi-infinite domains with different microstructural distributions are subjected to a moving Hertzian pressure. Using the fatigue damage model developed, the initiation and total lives of the 40 domains are obtained. Also, the effects of initial material flaws and inhomogeneous material properties (in the form of normal distribution of the elastic modulus) on the fatigue lives are investigated. It is observed that the fatigue lives calculated and their Weibull slopes are in good agreement with previous experimental and analytical results. It is noted that introducing inhomogeneous material properties and initial flaws within the domains decreases the fatigue lives and increases their scatters.

Contact Area and Static Friction of Rough Surfaces With High Plasticity Index

Abstract: A model for the contact area and static friction of nominally flat rough surfaces and rough spherical surfaces is presented. The model extends previously published models, which are limited to plasticity index values below 8, to higher plasticity index values by accounting for fully plastically deformed asperities based on finite element results by Jackson and Green (2005, "A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat, " Trans. ASME, J. Tribol., 127, pp. 343―354]. The present model also corrects some deficiencies of the earlier models at very small plasticity index values below 0.5.

Comparison Between Elastic Foundation and Contact Force Models in Wear Analysis of Planar Multibody System

Abstract: In this paper, two procedures to analyze planar multibody systems experiencing wear at a revolute joint are compared. In both procedures, the revolute joint of interest includes a clearance whose shape and size are dictated by wear. The procedures consist of coupled iterative analyses between a dynamic system analysis with nonideal joints and a wear prediction to determine the evolution of the joint clearance. In the first procedure, joint forces and contact pressures are estimated using the elastic foundation model with hysteresis damping via the dynamic analysis. In the second procedure, a contact force model with hysteresis damping is used to estimate the joint forces. In the latter case, however, the contact pressure is estimated using a finite element method (FEM). A comparison in performance of the two models is facilitated through the use of an experimental slider-crank mechanism in which wear is permitted to occur at one of the joints. It is observed that the two procedures provide similar estimates for the dynamic response and wear volumes but substantially different predictions on the wear profiles. Additionally, experimental results show that while predictions on the wear volume from both models are reasonably accurate, the FEM-based model produced more accurate predictions on the wear profile.

Vertical Stiffnesses of Preloaded Linear Guideway Type Ball Bearings Incorporating the Flexibility of the Carriage and Rail

Abstract: This article deals with the vertical stiffnesses of preloaded linear guideway type ball bearings (linear bearings) incorporating the flexibility of the carriage and rail. First the vertical stiffnesses of light and medium preloaded linear bearings were measured, as well as the outward carriage deformations in the width direction. Compared with the stiffnesses calculated by the conventional rigid model (assuming the carriage and rail are rigid, except for the contact points with the balls), the measured stiffnesses were about 40% less. In preloaded linear bearings under a vertical load, the side faces of the carriage deformed outward. The deformations were minimal at the top, increased toward the bottom, and had a tendency to be greater under either a larger preload or a smaller vertical load. The measured stiffnesses and outward carriage deformations cannot be explained using the conventional rigid model. To overcome these problems with the conventional rigid model, a flexible model (taking into account the flexibility of the carriage and rail) is presented in this article. The flexible model deformations were estimated through finite element (FE) analysis. The Hertzian contacts between the balls and the carriage or rail also were considered. With relative errors of 9-21%, the calculated stiffnesses using the flexible model more closely matched the measured stiffnesses. Also, the calculated outward carriage deformations matched the measured deformations well. Clearly, there is a better match between the calculated results of the flexible model and the measurements than with the conventional rigid model.

Design and Performance of Slurry Erosion Tester

Abstract: A slurry whirling arm erosion test ring was constructed and a series of erosion tests andpost-erosion analysis were carried out using a paint erosion indication technique. Thepattern of the paint removal presented a highly visual and accelerated map for theerosion process and its behavior. Also, the erosion rate of paint removal was investigatedunder a number of erosion variables. It was observed that the rebounding of the erodentparticles from the sample surface play an important role in developing erosion for thistester. The erosion pattern showed that the effect of the rebound particles depends on theimpact velocity and impingement angle. It was also observed that the erosion behavior ofpaint as a function of impingement angle, impact velocity, and erosion time was similarto that reported in literature for engineering materials. The slurry whirling arm erosiontester seems to be promising for simulating the slurry process in real cases.

An Approach for Modeling Material Grain Structure in Investigations of Hertzian Subsurface Stresses and Rolling Contact Fatigue

Abstract: The continuum theory of elasticity and/or homogeneously discretized finite element models have been commonly used to investigate and analyze subsurface stresses in Hertzian contacts. These approaches, however, do not effectively capture the influence of the random microstructure topology on subsurface stress distributions in Hertzian contacts. In this paper, a finite element model for analyzing subsurface stresses in an elastic half-space subjected to a general Hertzian contact load with explicit consideration of the material microstructure topology is presented. The random internal geometry of polycrystalline microstructures is modeled using a 3D Voronoi tessellation, where each Voronoi cell represents a distinct material grain. The grains are then meshed using finite elements, and an algorithm was developed to eliminate poorly shaped elements resulting from “near degeneracy” in the Voronoi tessellations. Hertzian point and line contacts loads are applied as distributed surface loads, and the model’s response is evaluated with commercial finite element software ABAQUS . Internal stress results obtained from the current model compare well with analytical solutions from theory of elasticity. The influence of the internal microstructure topology on the subsurface stresses is demonstrated by analyzing the model’s response to an over rolling element using a critical plane approach.

On the Behavior of Misaligned Journal Bearings Based on Mass-Conservative Thermohydrodynamic Analysis

Abstract: Misalignment affects nearly all the bearing performance parameters including the cavitation, thermal field, leakage flow-rate, and moments The present paper provides a comprehensive analysis of misaligned journal bearings based on a three-dimensional mass-conservative thermohydrodynamic model that appropriately takes into account the film rupture and reformation An extensive set of numerical solutions are presented to closely examine the effects of misalignment in journal bearings

Thermohydrodynamic Lubrication Analysis of Misaligned Plain Journal Bearing With Rough Surface

Abstract: Journal misalignment exists generally in journal bearings. When severe journal misalignment takes place, the minimum film thickness of journal bearings reduces greatly. In this condition, the surface roughness, the oil viscosity-pressure relationship (VPR), and the thermal effect have obvious effects on hydrodynamic lubrication performance of misaligned bearings. In this paper, the oil film pressure, oil film temperature, load-carrying capacity, end leakage flow rate, frictional coefficient, and misalignment moment of a journal bearing with different angles of journal misalignment and surface roughness, and considering oil VPR and thermal effect, were calculated based on the generalized Reynolds equation, energy equation, and solid heat conduction equation. The results show that the oil VPR and surface roughness have a significant effect on the lubrication of misaligned journal bearings under large eccentricity ratio. The thermal effect will affect obviously the lubrication of misaligned journal bearings when eccentricity ratio and angle of journal misalignment are all large. In the present design, the size of the journal bearing is compact more and more, and the eccentricity ratio and angle of journal misalignment are usually large in operating conditions. Therefore, it is necessary to take the effects of journal misalignment, surface roughness, oil VPR, and thermal effect into account in the design and analyses of journal bearings.

Plasto-Elastohydrodynamic Lubrication (PEHL) in Point Contacts

Abstract: Elastohydrodynamic lubrication (EHL) is an important branch of the lubrication theory, describing lubrication mechanisms in nonconformal contacts widely found in many mechanical components such as various gears, rolling bearings, cams and followers, metal-rolling tools, traction drives, and continuous variable transmissions. These components. often transmit substantial power under heavy loading conditions. Also, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the estimated average EHL film thickness. Consequently, most components operate in mixed lubrication regime with significant asperity contacts. Due to very high pressure concentrated in small areas, resulted from either heavy external loading or severe asperity contacts, or often a combination of both, subsurface stresses may exceed the material yield limit, causing considerable plastic deformation, which may not only permanently change the surface profiles and contact geometry but also alter material properties through work hardening as well. In the present study, a three-dimensional plasto-elastohydrodynamic lubrication (PEHL) model has been developed by taking into account plastic deformation and material work-hardening. The effects of surface/subsurface plastic deformation on lubricant film thickness, surface pressure distribution, and subsurface stress field have been investigated. This paper briefly describes the newly developed PEHL model and presents preliminary results and observed basic behavior of the PEHL in smooth-surface point contacts, in comparison with those from corresponding EHL solutions under the same conditions. The results indicate that plastic deformation may greatly affect contact and lubrication characteristics, resulting in significant reductions in lubricant film thickness, peak surface pressure and maximum subsurface stresses.

Ultrasonic Measurement for Film Thickness and Solid Contact in Elastohydrodynamic Lubrication

Abstract: The reflection of ultrasound can be used to determine oil film thickness in elastohydrodynamic lubricated (EHL) contacts if the opposing surfaces are fully separated by the liquid layer. The proportion of the wave amplitude reflected depends on the stiffness of the liquid layer, which is a function of its bulk modulus and thickness. However, in many practical applications, boundary or mixed film lubrication is a common occurrence as the nominal thickness of the separating film is of a similar order to the height of the surface asperities. The reflection is then dependent on both the liquid contact and solid contact parts and the total interfacial stiffness is the controlling parameter. In this paper an investigation was carried to study the reflection of ultrasonic waves from the lubricated contact between a sliding steel ball and a flat steel disc when substantial solid contact occurs. To interpret the ultrasonic reflection results, a mixed regime model for a circular point contact was established. The liquid film stiffness was calculated by using a predicted film thickness and a bulk modulus estimated from published rheological models of lubricants under high pressure. Solid contact stiffness was predicted using a statistical rough surface contact model. Under all operating conditions, the prediction of fluid stiffness was found to be much greater than the solid contact stiffness. The total stiffness predicted by the model showed good agreement with experimental measurements for kinematic cases. The model was used to separate the stiffness contributions from the asperity contact part and lubricant layer part from the experimental data. For contact pressures ranging from 0.42 to 0.84 GPa and sliding speed from zero to 2 m=s, the film thickness was found to vary from 0.01 to 0.8 lm, and the proportion of the load supported by asperity contact varied from 50% to 0%.

Analysis of Single-Grooved Slider and Journal Bearing With Partial Slip Surface

Abstract: In this paper, pressure and shear stress are derived under steady state using one-dimensional analysis of the single-grooved slider bearing and journal bearing with partial slip on the stationary surface. The Reynolds boundary conditions are used in the analysis of journal bearing to predict the extent of the full film region. In the cases of partial slip slider and journal bearing, the pressure distribution is higher compared with the conventional bearing with no slip. In the case of partial slip on both slider and journal bearing surfaces, the single-groove, immediately followed by the partial slip region, results in the increase in pressure distribution. The results also show that in comparison to the conventional bearing with no slip, in the cases of parrial slip slider and journal bearing, the shear stress increases before the region of slip/no slip interface, while the shear stress decreases in the region of no slip. In the case of the partial slip region on bearing surfaces, the shear stress distribution is lower in the region immediately after the groove. Significant pressure distribution is obtained due to the influence of partial slip on the slider bearing with uniform film thickness and the concentric journal bearing. The maximum pressure occurs at the end of the region of groove, immediately followed by the region of the partial slip. It is found that the pressure distribution of the slider and journal bearing with partial slip surface are not influenced with the further increase in the nondimensional slip coefficient (A) from 10 to 100.

Thermohydrodynamic Model Predictions and Performance Measurements of Bump-Type Foil Bearing for Oil-Free Turboshaft Engines in Rotorcraft Propulsion Systems

Abstract: An engineered thermal management is fundamental to the application of gas foil bearings (GFBs) as turboshaft supports in rotorcraft propulsion systems. The paper presents a model for the thermal energy transport in a rotor-GFB system operating at high temperature with typical inner and/or outer cooling flows. Predicted film temperatures agree with published test data, demonstrating the effectiveness of an outer cooling stream to remove heat and to control the operating temperature. The inner flow stream is not as efficient. The analysis shows paths of thermal energy by conduction and convection to assist in the design and troubleshooting of rotor-GFB systems operating hot. Bearing temperatures and shaft motions measurements are obtained in a test rotor electrically heated to 132°C. In speed-up tests to 26 krpm, the rotor motion amplitude drops suddenly just above the critical speed, thus, evidencing the typical hardening of compliant bearings. At the hottest test condition, since air is more viscous, the rotor peak motion amplitude decreases, not showing a jump. The coastdown tests show the critical speed increases slightly as the temperature increases.

Effect of Friction Modifiers and Antiwear Additives on the Tribological Performance of a Hydrogenated DLC Coating

Abstract: There has been a lot of attention on the effect of lubricant additives on the friction at carbon coated surfaces. But only few papers have addressed the effect of additives on the durability of some diamondlike carbon DLC coatings. This paper presents a systematic study assessing the additive/additive and additive/surface interactions, and their influences on the durability of a low hydrogen-containing (15 at. % hydrogen) metal-free DLC coating (a-C:15H). In this study, lubricating oils containing a zinc dithiophosphate (ZDDP) antiwear additive and/or organomolybdenum friction modifiers (moly dimer and moly trimer) were used. Tribological tests were carried out in a pin-on-plate tribometer under boundary lubrication conditions. To understand the effect of additives, tribofilms formed on the wear tracks were analyzed using surface sensitive analytical techniques such as atomic force microscope, scanning electron microscopy, energy dispersive X-ray analysis, X-ray photoelectron spectroscopy, and Raman spectroscopy. Results showed that the ZDDP formed a zinc phosphate containing an ultrathin antiwear tribofilm, which offered excellent durability/wear protection to the a-C:15H coating. However, the antiwear performance of this additive was compromised when it was used with moly dimer or moly trimer. Surface analysis revealed that unlike steel surfaces, MoS 2 formed on the DLC surfaces had negligible influence on friction, while the low friction DLC wear debris had strong influence on friction. Abrasive wear was found to be the dominating wear mechanism in the cases when additives showed poor wear protection on the a-C:15H coating.

Recess Depth Optimization for Rotating, Annular, and Circular Recess Hydrostatic Thrust Bearings

Abstract: Inertial effects due to the centripetal forces may become dominant at high rotational speeds in hydrostatic thrust bearings. Although this influence has been recognized in literature, bearings are commonly optimized with respect to the minimum friction, and the dissipation function has not been taken into account in the optimization procedures. It is observed that the secondary flow caused by the inertia term gives a large contribution to the dissipation for applications with a high rotational speed. In this study, the minimum dissipation for annular and circular recess thrust bearings operating at a certain rotational speed is determined by finding the optimum film thickness in the recess. An example is given for annular recess thrust bearings.

A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Oil Seal Rings

Abstract: Squeeze film damper (SFD) designs typically implement supply grooves to ensure adequate lubricant flow into the film lands. Oil seal rings, of land film clearance c, also incorporate short and shallow grooves (length ≤ 30c, depth ≤ 15c) to reduce cross-coupled stiffnesses, thus promoting dynamic stability without a penalty in increased leakage. However, extensive experimental results in the archival literature demonstrate that grooves do not reduce the force coefficients as much as theory predicts. A common assumption is that deep grooves do not influence a damper or oil seal ring forced response. However, unexpected large added mass coefficients, not adequately predicted, appear to be common in many tested SFD and oil seal configurations. In the case of oil seals, experiments demonstrate that circumferential grooves do reduce cross-coupled stiffnesses but to a lesser extent than predictions would otherwise indicate. A linear fluid inertia bulk-flow model for analysis of the forced response of SFDs and oil seal configurations with multiple grooves is advanced. A perturbation analysis for small amplitude journal motions about a centered position yields zeroth and first-order flow equations at each flow region (lands and grooves). At a groove region, a groove effective depth d η , differing from its actual physical value, is derived from qualitative observations of the laminar flow pattern through annular cavities. The boundary conditions at the inlet and exit planes depend on the actual seal or SFD configuration. Integration of the resulting first-order pressure fields on the journal surface yields the force coefficients (stiffness, damping, and inertia). Current model predictions are in excellent agreement with published test force coefficients for a grooved SFD and a grooved oil seal. The results confirm that large added mass coefficients arise from the flow interactions between the feed/discharge grooves and film lands in the test elements. Furthermore, the predictions, benchmarking experimental data, corroborate that short length inner-land grooves in an oil seal do not isolate the pressure fields of adjacent film lands and hence contribute greatly to the forced response of the mechanical element.

A New Analytic Approximation for the Hydrodynamic Forces in Finite-Length Journal Bearings

Abstract: A new method for determining a closed form expression for the hydrodynamic forces in finite-length plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely long (IL) or infinitely short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. A comparative computational study is presented for the steady-state behavior of the bearing system under static and unbalance loads. The results show the proposed models outperforming the standard limiting approximations as well as a model based on the finite-length impedance method.

Experimental Studies Using Response Surface Methodology for Condition Monitoring of Ball Bearings

Abstract: The presence of defect in the bearing (outer race, inner race, or ball) results in increased vibrations. Time domain indices such as rms, crest factor, and kurtosis are some of the important parameters used to monitor the condition of the bearing. Radial load and operating speed also have an important role in bearing vibrations. The interaction between the defect size, load, and speed helps to study their effect on vibrations more effectively. Response surface methodology (RSM) is a combination of statistical and mathematical techniques to represent the relationship between the inputs and the outputs of a physical system. But so far, the literature related to its application in bearing damage identification is scarce. The proposed study uses RSM to study the influence of defect size, load, and speed on the bearing vibrations. Kurtosis is used as response factor. Experiments are planned using Box Behnken design procedure. Experiments are performed using 6305 ball bearings and the results have been presented. MINITAB statistical software is used for analysis. It is seen from the analysis of the experimental results that the defect size, interaction effect of defect size and load, and interaction effect of defect size and speed are significant. Response surface method using Box Behnken design and analysis of variance has proved to be a successful technique to assess the significant factors related to bearing vibrations.

A Study of Worn Hybrid Journal Bearing System With Different Recess Shapes Under Turbulent Regime

Abstract: The objective of the present paper is to study analytically the influence of wear on the performance of a capillary-compensated, four-pocket, hybrid journal bearing system operating in a turbulent regime by considering various geometric shapes of recess. The present study deals with bearings having four different geometric shapes of recess, i.e., square, circular, elliptical, and triangular recessed bearings. The wear on the bearing surface is modeled using Dufrane's abrasive wear model. The Reynolds equation based on Constantinescu's turbulent lubrication theory has been solved using finite element method along with a restrictor flow equation as a constraint together with appropriate boundary conditions. The numerically simulated results have been presented for a wide range of nondimensional external loads, wear depth parameters, and Reynolds numbers. The numerically simulated results suggest that the combined influence of wear, turbulence, and geometric shape of recess significantly affects the bearing performance. It has been observed that a triangular recessed bearing provides a greater value of minimum fluid film thickness when operating in a turbulent regime. It is also noticed that direct fluid film stiffness coefficients get reduced significantly when bearings operate in a turbulent regime compared with a laminar regime. Further, it is observed that from the viewpoint of fluid film stiffness, a square recessed bearing is found to be most suitable when operating in a turbulent regime.