Effect of Roller Geometry on Roller Bearing Load–Life Relation

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

Influence of the Mechanical Seals on the Dynamic Performance of Rotor–Bearing Systems

In this paper, to consider the effects of mechanical seals, a lumped-mass model and the transfer matrix method are used to establish the equations for the dynamics performance of rotor bearing system. The general inverted iteration method is also used to solve the eigenvalue problem of these equations. To check the response of the rotor bearing system under unbalance motivation, the Gauss method is used to calculate the dynamic response of the constrained vibration. The results, based on the dynamic properties calculation of a typical mechanical spiral seal, such as stiffness coefficients and damping coefficients, exert the influence of the mechanical seal on the rotor bearing system of the high-speed machinery. Meanwhile, some structure parameters that may affect the dynamic performance and forced vibration under unbalance motivation of the rotor bearing system considering mechanical seals are analyzed in the paper. The analysis results show that the mechanical seal more or less has effects on the rotor bearing system. The mechanical seal has much more effects on the flexible rotor bearing system than on the rigid one. For instance, in a certain case, if the effects of the mechanical seal were taken into account, the system s critical speed may increase by 70 80%.     

Wave Journal Bearing with Compressible Lubricant—Part II: A Comparison of the Wave Bearing with a Wave-Groove Bearing and a Lobe Bearing

To identify the potential advantages of the wave journal bearing, a three-wave journal bearing was compared to both a three-wave-groove bearing (a wave bearing with axial grooves that isolate each wave) and a three-lobe bearing. The lobe bearing's profile was selected to approximate the wave journal bearing's profile. The lubricant was assumed to be compressible (gas). The bearing number, A, was parameterized from 0.01 to 100, and the eccentricity ratio, ε, was varied from 0 to 0.4. Data at bearing numbers 0.1, 1, and 50, and eccentricity ratios of 0.1 and 0.4, were selected as representative of the bearing performance. The calculated load capacity and the critical mass are presented for the three bearings. The wave bearing shows a better load capacity than the other bearings at any applied load and running regime. However, at high bearing numbers the lubricant compressibility effect is predominant and all three analyzed bearings show similar load capacity. The critical masses of the wave-groove and lobe bearing are greater than the critical mass of the wave bearing if the applied load is small. For low and intermediate bearing numbers the wave-groove bearing is more stable than the other bearings especially at low wave's amplitude ratio. The lobe bearing is more stable than the other analyzed bearings at high bearing numbers or at large preload ratios. If the applied load increases, the wave bearing dynamic performance is competitive with both wave-groove and lobe bearings. In addition, at high bearing numbers, the wave bearing could run stably for any allocated rotor mass over a wide range of wave position angle. Three wave bearings are more sensitive to the direction of the applied load than the other bearings especially at low and intermediate bearing numbers. Therefore, a careful selection of the waves position angle has to be done to maximize the wave bearing performance.     

Application of Computational Fluid Dynamics and Fluid–Structure Interaction Method to the Lubrication Study of a Rotor–Bearing System

Computational methods were used to analyse the elasto-hydrodynamic lubrication of a complex rotor–bearing system. The methodology employed computational fluid dynamics (CFD), based on the Navier–Stokes equation and a fluid–structure interaction (FSI) technique. A series of models representing the system were built using the CFD–FSI methodology to investigate the interaction between the lubrication of the fluid film, and elastic dynamics of the rotor and journal bearing. All models followed an assumption of isothermal behaviour. The FSI methodology was implemented by setting nodal forces and displacements to equilibrium at the fluid–structure interface, therefore allowing the lubrication of the fluid and the elastic deformation of structures to be solved simultaneously. This is significantly different to the more common techniques—such as the Reynolds equation method—that use an iterative solution to balance the imposed load and the force resulting from the pressure of the fluid film to within a set tolerance. Predictions using the CFD–FSI method were compared with the results of an experimental study and the predictions from an ‘in-house’ lubrication code based on the Reynolds equation. The dynamic response of the system was investigated with both rigid and flexible bodies for a range of different bearing materials and dynamic unbalanced loads. Cavitation within the fluid film was represented in the CFD–FSI method using a simplified phase change boundary condition. This allowed the transition between the liquid and vapour phases to be derived from the lubricant’s properties as a function of pressure. The combination of CFD and FSI was shown to be a useful tool for the investigation of the hydrodynamic and elasto-hydrodynamic lubrications of a rotor–bearing system. The elastic deformation of the bearing and dynamic unbalanced loading of the rotor had significant effects on the position of its locus.     

Calculation of Journal Bearing Dynamic Characteristics Including Journal Misalignment and Bearing Structural Deformation©

A detailed journal bearing analysis for accurate evaluation of film dynamic characteristics is presented. The new formulation is based on a local perturbation of the oil film at each computational node that captures the important effects of journal misalignment and bearing structural deformation in rotor dynamics and engine NVH applications. The new algorithm is an extension to the classical approach of evaluating film dynamic characteristics based on journal eccentricity perturbation. The governing equations for the oil film pressure, stiffness, and damping are solved using a finite difference approach and their output is validated with numerical results from the literature.     

Measured Performance of a Highly Preloaded Three-Lobe Journal Bearing–-Part II: Dynamic Characteristics

The dynamic coefficients of a three-lobe bearing with a preload factor of 0.75 were determined. Principal and cross-coupled stiffness and damping coefficients were derived from measured responses to forced harmonic excitation. Three operating speeds were tested and, for each speed, the load was varied so that the Sommerfeld number ranged from 0.23 to 2.87. Three orbits were used for each test condition, which resulted in three data points for each condition. At each condition the nominal data points fell within the uncertainties of the data. Non-dimensionalized data at all three speeds were independent of any given Sommerfeld number; thus, the Reynolds number had little influence for the range of conditions tested. Data indicated that minimization of the uncertainties is possible with optimal orbit selection.     

Influence of Cage Clearance on Bearing Lubrication©

The effect of the cage clearance on the lubricant supply and elastohydrodynamic (EHL) film thickness has been studied in a ball-on-disc device. A single pocket from a standard nylon cage was mounted around the ball. The cage was instrumented so that the clearance between the cage and ball could be altered. Film thickness measurements were made with and without the cage present and for different clearances. Two lubricants were tested: a lithium hydroxystearate grease and its base oil. Film thickness was measured with increasing speed to determine the onset of lubricant starvation. Without a cage present the grease lubricated contact starved at a very low speed, typically 0.02 m/s and the film thickness dropped to a fraction of the fully flooded value. Starvation did not occur within the speed range for the base oil.

The presence of the cage significantly changed the starvation response. For the base oil reducing the clearance induced starvation by locally removing the lubricant from the track. The grease gave a very different result as reducing cage clearance increased the starvation speed thus ensuring fully flooded behavior over a much greater speed range. The improvement in grease performance with the cage present is attributed to two effects. First, the cage with reduced clearance helps to redistribute the grease into the track. Second, the close conformity between cage and ball promotes shear degradation of the grease structure generating low-viscosity material, which improves replenishment.     

Analysis of Micropolar and Power Law Fluid–Lubricated Slider and Journal Bearing with Partial Slip–Partial Slip Texture Configuration

An analysis of micropolar and power law fluid–lubricated partial slip–partial slip texture slider and journal bearings is presented. The nondimensional pressure and shear stress expressions for a partial slip texture configuration are analyzed using narrow groove theory. The parameters used in the analysis are nondimensional partial slip length, nondimensional partial slip–partial slip texture length, nondimensional depth of recess, ratio of land with slip to recess, nondimensional slip coefficient, coupling number; ratio of characteristic length to film gap, and power law index. A partial slip configuration with a higher slip coefficient yields an improvement in load capacity and reduction in coefficient of friction compared to a partial slip texture configuration for micropolar and power law shear thinning (pseudoplastic) fluid-lubricated slider and journal bearings.     

Nonlinear Numerical Prediction of a Rotor–Bearing System Using Damped Flexure Pivot Tilting Pad Gas Bearings

Flexure pivot tilting pad gas bearings with pad radial compliance (FPTPGB-Cs) and metal mesh dampers (MMDs) in parallel (FPTPGB-C-MMDs) have been considered for application to high-speed and high-performance turbomachinery because of their advantages of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Although the dynamic coefficients of FPTPGB-C-MMDs have been predicted using the linear method, a nonlinear study is urgently needed for their high nonlinear behavior. A nonlinear numerical investigation on the rotor–bearing system supported by FPTPGB-C-MMDs is presented in this study by using the time domain orbit simulation method that couples rotor motion equations, the unsteady Reynolds equation, and pad motion (considering MMDs) equations. The nonlinear predictions are verified by the prediction and experimental results of a published paper.FPTPGB-C-MMDs can effectively suppress the subsynchronous vibrations compared with the rotor system supported by FPTPGB-Cs. The prediction results show that a high damper mesh density has a more positive effect on improving the stability of the rotor system by reducing the subsynchronous vibrations. Investigation shows that MMDs can improve the ability of the rotor system to sustain the effect of destabilizing forces. A high damper mesh density can sustain large destabilizing forces. The simulation results also indicate that low pad radial stiffness or preload leads to high amplitudes of subsynchronous vibrations. A small clearance results in an increase in critical speed and its synchronous amplitude. Moreover, large clearance results in a wide speed range that leads to the occurrence of subsynchronous vibrations with large amplitudes.     

Experimental and Numerical Study of Multibody Contact System with Roller Bearing–-Part II: Semi-Finite Element Analysis and Optimal Design of Housing

A typical roller bearing system consists of five contact parts: the housing, outer ring, inner ring, roller set, and the shaft. A finite element calculation procedure is described to analyze a five-body contact roller bearing system. If an analytical solution is used to calculate the deformations of the roller and the ring/shaft combination, a semi-finite element governing equation can be derived by simplifying the five-body contact bearing system into a three-body contact system. The semi-finite element calculation results correlate closely with the test results obtained in Part I of this paper (1). The analysis indicates that the initial gap between the housing and the outer ring and the loading positions have significant influence on the load distribution in the bearing. By optimal design of the housing, the load distribution becomes more uniform and the fatigue life of the bearing can be increased.     

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Thermohydrodynamic Analysis of a Journal Bearing in a Turbulent Flow Regime—Part II: Application to an Axial Groove Bearing

The governing equations developed in (1), where a perturbation method is applied in the equation of motion and the energy equation is linearized, are used to study journal bearings of finite length operating in turbulent flow regimes. The thermohydrodynamic solutions are obtained for a journal bearing with four axial grooves. Heshmat and Pinkus' mixing theory (2) is used to evaluate the inlet temperature of each sector. These governing equations are solved to yield pressure, mass-mean velocity and temperature distributions, the mixing temperature at the inlet and the flow rates at the entry and exit of each sector, and the fictional forces.     

Microstructure–Property Relationships in M50-NiL and P675 Case-Hardened Bearing Steels

Case-hardened steels, widely used in high-performance ball and roller bearings, have high surface hardness and a gradient in material properties (hardness, yield strength, etc.) as a function of depth; therefore, they behave as functionally graded materials. Understanding the mechanical properties due to gradients in the subsurface microstructure of case-hardened steels is important for modeling the effects of cyclic damage induced by rolling contact fatigue. In the current study, two different commercially available case-carburized steels (P675, M-50 NiL) and two through-hardened steels (M-50, case P675) were characterized to obtain relationships among the volume fraction of subsurface carbides, indentation hardness, elastic modulus, and yield strength as a function of depth. A variety of methods including microindentation, nanoindentation, ultrasonic measurements, compression testing, rule of mixtures, and upper and lower bound models were used to determine the above relationships and compare the experimental results with model predictions. In addition, the morphology, composition, and properties of the carbide particles are also discussed. It was found that the subsurface hardness and volume fraction of carbides are linearly related. Finally, it was found that the estimation of composite modulus from a well-established model compares with measurements from the ultrasonic method and compression tests. The results presented are of immediate engineering relevance to the bearing industry, with importance to modeling of microstructure and its effects on rolling contact fatigue life.     

Investigations on the Influence of Surface Texturing on a Couple Stress Fluid–Based Journal Bearing by Using JFO Boundary Conditions

The present study was conducted to examine the effect of laser surface texturing combined with couple stress fluids on the hydrodynamic lubrication of finite journal bearing in this work. The Jakobsson-Floberg-Olsson (JFO) boundary conditions were engaged instead of Reynolds boundary conditions to achieve realistic results. Moreover, the results were computed and authenticated with the previous published work. It was observed that the load-carrying capacity is increased with couple stresses for smooth journal bearings at different eccentricity ratios. However, the increment in load-carrying capacity with texture affects only at low eccentricity ratios. The combined effects of texturing with couple stress fluids lower the performance of journal bearings at different eccentricity ratios.     

Wave Journal Bearing with Compressible Lubricant—Part I: The Wave Bearing Concept and a Comparison to the Plain Circular Bearing

To improve hydrodynamic journal bearing steady-stale and dynamic performance, a new bearing concept, the wave journal bearing, was developed at the author's lab. This concept features a waved inner bearing diameter. Compared to other alternative bearing geometries used to improve bearing performance such as spiral or herringbone grooves, steps, etc., the wave bearing's design is relatively simple and allows the shaft to rotate in either direction. A three-wave bearing operating with a compressible lubricant; i.e., gas, is analyzed using a numerical code. Its performance is compared to a plain (truly) circular bearing over a broad range of bearing working parameters, e.g., bearing numbers from 0.01 to 100. The geometry of the wave bearing gives the bearing its high load; i.e., stiffness, and stability characteristics. The wave bearing's performance is dependent upon the amplitude of the wave and the position of the waves relative to the applied load. To maximize wave bearing performance, the waves' position relative to the applied load should be carefully selected. The wave journal bearing offers better stability than the plain circular bearing' under all operating conditions and all wave-load orientations. Specifically, an unloaded journal bearing can be made to run stably in any operating regime by incorporating the wave geometry.     

Test of a Fluid-Film Wave Bearing at 350°C with Liquid Lubricants

A novel fluid-film wave bearing has been run at a higher temperature (350°C) than ever before with a perfluoropolyether (PFPE)-K liquid lubricant. Additionally, the wave journal bearing (45 mm diameter and 24 mm long) completed an 8-h endurance test at the NASA Glenn Research Center. The lubricant was PFPE-K XHT 500. After being maintained at 350° C for 8 h, the bearing temperature was raised to 356°C for the last 30 min of the run. The speed was 29,000 rpm and the load ranged from 2670 to 3560 N. The bearing was perfectly stable both dynamically and thermally. The observed temperature was more than 150°C above that run with current turbine engine lubricants. The use of high-temperature bearings as tested here would allow efficiency increases of more than 5% in aero or terrestrial turbine engines.     

Analysis of Viscosity Interaction and Heat Transfer on the Dual Conical-Cylindrical Bearing©

Viscosity is an essential property in hydrodynamic lubrication. In general, the lubricant is not considered to have uniform viscosity within a given bearing. The viscosity of the lubricant is affected by both pressure and temperature. The viscosity of the lubricant increases with pressure and, for most lubricants, this effect is much larger than that of temperature or shear when the pressure is significantly above atmospheric pressure. This study analyzes the thermal effect of dual conical-cylindrical bearing performance parameters via the viscosity-pressure-temperature relationships of lubricants. The results reveal that pressure increases both the film viscosity and temperature.     

A Theoretical Study of the Effect of Offset Loads on the Performance of a 120° Partial Journal Bearing

Reynolds' equation for a 120° partial journal bearing of the clearance type having an L/D ratio of 1 is solved numerically to determine the effect of positioning circumferentially the line of action of the load at various points along the bearing arc. The influence of the load position (α/β) on film thickness, eccentricity, journal position, friction, flow, temperature rise, and maximum film pressure is investigated and performance curves given. It is shown that the position of the load has a significant effect on bearing performance.     

Comparative study of the tribological behavior of self-lubricating W–S–C and Mo–Se–C sputtered coatings

Transition metal dichalcogenides (TMD) have been one of the best alternatives as low friction coatings for tribological applications, particularly in dry and vacuum environments. However, besides their deficient behavior in humid containing atmospheres, their extensive application has also been restricted due to their low load-bearing capacity. In order to overcome these problems, recently the alloying with C has been tried with the expectation of simultaneously improving the coatings hardness and reaching sliding contacting phases more convenient for achieving low friction in humid environments.The practical application of this concept was extensively studied with the W–S–C system, with the C addition being achieved either by reactive or co-sputtering processes. The best tribological results were obtained by co-sputtering from a C target embedded with an increasing number of WS₂ pellets. Excellent results were reached from the more than one order of magnitude increase in the coatings hardness up to friction coefficients which are close to those of the references of self-lubricating coatings: TMD for dry or vacuum atmospheres or C-based coatings for terrestrial sliding conditions.Following the good results achieved with W–S–C system, other TMDs systems have been envisaged to be studied. The main focus was placed on the Mo–Se–C system.In this paper, the general comparison between W–S–C and Mo–Se–C coatings is presented. The main effort is pointed on the tribological behavior of both systems when tested by pin-on-disk against steel counterpart balls under different testing conditions: applied normal loads, temperatures and relative humidity of the atmospheres. Both coatings were deposited by co-sputtering from a C target with a varying number of TMD pellets which could lead to C contents in the films in the range from 30  up to 70 at.%. A Ti interlayer was interposed between the films and the substrates for improving the adhesion.Typically, W–S–C films are harder than Mo–Se–C films. From the tribological point of view, W–S–C films are more thermally stable than Mo–Se–C films although the friction coefficients of these last ones are lower when tested in humid containing atmospheres.