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.     

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.     

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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.     

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.     

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.     

A Pressure Dam Bearing Analysis with Adiabatic Thermal Effects©

To improve the stability of fixed geometry journal bearings in high-speed rotating machinery, pressure dam or stepped bearings have often been used in place of plain or other bearings. Despite their long history and wide range of applications in industry, only isoviscous analyses have been reported in the literature. Since stability problems usually occur at relatively high speeds where considerable heating occurs, it is desirable to include the thermal effects in pressure dam bearing analysis. This study presents a full adiabatic thermohydrodynamic analysis for pressure dam bearings. The theoretical results show that the pressure and temperature distributions on a stepped pad are quite different from those on a smooth pad. The thermal effects have significant influence on the predicted bearing performance, such as journal eccentricity, dynamic coefficients, and rotor stability. The example of a flexible rotor indicates improved stability prediction with the thermal effects included.     

White Etching Cracking—Simulation in Bearing Rig and Bench Tests

White etching cracking (WEC) is a contact fatigue bearing failure commonly observed in wind turbine applications. It can lead to fatigue lifetimes more than an order of magnitude shorter than expected lifetimes. Though various mechanical and chemical factors have shown direct or indirect impacts of on WEC failure, the correlations between these factors are yet to be fully understood. The critical intersection among various lubricant- and non-lubricant-related parameters and their influence on hydrogen diffusion and WEC formation are discussed in this article. Experimental results are shown under diverse operating conditions and contact configurations using three test rigs. This study confirms that the mechanical properties of a rolling contact and lubrication parameters alone cannot predict WEC failure. The formation of a tribofilm and accumulation of atomic hydrogen below the contact surface can be essential to explain WEC events. Higher hydrogen concentration in the WEC zone depends on contact area size, the presence of metal-containing additives in lubricants, and higher frictional energy dissipation. Finally, a mechanism of WEC failure has been proposed that intersects the overlap of hydrogen and subsurface shear stress.     

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.     

The Wave Complex of the СПРУТ-VI Instrument Package

The wave complex of the -VI instrument package was designed for monitoring the electromagnetic state around orbital stations. The method of combined wave probes enables simultaneous vector measurements of magnetic field fluctuations (in a frequency range from 0.1 Hz to 40 kHz) and the electric current density in plasma (in a range of 10^–6–10^–13 cm^–2), as well as determination of the station surface potential (in a range of 10^–3–20 V). The complex was used onboard the Mir station for investigating the fine structure of distributions of ionospheric charged particles at low and near-equatorial latitudes.     

Using µPIV to Investigate Fluid Flow in a Pocketed Thrust Bearing

This article presents the results of an experimental and analytical investigation of the fluid flow in a pocketed thrust bearing. An experimental test rig was designed, developed, and used to visualize fluid flow in pocketed thrust bearings. Microparticle image velocimetry (μPIV) was used to measure fluid flow inside the pocket of a thrust bearing. The thrust bearings were constructed by gluing precision shim stocks to a flat BK7 glass disk in contact with a polished steel disk. The precision shim stock provides the desired pocket depth for the bearing. A polished steel disk in contact with the thrust bearing was driven by a motor in order to induce fluid flow within the pockets. μPIV was then employed to measure the shear-driven cavity flow and generate the quiver plots of the flow field. Three different lubricants were used at various speeds and a constant load to measure the effects of speed and viscosity on the flow out of the pocketed thrust bearing. In order to achieve the analytical aspect of this research, a model was developed to predict the film thickness, cavitation area, and pressure distribution generated within the bearing. The cavitation areas obtained from the model were compared with the experimental results. The results corroborate well. The calculated pressure and film thickness were then used to determine the 3D velocity profiles within the pocketed thrust bearing. The measured velocities obtained from the experimental images were compared to the analytical velocity fields. Comparing the measured velocities with the analytical model, the depth of the microparticles in the bearing pocket was determined. Using this approach, the μPIV-measured 2D velocity field was converted into a 3D velocity field, which illustrates the fluid motion inside a pocketed thrust bearing at various speeds and viscosities.     

Nonlinear Dynamic Response of Cylindrical Roller Bearing–Rotor System with 9 Degree of Freedom Model Having a Combined Localized Defect at Inner–Outer Races of Bearing

This article presents a nonlinear dynamic model for a cylindrical roller bearing–rotor system with interaction forces between the inner race, outer race, and roller. Roller–race contacts are modeled predicting nonlinear stiffness (Hertz contact theory) and nonlinear damping for a rotor–cylindrical roller bearing system. Here a shaft–rotor bearing system is modeled with 9 degrees of freedom with one defect on the inner race and one defect on the outer race for a case of combined localized defects. In the mathematical formulation, contacts between rolling elements and inner and outer races are considered as nonlinear springs and nonlinear damping is taken into consideration. Contact force calculations with nonlinearity are solved using the Newton-Raphson method for n unknown nonlinear simultaneous equation. The Newmark-β implicit integration technique coupled with the Newton-Raphson method is used to solve the differential equations. The results are obtained in the form of a time domain plot, frequency domain plot, and phase plot/Poincare map. The validity of the proposed model is compared with experimental results. A bifurcation graph of speed versus peak amplitude predicts the behavior of the system.     

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Rolling Bearing Service Life Based on Probable Cause for Removal—A Tutorial

In 1947 and 1952 G. Lundberg and A. Palmgren developed what is now referred to as the Lundberg-Palmgren model for rolling bearing life prediction based on classical rolling-element fatigue. Today, bearing fatigue probably accounts for less than 5% of bearings removed from service for cause. A bearing service life prediction methodology and tutorial indexed to eight probable causes for bearing removal, including fatigue, are presented that incorporate strict series reliability; Weibull statistical analysis; available published field data from the Naval Air Rework Facility; and ～224,000 rolling-element bearings removed for rework from commercial aircraft engines. Bearing service life L_serv can be benchmarked and calculated to the bearing L₁₀ fatigue life as follows: L_serv = X^1/m L₁₀, where X is the number of bearings removed from service because of fatigue divided by the total of all bearings removed from service regardless of cause and m is the Weibull modulus of the bearings removed from service. The most conservative bearing L₁₀ service life calculation is obtained assuming an exponential distribution where m = 1.1. Of the ～224,000 commercial engine bearings removed from service for rework, 1,977 or 0.88% were rejected because of fatigue. From the Naval Air Rework Facility bearing data, eliminating rolling–element fatigue as a cause for removal, the L₁₀ service life of these bearings would increase by approximately 3%.     

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.     

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.     

A Model for Rolling Bearing Life with Surface and Subsurface Survival—Tribological Effects

Until now the estimation of rolling bearing life has been based on engineering models that consider an equivalent stress, originated beneath the contact surface, that is applied to the stressed volume of the rolling contact. Through the years, fatigue surface–originated failures, resulting from reduced lubrication or contamination, have been incorporated into the estimation of the bearing life by applying a penalty to the overall equivalent stress of the rolling contact. Due to this simplification, the accounting of some specific failure modes originated directly at the surface of the rolling contact can be challenging. In the present article, this issue is addressed by developing a general approach for rolling contact life in which the surface-originated damage is explicitly formulated into the basic fatigue equations of the rolling contact. This is achieved by introducing a function to describe surface-originated failures and coupling it with the traditional subsurface-originated fatigue risk of the rolling contact. The article presents the fundamental theory of the new model and its general behavior. The ability of the present general method to provide an account for the surface–subsurface competing fatigue mechanisms taking place in rolling bearings is discussed with reference to endurance testing data.     

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%.     

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.     

Polarographic Reduction Wave of Hemoglobin and its Application to Micro‐Determination

Abstract

An adsorptive reduction wave of hemoglobin at about ?1.43 V (vs. SCE), in phosphate buffer solution, pH 6.8, was found by using single sweep polarography. Based on this wave, a simple, rapid, and reliable polarographic method for hemoglobin determination was developed. The wave height is linearly proportional to the concentration of hemoglobin in the range of 1.0–28 mg/L (correlation coefficient 0.997). The detection limit is 0.5 mg/L. Serum albumin, common amino acids, and metal ions present no interference with the hemoglobin determination.

The proposed method was applied to the determination of hemoglobin in human blood samples with satisfactory results. The polarographic wave is attributed to the direct reduction of hemoglobin at the dropping mercury electrode. The new method could be useful in biochemical, clinical, and pharmaceutical analysis.