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.     

Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications

This paper introduces a simple “Rule of Thumb” (ROT) method to estimate the load capacity of foil air journal bearings, which are self-acting compliant-surface hydrodynamic bearings being considered for Oil-Free turbomachinery applications such as gas turbine engines. The ROT is based on first principles and data available in the literature and it relates bearing load capacity to the bearing size and speed through an empirically based load capacity coefficient, D. It is shown that load capacity is a linear function of bearing surface velocity and bearing projected area. Furthermore, it was found that the load capacity coefficient, D, is related to the design features of the bearing compliant members and operating conditions (speed and ambient temperature). Early bearing designs with basic or “first generation” compliant support elements have relatively low load capacity. More advanced bearings, in which the compliance of the support structure is tailored, have load capacities up to five times those of simpler designs. The ROT enables simplified load capacity estimation for foil air journal bearings and can guide development of new Oil-Free turbomachinery systems.     

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.     

Stiffness and Damping Coefficient Estimation of Compliant Surface Gas Bearings for Oil-Free Turbomachinery

Gas foil bearings are a key technology in many commercial and emerging oil-free turbomachinery systems. These bearings are nonlinear and have been difficult to analytically model in terms of performance characteristics such as load capacity, power loss, stiffness, and damping. Previous investigations led to an empirically derived method, a rule-of-thumb, to estimate load capacity. This method has been a valuable tool in system development. The current article extends this concept to include rules for stiffness and damping coefficient estimation. It is expected that these rules will further accelerate the development and deployment of advanced oil-free machines operating on gas foil bearings.     

Fixed-Geometry,Hydrodynamic Bearing with Enhanced Stability Characteristics

This article presents the results of a successful bearing optimization study aimed at identifying a fixed-geometry, hydro-dynamic journal bearing that does not suffer from the low load instability typical of this class of bearings. This goal was met through optimization of a fairly simple objective function based on the rigid rotor whirl-speed ratio, using a constrained, nonlinear algorithm based on sequential quadratic programming. In the interests of reducing computational time, a two-dimensional isoviscous formulation of the Reynolds equation was used for this work. The equation was solved using a finite element approach.

This article includes a discussion of the optimization approach, the finite element solution approach, the resulting bearing design, and its performance characteristics. It concludes with an application example comparing the optimized bearing's predicted performance to a tilting-pad bearing's predicted performance for a centrifugal compressor-like rotor. The mismatch between shaft and bearing stiffness due to the rigid rotor optimization makes the optimized bearing less desirable from an unbalance response point of view. However, the optimized bearing is shown to have very good stability characteristics, which compare favorably to a tilting-pad bearing.     

Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery

The performance and durability of advanced, high temperature foil air bearings are evaluated under a wide range (10 to 50 kPa) of loads at temperatures from 25° to 650 °C. The bearings are made from uncoated nickel based superalloy foils. The foil surface experiences sliding contact with the shaft during initial start/stop operation. To reduce friction and wear, the solid lubricant coating, PS304, is applied to the shaft by plasma spraying. PS304 is a NiCr based Cr₂O₃ coating with silver and barium fluoride/calcium fluoride solid lubricant additions.

The results show that the bearings provide lives well in excess of 30,000 cycles under all of the conditions tested. Several bearings exhibited lives in excess of 100,000 cycles. Wear is a linear function of the bearing load. The excellent performance measured in this study suggests that these bearings and the PS304 coating are well suited for advanced high temperature, oil-free turbomachinery applications.     

Analysis of Foil Journal Bearings with Backing Springs

Gas-lubricated foil journal bearings are simple, in construction, lightweight and well suited for high-temperature applications in turbomachinery. Hearing stiffness is governed primarily by the foil flexural stiffness. The bearing consists essentially of thin overlapping circular metal foils, one end of which is cantilevered to the bearing housing and. the other end rests on an adjacent foil.

An analysis of gas-lubricated foil bearings is presented with a specific type of backing spring used under the foils to control bearing preload, and stiffness. The backing spring acts like, an elastic foundation tinder the foil and radically changes the hydrodynamic pressure distribution generated in the gas film. The pressure distribution is obtained by simultaneously solving the compressible Reynolds equation and. the elasticity equations governing the compliant bearing surface, consisting of foils and backing springs. An iterative scheme is used, to obtain pressure distributions for heavily loaded cases, involving extensive computation, because of the sensitivity of pressure solution to small changes in film thickness distributions attributable to the compliant bearing surface. Pressure distribution, film thickness, bearing load capacity, iterative solution convergence characteristics and bearing power dissipation are presented as a function of journal eccentricity.     

Experimental Determination of the Dynamic Characteristics of a Two-Axial Groove Journal Bearing

A hydrodynamic bearing test rig was used to experimentally study the steady operating characteristics and dynamic coefficient of a plain two-axial groove journal bearing. Using two electrodynamic shakers to generate synchronous sinusoidal excitations, two small independent elliptical displacement orbits were produced for different static equilibrium positions. Data was measured for two fixed shaft speeds, while the steady load was varied to achieve Sommerfeld numbers ranging from 0.063 to 0.344. The four linearized stiffness and four linearized damping coefficients were determined for each speed-load condition by reducing the orbital data using an average magnitude and phase method. The coefficients are presented in dimensionless form as functions of the Sommerfeld number. Typical average uncertainty was found to be 12 percent for the coefficients and 8 percent for the Sommelfeld number. For the speed, load, and temperature ranges tested herein, the dynamic coefficient results for each speed agreed within the uncertainty of the data, supporting the first order approximation that, for the operating range studied, a coefficient's magnitude is independent of the absolute speed, load, and viscosity so long as the Sommerfeld number is matched. The same conclusion was reached for the steady operating location within the bearing clearance space. The overall consistency of these results also lends confidence as to their reliability. Additional experimental results presented include three sets of continuous circumferential oil film thickness and pressure profiles, and discrete temperatures.     

Journal Design Considerations for Turbomachine Shafts Supported on Foil Air Bearings

Foil air bearings can offer substantial improvements over traditional rolling element bearings in many applications and are attractive as a replacement to enable the development of advanced oil-free turbomachinery. In the course of rigorous testing of foil journal bearings at NASA Glenn Research Center, shaft failure was repeatedly encountered at high ambient temperature and rotational speed, with moderate radial load. The cause of failure is determined to be excessive non-uniform shaft growth, which increases localized viscous heating in the gas film and eventually leads to a high-speed rub and destruction of the bearing and journal. Centrifugal loading of imbalance correction weights and axial temperature gradients within the journal due to the hydrodynamic nature of the foil bearings, determined by experiment and finite element analysis, are shown to be responsible for the non-uniform growth. Qualitative journal design guidance is given to aid in failure prevention.     

An Experimental Investigation into the Temperature Profile of a Compliant Foil Air Bearing

A series of tests was performed to determine the internal temperature profile in a compliant bump-type foil journal air bearing operating at room temperature under various speed and load conditions. The temperature profile was collected by instrumenting a foil bearing with nine type-K thermocouples arranged in the center and along the bearing's edges in order to measure local temperatures and estimate thermal gradients in the axial and circumferential directions. To facilitate the measurement of maximum temperatures from viscous shearing in the air film, the thermocouples were tack-welded to the backside of the bumps that were in direct contact with the top foil. The mating journal was coated with a high-temperature solid lubricant that, together with the bearing, underwent high-temperature start-stop cycles to produce a smooth, steady-state run-in surface. Tests were conducted at speeds from 20 to 50 krpm and loads ranged from 9 to 222 N.

The results indicate that, over the conditions tested, both journal rotational speed and radial load are responsible for heat generation with speed playing a more significant role in the magnitude of the temperatures. The temperature distribution was nearly symmetric about the bearing center at 20 and 30 krpm but became slightly skewed toward one side at 40 and 50 krpm. Surprisingly, the maximum temperatures did not occur at the bearing edge, where the minimum film thickness is expected, but rather in the middle of the bearing, where analytical investigations have predicted the air film to be much thicker. Thermal gradients were common during testing and were strongest in the axial direction from the middle of the bearing to its edges, reaching 3.78° C/mm. The temperature profile indicated the circumferential thermal gradients were negligible.     

An Investigation of the Steady-State Performance of a Pivoted Shoe Journal Bearing with ISO VG 32 and VG 68 Oils

This article presents a report on an investigation into the performance characteristics of a steadily loaded pivoted shoe journal (PSJ) bearing that is lubricated with ISO VG 32 and VG 68 oils. The article describes a testing machine on which the experimental investigation was performed. Measurements of shaft torque, pad temperature distributions, oil inlet and outlet temperatures, oil flow rate, and eccentricity have all been recorded as functions of load and speed. The experimental results from both test oils are presented in graphical form and are compared with theoretical predictions obtained from the author's computer model of the PSJ bearing. These results showed that the thicker ISO VG 68 oil provided thicker oil films. However, it also had higher bearing temperatures and power losses. A good correlation between the theoretical and experimental results has been found. Theoretical analysis of the bearing friction losses indicate that shear losses predominate and churning losses account for approximately 20% of the total losses.     

评价箔片径向空气轴承载荷性能的一种经验方法

介绍一种简单的“经验法则”来评价箔片空气轴承的载荷性能,它是一种可挠面的动压气体轴承,正在研究其在无油透平机械中的应用。经验法则是基于基本原理和文献中报道的可靠实验数据得出的,通过一个经验值——载荷系数D,将轴承的载荷性能和轴承的尺寸、速度联系起来。在经验法则中,轴承承载力是轴承转速和轴承设计面积的线性函数。轴承载荷系数D和轴承弹性支承结构的设计特点和轴承运行工况(温度、速度)有关。     

The Role of Radial Clearance on the Performance of Foil Air Bearings

Load capacity tests were conducted to determine how radial clearance variations affect the load capacity coefficient of foil air bearings. Two Generation III foil air bearings with the same design but possessing different initial radial clearances were tested at room temperature against an as-ground PS304 coated journal operating at 30000 rpm. Increases in radial clearance were accomplished by reducing the journal's outside diameter via an in-place grinding system. From each load capacity test the bearing load capacity coefficient was calculated from the rule-of-thumb (ROT) model developed for foil air bearings.

The test results indicate that, in terms of the load capacity coefficient, radial clearance has a direct impact on the performance of the foil air bearing. Each test bearing exhibited an optimum radial clearance that resulted in a maximum load capacity coefficient. Relative to this optimum value are two separate operating regimes that are governed by different modes of failure. Bearings operating with radial clearances less than the optimum exhibit load capacity coefficients that are a strong function of radial clearance and are prone to a thermal runaway failure mechanism and bearing seizure. Conversely, a bearing operating with a radial clearance twice the optimum suffered only a 20% decline in its maximum load capacity coefficient and did not experience any thermal management problems. However, it is unknown to what degree these changes in radial clearance had on other performance parameters, such as the stiffness and damping properties of the bearings.     

An Original Definition of the Profile of Compliant Foil Journal Gas Bearings: Static and Dynamic Analysis

This article deals with a numerical analysis of the static and dynamic performance of a compliant journal gas bearing. The common approach found in foil bearing literature consists in calculating the carrying capacity for a given shaft position. In this study the external load is fixed (magnitude and direction) and the related shaft position is investigated. Nevertheless, a rigid profile, able to support high imposed loads, is no longer valid if one considers that the bearing becomes compliant. An original calculation method of the initial profile considering rigid surfaces is proposed to overcome this problem. The prediction of nonlinear dynamic behavior, i.e., stability and response to external excitation, is investigated. Finally, a viscous damping model is introduced into the dynamic model in order to obtain the amount of structural damping necessary to increase the stability of the compliant journal gas bearing.     

Air Injection as a Thermal Management Technique for Radial Foil Air Bearings

A thermal management technique for radial foil air bearings was experimentally evaluated. The technique is based on injecting air directly into the internal circulating fluid-film to reduce bulk temperatures and axial thermal gradients. The tests were performed on a single top foil, Generation III, radial foil bearing instrumented with three thermocouples to monitor internal temperatures. A through hole in the bearing shell coincident with the gap between the top foil's fixed and free ends provided entry for the injection air. The tests were conducted at room temperature with the bearing operating at speeds from 20 to 40 krpm while supporting 222 N. Two different mass flow rates of injection air were evaluated for this method, 0.017 and 0.051 kg/min. Test results suggest that the air injection approach is a viable thermal management technique capable of controlling bulk temperatures and axial thermal gradients in radial foil air bearings.     

Residual life predictions for ball bearings based on self-organizing map and back propagation neural network methods

This paper deals with a new scheme for the prediction of a ball bearing's remaining useful life based on self-organizing map (SOM) and back propagation neural network methods. One of the key components needed for effective bearing life prediction is the set-up of an appropriate degradation indicator from a bearing's incipient defect stage to its final failure. This new method is different from the others that have been used in the past, in that it uses the minimum quantisation error (MQE) indicator derived from SOM, which is trained by six vibration features, including a new designed degradation index for performance degradation assessment. Then, using this indicator, back propagation neural networks focusing on the degradation periods can be trained. Thanks to weight application to failure times (WAFT) technology, a useful life prediction model for ball bearings has been developed successfully. Finally, a set of accelerated bearing run-to-failure experiments is carried out, with the experimental results showing that the new proposed methods are greatly superior to those, based on L10 bearing life prediction, currently being used.     

On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal

Foil gas bearings have been applied successfully to a wide range of high-speed rotating machinery such as air cycle machines (ACMs) and auxiliary power units (APUs). The performance of these bearings are based on the high pressure gas in a very thin layer between the journal and the bearing governed by the Reynolds equations. Generation of heat in these bearings especially at high journal rotating speed and high loads or at high ambient temperature directly affect their performance. Thermal and fluid flow analysis of an advanced compliant foil journal bearing/seal are presented. The side flow (known as leakage) and the approximate temperatures are the results of this analysis. The result of preliminary analysis shows that the major portion of the heat is carried through conduction and using the modified Couette flow approximation for the present working fluid, air, helped in analysis of the temperature magnitude, which can be related to the gas viscosity behavior and thin gas film thicknesses.     

Dynamic characteristics of a flexible rotor system supported by a viscoelastic foil bearing (VEFB)

Foil bearings have been considered as an alternative to traditional bearings with the increasing need for high-speed, high-temperature turbomachinery. However, the lack of adequate load capacity and sufficient damping capacity is a key technical hurdle to super-bending-critical operation as well as widespread use of foil bearings in turbomachinery such as turbopumps, turbocompressors and turbochargers. A new foil bearing, ViscoElastic Foil Bearing (VEFB) is suggested in this paper. The super-bending-critical operation of the conventional bump foil bearing and the VEFB is examined, as well as the structural dynamic characteristics. The structural dynamic test results show that the equivalent viscous damping of the VEFB is much larger than that of the bump bearing and that the structural dynamic stiffness of the VEFB is comparable or larger than that of the bump bearing. The results of super-bending-critical operation of the VEFB indicate that the enhanced structural damping of the viscoelastic foil dramatically reduces the vibration near the bending critical speed. With the help of increased damping resulting from the viscoelasticity, suppression of the nonsynchronous orbit is possible beyond the bending critical speed.     

A Method for Measuring the Intensity of a Line Load Around a Shaft or Tube

The slip flow effect is considered to estimate the load capacity and the dynamic coefficients of an elastically-supported gas foil hearing when the local Knudsen number for the minimum film thickness is greater than 0.01. The compressible Reynolds equation with slip flow conditions is used to evaluate the load capacity. The linearized dynamic coefficient equations are obtained by the perturbation method. Numerical predictions compare the static and dynamic force performances considering slip flow at room-to-high temperate with the performance of elastically-supported foil bearing without slip flow for a range of bearing compliances and bearing numbers. It has been shown that the slip flow effect on the load capacity and the dynamic coefficients at high temperature is significant in the region of low bearing numbers.     

Ultra-High-Speed Performance of Ball Bearings and Annular Seals in Liquid Hydrogen at Up to 3 Million DN (120,000 rpm)©

The ultra-high-speed performance of a hybrid ceramic 25-mm-bore ball bearing, as well as that of floating-ring seals with a sealing diameter of 30 mm, was determined in liquid hydrogen at speeds to 120,000 rpm, 3 million DN, under thrust loads to 3,140 N and sealed pressures to 1.7 MPaG. The bearings had Si₃N₄ balls and a single outer land-guided retainer. The hybrid ceramic bearing exhibited excellent performance at high load, contrasting with the seized all-steel bearing; however, the ceramic balls developed superficial micro-cracks due to frictional heating. Effective cooling of the bearing was achieved by increasing the jet speed through the nozzles. The bearing power loss drastically increased with increasing speed and cooling flow rate. The critical load capacity without bearing damage was also evaluated. Furthermore, the sealing performance of the one-ring seal was superior to that of the two-ring seal in preventing the sealing ring seizure against the runner.