Hydrodynamic Fluid Film Research Articles

Dynamic Response of a Rotor Supported on Hybrid Bearings in Air, Water, and Liquid Nitrogen: Measurements and Comparisons to Predictions

Abstract Modern liquid rocket engine turbopumps implement hybrid bearings, which combine hydrostatic and hydrodynamic fluid film principles, in compact and lightweight units known for their superior reusability, durability, and reliability. This study aims to provide extensive and reliable test data for the purpose of anchoring and benchmarking predictive tools for these bearings. This paper provides comprehensive dynamic response measurements of a rotor weighing 10.40 kg and approximately 60 mm in diameter at the bearing locations. The test rotor is supported on two hybrid journal bearings with a bearing length to bearing diameter ratio of approximately 0.42 and a bearing radial clearance to rotor radius ratio of around 0.0017. The bearings are tested with air, water, and liquid nitrogen, serving as surrogate test fluids for common propellants in liquid rocket engines. Rotor run-up and speed coast-down tests are conducted to measure shaft motion responses. The results clearly demonstrate that the rotordynamic characteristics of the test rotor supported on the hybrid journal bearings largely rely on properties of the test fluids and their feeding conditions. Notably, when air is pressurized into the test bearings, the shaft motion responses differ markedly from those observed with water and liquid nitrogen, primarily due to significantly lower stiffness and damping coefficients. Furthermore, rotor speed coast-down tests for each test fluid exhibit notable differences in coast-down speed over time characteristics, depending on the test fluid properties. The predicted rotor imbalance responses exhibit excellent correlation with the measurement data. The steady increase of demand and growth of the fluid film bearing technology for reusable rocket engines require accurate bearing design tools, the extensive component testing, and the implementation of the technology. The validated and developed bearing predictive models from previous research demonstrate well the characteristics of bearings under various operating fluids conditions. The findings and database presented in this work contribute not only to comprehending the performance of hybrid bearings but also to understanding and enhancing the dynamic characteristics of rotor systems supported on hybrid bearings.

Topological optimization and fatigue life prediction of a single pad externally adjustable fluid film bearing

This work focuses on the prediction and comparison of the fatigue life of topologically optimized pads in an externally adjustable fluid film (EAFF) bearing. It integrates one-way/two-way fluid–structure interaction analysis, topological optimization (TO), and design modifications of the pad of an externally adjustable fluid film bearing. The major goal is to create an optimum pad design that minimizes weight and maintains structural integrity, and then to predict and compare the fatigue life of these alternative designs. The outcomes of the present study are as follows: (i) Two-way FSI results show a decrease of 65.64% in hydrodynamic fluid film pressure when compared to one-way FSI results because they take into account modifications in the fluid region's geometry caused by pad deformation; (ii) even though the maximum pad deformation in optimized pad geometry (Type-4) resulting from oil film pressure is relatively small (0.0036551 mm), the influence of pad deformation on the fluid domain due to hydrodynamic fluid film pressure cannot be understated; and (iii) when comparing the TO technique's results with fatigue life results, four elongated holes in the radial direction (Type-4) are most appropriate.

Design a cooling pillow to support a high-speed supercritical CO2 turbine shaft

• High speed supercritical CO 2 turbine rotor shaft cooling zone. • Modeling a cooling pillow to cool the shaft and to provide dynamic support. • Design charts and figures for the cooling zone. • Rotor dynamic analysis through the Campbell diagram. • Trade-off analysis in designing the cooling zone. Supercritical CO 2 cycles offer a new thermal power generation paradigm but their commercial deployment has been slow due to significant turbine design challenges. Rotor bearings and seal design are identified as the critical challenges due to the high temperatures, high pressures, and high rotational speeds, a combination of extreme values not encountered in any other past turbine applications. This paper presents a new supercritical CO 2 turbine configuration that addresses these challenges by introducing a rotor shaft cooling zone to control the temperatures encountered by the seals and the bearings. This makes it possible to use proven conventional seal and bearing technology. The salient feature is referred to as a ‘cooling pillow’ that cools the rotor shaft to a tolerable seal temperature by circulating supercritical CO 2 fluid through the annulus and at the same time provides dynamic support to the rotating shaft against vibration. Turbulent heat transfer and frictional heat generation correlations for the annuli have been employed to evaluate the cooling performance and the simplified Reynolds equation for hydrodynamic fluid film lubrication has been employed to evaluate the dynamic performance. Design charts and figures are presented using non-dimensional parameters to help with the design of supercritical CO 2 turbines at different temperatures and sizes. The COMSOL rotor-bearing system simulator consisting of bearing and disks with the main shaft has been employed to produce Campbell plots and carry out a parametric study of rotor vibration frequencies varying with the cooling zone design. The cooling capacity is found to be significantly higher than the cooling load required. Moreover, the convection heat transfer coefficient and dimensionless temperature distribution are independent of radial clearance and this offers trade-offs in terms of controlling rotor vibrations. Through the pursuit of such trade-offs, it is demonstrated that dynamic performance can be improved by up to 55% and 60% for the 0.5 MW and 10 MW turbine sizes, respectively.

Experimental study on the effect of surface texture on tribological properties of nanodiamond films under water lubrication

The effect of nanoscale surface texture on the frictional and wear performances of nanocrystalline diamond films under water-lubricating conditions were comparatively investigated using a reciprocating ball-on-flat tribometer. Although the untreated nanocrystalline diamond film shows a stable frictional state with an average friction coefficient of 0.26, the subsequent textured films show a beneficial effect on rapidly reducing the friction coefficient, which decreased to a stable value of 0.1. Furthermore, compared with the nanocrystalline diamond coating, the textured films showed a large decreasing rate of the corresponding ball wear rate from 4.16 × 10−3 to 1.15 × 10−3 mm3/N/m. This is due to the fact that the hydrodynamic fluid film composed of water and debris can provide a good lubrication environment, so the entire friction process has reached the state of fluid lubrication. Meanwhile, the surface texture can greatly improve the hydrophilicity of the diamond films, and as the texture density increases, the water contact angle decreases from 94.75° of the nanocrystalline diamond film to 78.5° of the textured films. The proper textured diamond film (NCD90) exhibits superior tribological properties among all tested diamond films, such as short run-in period, low coefficient of friction, and wear rate.

Experimental investigations on the effect of rod surface roughness on lubrication characteristics of a hydraulic O-ring seal

The surface roughness of friction pairs plays a significant role in the formation of hydrodynamic fluid film between rod-seal interface. To investigate the influence of rod surface roughness on lubrication characteristics of hydraulic reciprocating seal, the friction force and the net leakage of seal under quasi-constant speed conditions and variable speed conditions are compared and analyzed, by using a self-designed experimental device. The results show that the rod surface roughness has an important influence on seal behavior and cannot be ignored. The rougher the rod surface is, the greater the friction force and the net leakage are, and the seal is more prone to meet with the rolling torsion or fatigue failures under the conditions of frequent start-up and shut-down.

Hydrodynamic Fluid Film and Tribofilm Formation—Combining the Friction Signals with Contact Resistance

Abstract Under unidirectional sliding, the Stribeck-type curve traverses different lubrication regimes. Under mixed/boundary conditions, tribofilms formed by additives in lubricants represent a key mechanism for preventing wear but are difficult to investigate because of the complex composition of lubricants, their small thickness, and their amorphous nature. The formation of a hydrodynamic fluid film depends on the topography and the viscometric fluid properties. Low coefficients of friction do not consequently indicate that hydrodynamic fluid films were formed. The electric contact resistance serves here as a complementary indicator to identify the hydrodynamic fluid film and tribofilm formation under transient or static sliding conditions. The frictional work (WR) is a useful quantity to assess the contribution to the frictional losses of all lubrication regimes in a Stribeck-type curve.

Implication of Surface Texture and Slip on Hydrodynamic Fluid Film Bearings: A Comprehensive Survey

Implication of Surface Texture and Slip on Hydrodynamic Fluid Film Bearings: A Comprehensive Survey

Computational evaluation of dynamic coefficients of thrust bearings; effect of artificial texturing on thermohydrodynamic performance

Fluid film thrust bearings are commonly used in industry, providing durable and reliable operation at high values of load carrying capacity, accompanied by low friction losses. A major advantage of hydrodynamic fluid film bearings, over other types of bearings, is their enhanced dynamic behaviour, especially under transient or impact loads. Currently, a systematic approach to identify the dynamic coefficients of thrust bearing geometrical configurations utilising high complexity CFD simulation data has not yet been established. It is therefore imperative to develop a method, capable of evaluating the dynamic characteristics of complex bearing designs and allow the evaluation of bearing response under transient loads. In the present work, a computational approach is proposed to estimate the stiffness and damping coefficients of fluid-film thrust bearings. A CFD-based ThermoHydroDynamic (THD) numerical model of the bearing is developed and utilised for performing an initial steady-state simulation at given rotational speed and thrust load, as well as subsequent transient simulations at increasing or decreasing thrust loads. The former simulation is used to calculate the stiffness coefficient of the bearing at the specified conditions, while the latter are appropriately post-processed to estimate the damping coefficient of the bearing at different values of rotor acceleration. The procedure is repeated at different operating conditions, yielding a map of the dynamic coefficients of the bearing. Finally, a single degree of freedom model is generated, which utilises the calculated values of dynamic coefficients to evaluate transient bearing performance under any given thrust load history. The proposed methodology is applied to compare the dynamic response characteristics of a conventional sector-pad tapered-land thrust bearing and a textured tapered-land thrust bearing of the same principal dimensions.

Compressible fluid film lubrication of rollers with thermal effects

The present paper squarely aims to analyze the squeezing velocity of a hydrodynamic lubrication used for symmetric roller bearings. Hydrodynamic compressible fluid film lubrication of cylindrical rollers is here considered under the influence of non Newtonian power law lubricants with squeezing velocity and cavitations. The changes that show up in lubrication consistency due to pressure, density and temperature are shown via ures and tables. Further, pressure, density, temperature, load, traction and coefficient of traction for various consistency index n and normal speeds are calculated and compared with the previous results. Those results are united with the previous findings.

Influence of micro-groove attributes on frictional power loss and load-carrying capacity of hybrid thrust bearing

PurposeMicro-surface texturing is emerging as a possible way to enhance the tribological performance of hydrodynamic fluid film bearings. In view of this, numerical simulations are carried out to examine the influence of surface texture on performance of hybrid thrust bearing system. This paper aims to determine optimum attributes of micro-grooves for thrust bearing operating in hybrid mode.Design/methodology/approachAn iterative source code based on finite element formulation of Reynolds equation has been developed to numerically simulate flow of lubricant through the bearing. Mass-conserving algorithm based on Jakobsson–Floberg–Olsson (JFO) condition has been used to numerically capture cavitation phenomenon in the bearing. Gauss Siedel method has been used to obtain steady state performance parameters of the bearings.FindingsA parametric study has been performed to improve the load supporting capacity of the bearing by optimizing micro-groove attributes and configuration. It is noticed that use of full-section micro-groove is beneficial in improving the efficiency of bearing by enhancing the fluid film reaction and reducing the film frictional power losses.Originality/valueThis study is helpful in examining the usefulness of micro-groove textured surfaces in hybrid thrust bearing applications.

Squeeze film dampers supporting high-speed rotors: Fluid inertia effects

This work represents closed-form analytical expressions for the operating parameters for short-length open-ended squeeze film dampers, including the lubricant velocity profiles, hydrodynamic pressure distribution, and lubricant reaction forces. The proposed closed-form expressions provide an accelerated calculation of the squeeze film damper parameters, specifically for rotordynamics applications. In order to determine the analytical solutions for the squeeze film damper parameters, the thin film equations for lubricant are introduced in the presence of the influence of lubricant inertia. Subsequently, two different analytical techniques, namely the momentum approximation method, and the perturbation method are applied to the thin film equations. Moreover, the solution for the lubricant flow equations are analytically determined to represent closed-form expressions for the hydrodynamic pressure distribution and the velocity component profiles in squeeze film dampers. Additionally, the expressions for the hydrodynamic pressure distribution are integrated over the journal surface, either numerically or analytically by using Booker’s integrals, to develop expressions for the fluid film reaction forces. Lastly, the developed squeeze film damper models are incorporated into simulation models in Matlab and Simulink®, and the results are compared against a well-established force coefficient model to verify the accuracy of the calculations. The results of the simulations verify the effect of the lubricant inertia components, namely the convective and temporal (i.e., unsteady) inertia components on the squeeze film damper dynamics, including hydrodynamic pressure distribution and fluid film reaction forces. Additionally, the simulation results suggest a close agreement between the proposed models and the results in the literature.

Lithium Based Grease with Additives as an Alternative Lubricant for Conventionally Oil Lubricated Journal Bearings of Sugarcane Crushing Mills

The purpose of this work was to examine the tribological issues related to failure of heavily loaded split journal bearings sugarcane crushing mills. . It was also identified that hydrodynamic fluid film was not formed due to low speed of journal. Regime of lubrication for such journal bearings is thin film lubrication. In such situations journal and bearing surface has physical contact and adhesive or abrasive wear may occur. For such situations grease lubrication can be adopted for journal bearings. Suitability of Lithium Grease with additives as lubricant for sugarcane crushing mills is verified using four ball tester machine.

Stability Analysis of Various Lengths Conical Hydrodynamic Bearing for Variable Load Conditions

Conical hydrodynamic journal bearing is used to sustain radial load and observed to adjust the effect of axial load on rotating elements. Small compact size conical hydrodynamic fluid film bearings are used in many applications, such as compact hard disc drive. Hence need arises to explore the performance of these bearing for variable load condition and various sizes in terms of aspect ratio. These conical bearings also emerge with better feature to replace two separate bearings (journal and thrust bearings) in various applications. The present study proposed the stability analysis of conical hydrodynamic journal bearing in terms of stiffness and damping coefficients for bearing of semi cone angle (γ = 30o) and bearing size in terms of aspect ratio (λ = 0.5, 0.8, 1.0) for a wide range of radial load ((W_r ) =0.1-0.9) on rotating journal at a speed of 500 rpm. Finite element method has been used to solve the modified Reynolds equation in spherical coordinate system to investigate the flow of lubricant in the clearance space. Stability parameters for various configuration of conical hydrodynamic bearing have been presented and discussed in terms of direct and cross coupled stiffness coefficients, damping coefficients and threshold speed margin. Results show that threshold speed (ω _th) of conical journal bearing is improved for short bearings when aspect ratio changes from 1.0 to 0.5.

Cartilage and Joint Lubrication: New Insights Into the Role of Hydrodynamics

Cartilage is slippery when hydrated but it loses hydration and lubricity during loading. However, dehydrated cartilage regains lubricity during high-speed sliding in the stationary contact area; this result is often interpreted as experimental evidence of fluid film lubrication based on theoretical predictions that pre-equilibrated cartilage remains equilibrated during sliding in this testing configuration. In-situ compression measurements were made during variable speed stationary contact area experiments with fully and partially equilibrated osteochondral cores under saline lubrication to test this prediction. Reduced friction coefficients and compression were observed during high speed sliding, at near-physiological speeds. The results suggest that the marked friction reductions observed during high-speed sliding following equilibration were likely consequences of interstitial fluid recovery, a mechanism we term tribological rehydration, rather than the formation of a hydrodynamic fluid film. The results also suggest that hydrodynamic pressurization was the likely driving force underlying the tribological rehydration phenomenon. We propose that external hydrodynamic pressures in the convergent wedge near the leading edge of contact pushed fluid into the porous surface to restore hydration, thickness, mechanical stiffness, and lubrication following periods of static exudation.

Levitation force of small clearance superconductor–magnet system under non-coaxial condition

A novel superconducting tilting-pad bearing was proposed for the advanced research of reusable liquid hydrogen turbopump in liquid rocket. The bearing is a combination of superconducting magnetic bearing and hydrodynamic fluid-film bearing. Since the viscosity of cryogenic fuel to activate superconducting state and form hydrodynamic fluid-film is very low, bearing clearance will be very small. This study focuses on the investigation of superconducting levitation force in this kind of small clearance superconductor–magnet system. Based on Bean critical state model and three-dimensional finite element method, an analysis method is presented to obtain the levitation force under such situation. Since the complicated operational conditions and structural arrangement for application in liquid rocket, center lines of bulk superconductor and magnet rotor will usually be in non-coaxial state. Superconducting levitation forces in axial direction and radial direction under non-coaxial situation are also analyzed by the presented method.

Soft micro-elastohydrodynamic lubrication and friction at rough conformal contacts

Conformal surfaces in parallel sliding lack a macroscopic hydrodynamic pressure and fluid film formation mechanism. However, such a mechanism still exists on a microscopic level due to roughness. It is common to translate roughness into a variation of fluid film thickness which in turn yields a hydrodynamic pressure distribution resulting in a net hydrodynamic lift. Reynolds equation and a suitable cavitation algorithm suffice to describe this effect mathematically. In case one surface consists of a compliant material with low modulus of elasticity, the deformation of asperities due to pressures and shear stresses in the fluid cannot be neglected—in fact, besides cavitation, it significantly contributes to the net hydrodynamic lift. Therefore, a coupling between fluid dynamics and elastic solid body deformations needs to be introduced. An additional complication arises when the hydrodynamic lift and the subsequent separation of the mean lines of the contacting rough surfaces is not enough to prevent asperity contacts completely. This situation is known as mixed lubrication where part of the normal load is transmitted at asperity contacts. These contacts are commonly treated as solid body contacts with a Coulomb-like friction law or more sophisticated solid friction models. However, when considering asperities as contraformal Hertzian contacts, elastic deformation may allow for the existence of thin micro-elastohydrodynamic lubricant films preventing direct solid body contact even at speeds which otherwise would be regarded as deep within the mixed lubrication regime close to boundary lubrication. These films may not be able to prevent wear completely, but may reduce friction significantly in comparison to dry friction. In this paper, the existence of such effects is demonstrated both by simulation and by experiments with elastomeric radial lip seals.

Dynamic Characteristics of High- $T_{c}$ Superconductor and Hydrodynamic Fluid-Film Compound Bearing for Rocket Engine

A kind of superconducting tilting-pad bearing, which is a compound bearing of high-T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> superconductor and hydrodynamic fluid film, is proposed for the application of liquid rocket engine in this paper. Cryogenic fuel in rocket engines can be used as cooling and lubricating medium at the same time. The structure of the tilting pad can realize the introduction of hydrodynamic fluid-film force. Structural features of the superconducting compound bearing are discussed to satisfy practical application. Dynamic characteristics of the compound bearing are analyzed through experimental results of the superconducting magnetic field and theoretical results of the hydrodynamic fluid field. The results indicate that the superconducting compound bearing can make full use of the advantages of superconducting magnetic bearing and hydrodynamic fluid-film bearing, and possesses the advantages of being friction free and high stiffness.

Static Characteristics of High-Temperature Superconductor and Hydrodynamic Fluid-Film Compound Bearing for Rocket Engine

With the application prospect of a new generation of a liquid rocket engine and the status that system safety and reliability are weakened by the friction and wear of existing rolling bearings, a kind of compound bearing for axial balance is proposed in this paper, which is a combination of a high-temperature-superconducting bearing and a hydrodynamic fluid-film bearing. The most important feature of the compound bearing lies in a kind of “superconducting tilting pad” structure. The structure of the compound bearing and its detailed feasible application scheme in a rocket engine are given. The static characteristics of the compound bearing based on a decoupling analytical method are studied, such as the pressure distribution, the temperature distribution of the film, the minimum film thickness, and the bearing capacity. Theoretical results indicate that a compound of a high-temperature superconductor and a hydrodynamic fluid film is an effective approach to improve the static characteristics of bearings for a rocket engine.

Optimum Groove Location for Two Groove Hydrodynamic Fluid Film Bearing

Optimum Groove Location for Two Groove Hydrodynamic Fluid Film Bearing

A finite strain contact model for mixed lubricated surfaces in forming processes

For an accurate simulation of forming processes, it is of paramount importance to model the different lubrication regimes that can develop at the contact interface. These might vary from zone to zone of the forming piece, and from one regime to another, resulting in forces of different nature and magnitude. In these cases, the use of the classical Coulomb friction law will be clearly not sufficient to capture, in a suitable manner, the variety of forces applied on the forming piece.Objective of this paper is the development of a constitutive model for the contact interface that is able to capture the different lubrication regimes. The load bearing capacity of the contact interface is assumed to be the resultant of two mechanisms: dry friction arising from the solid contact asperities, and hydrodynamic fluid film lubrication. The activation of one, the other or both mechanisms is controlled by a parameter α that, in the proposed model, depends on the current value of the sliding velocity V, the interfacial separation D and the surface roughness σs. The functional relation defining α can be derived either from experimental fitting of some parameters, which can be introduced into a predefined analytical expression designed to reflect the variation of the different regimes, or from the application of a sequential multiscale analysis through the use of microscale models.The model is formulated with respect to a convected reference frame, so to make it amenable for large deformation simulations. The numerical integration scheme of the resulting initial constitutive value problem is presented and implemented into an explicit finite element code. The mechanisms of the interface model have been separately tested and the numerical results correlate well with the available experimental findings. Comparisons with the Coulomb friction model are also provided. The applicability of the model for forming simulations is then demonstrated by reproducing the manufacturing of a ridge on an aluminum tube for the cosmetic industry, using the hydroforming technique. Both an elastomer and the fluid have been employed as pressure medium, and their performance has been compared in terms of the stresses and deformations produced in the finished product.