Analysis on the thrust bearing lubrication in pumped storage unit based on fluid-solid-thermal interactions

Tilting pad thrust bearings (TPTBs) control rotor axial placement in rotating machinery, and their main advantages include low drag power loss, simple installation, and low-cost maintenance. The paper details a novel thermo-elasto-hydrodynamic (TEHD) analysis predictive tool for TPTBs that considers a three-dimensional (3D) thermal energy transport equation in the fluid film, coupled with heat conduction equations in the pads, and a generalized Reynolds equation with cross-film viscosity variation. The predicted pressure field and temperature rise are employed in a finite element (FE) structural model to produce 3D elastic deformation fields in the bearing pads. Solutions of the governing equations delivers the operating film thickness, required flowrate, and shear drag power loss, and the pad and lubricant temperature rises as a function of an applied load and shaft speed. To verify the model, predictions of pad subsurface temperature are benchmarked against published test data for a centrally pivoted eight-pad TPTB with 267 mm in outer diameter (OD) operating at 4–13 krpm (maximum surface speed = 175 m/s) and under a specific load ranging from 0.69 to 3.44 MPa. The current TEHD temperature predictions match well the test data with a maximum difference of 4 °C and 11 °C (<10%) at laminar and turbulent flow conditions, receptively. Next, the TEHD predictive tool is used to study the influence of both pad and liner material properties on the performance of a TPTB. The analysis takes a whole steel pad (without a liner or babbitt), a steel pad with a 2-mm-thick babbitt layer (common usage), a steel pad with a 2-mm-thick hard-polymer (polyether ether ketone, e.g., PEEK®) liner, and a pad entirely made of hard-polymer material, whose elastic modulus is just 12.5 GPa, only 6% that of steel. The bare steel pad reveals the poorest performance among all the pads as it produces the smallest fluid film thickness and consumes the largest drag power loss. For laminar flow operations (Reynolds number Re < 580), the babbitted-steel pad operates with the thickest fluid film and the lowest film temperature rise. For turbulent flow conditions Re > 800, the solid hard-polymer pad, however, shows a 23% thicker film than that in the babbitted pad and produces up to 25% lesser drag power loss. In general, the solid hard-polymer TPTB is found to be a good fit for operation at a turbulent flow condition as it shows a lower drag power loss and a larger film thickness; however, its demand for a too large supply flowrate is significant. Predictions for steel pads with various hard-polymer liner and babbitt thicknesses demonstrate that using a hard-polymer liner, instead of white metal, isolates the pad from the fluid film and results in an up to 30 °C (50%) lower temperature rise in the pads than that for a babbitted-steel pad. For operations under a heavy specific load (>3.0 MPa), however, a thick hard-polymer liner extensively deforms and results in a small film thickness.

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.

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of Computational Fluid Dynamics (CFD) simulations, based on the numerical solution of the Navier-Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth and texture density on the bearing performance indices (load carrying capacity, friction torque and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

The axial thrust load of a turbocharger is generated due to the pressure differential between the compressor and turbine. Changes in compressor and turbine geometry and variations in test conditions can influence the thrust load. Once the axial force exceeds the loading capacity limit of a thrust bearing, the balance of the thrust bearing system cannot be maintained, which may lead to a catastrophic failure of the turbocharger. In this paper, a fault diagnosis of a turbocharger that experienced a catastrophic failure during flow bench testing is analyzed. A detailed analysis of a turbocharger thrust load, based on empirical formulae and CFD verification, is presented. The thrust prediction at high rotation speed is helpful for further flow bench testing and to avoid the future turbocharger failure.

As the interface problem of discontinuity boundary condition between the oil film and the pad in thrust bearing, a conjugated solution method by using the temperature continuity and the heat flux continue is proposed. The three-dimensional calculated model of thrust bearing is constructed and solved by using finite difference method. Comparing with 2D model, the characteristics of the lubrication performance of 3D model are more different. The results show that the three-dimensional calculated model not only revealed the relation of temperature variation between the oil film layer and the pad in axial direction, but also exactly reflected real temperature distribution in the pad surface. In the same oil feed temperature condition, the minimum film thickness is 63.8μm and the maximum temperature on the pad surface reached 55°C for 3D mode, 72.6μm and 60°C for 2D mode.

An extended computational bulk-flow analysis for prediction of performance in angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings is presented. The fluid motion within the thin film lands is governed by mass conservation and momentum transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. A perturbation analysis for small amplitude shaft axial motions and angulations leads to zeroth and first-order equations describing the equilibrium and perturbed fluid flows. The computational procedure predicts the bearing flow rate, thrust load and restoring moments, drag torque, and 27 force and moment coefficients. The effects of misalignment on the dynamic performance of a refrigerant fluid-hybrid thrust bearing are evaluated at an optimal operating condition. The axial force/displacement stiffness coefficient and the direct moment/angle stiffness coefficients show a maximum for a certain recess pressure ratio, while the damping coefficient steadily increases with the applied load. As the misalignment angle increases, both moment and force coefficients also increase. Most operating conditions show a whirl frequency ratio equal to 0.50. Thus, thrust hybrid bearings offer the same limited stability characteristics as hydrodynamic thrust bearings when undergoing self-excited shaft angular motions.

Paper IV(iv) An experimental study of sector-pad thrust bearings and evaluation of their thermal characteristics

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of computational fluid dynamics (CFD) simulations, based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth, and texture density on the bearing performance indices (load carrying capacity, friction torque, and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

Thrust bearing is a key component of large-scale water turbine. It closely relates to the efficiency of large-scale water turbines, and even determines whether the large-scale turbine can operate normally. With the development of the capacitance of water turbines, thrust bearing will develop to the direction of high speed and heavy load. The structure, strength, lubrication and the characteristic of heat radiation of large-scale thrust bearing were often researched in the past. To study the flow condition of the large-scale thrust bearing and analyze the load characteristics, CFD simulation was carried out on the model of thrust bearing. In this study, CFD method was used to simulate the internal flow field of the large-scale thrust bearing. The model researched was a thrust bearing for 1000MW water turbines. The diameter of the thrust bearing was over 5.8 meters, and the maximum thrust load of the bearing can reach to 60MN. The thin gap between the runner and the pad was usually neglected in the published CFD calculations of thrust bearing. But the thin gap was taken into account in this investigation. 1/12 of the model was used as the computational field and periodic boundary was used in the calculation. The standard κ-ε turbulence model was used to simulate the thrust bearing model, and the flow field in the thrust bearing was obtained. The thin gap between the runner and the pad is a wedge. The pressure and velocity distribution in the thrust bearing and thin gap was calculated respectively with conditions of different thin gaps and different rotational speeds of runner. After that, the relationship between carrying capacity and the size of clearance or the speed of the runner through analyzing the data has been obtained from the results of the calculation.

Effect of varnish on the performance and stability of journal bearings

The performance of air foil thrust bearings (AFTBs) is studied for aligned, distorted and misaligned operating conditions on the basis of a very detailed numerical model for the foil sandwich. The exact geometry of the bump foil is modeled by a Reissner–Mindlin-type shell theory. A penalty-type contact formulation including frictional effects is applied for the contact between top foil and bump foil as well as between bump foil and base plate. The minimal film thickness within the thrust bearing is used as a criterion for comparing different air foil thrust bearings with rigid thrust bearings. If the rotor disk and the base plate are perfectly parallel (aligned conditions), AFTBs are proved to have always a lower load capacity than (optimized) rigid thrust bearings due to unequal bump foil deformations and top foil sagging effects. This finding is in contradiction to previous works based on simplified foil models, which claimed AFTBs to be superior to rigid thrust bearings. Furthermore, for both operating conditions—thermally induced distortions of the rotor disk as well as misalignment—an individual pad of an AFTB is found to be unable to effectively compensate for the disturbance in the gap function. Consequently, a tailoring of the stiffness distribution in the AFTB is shown to be of limiting effect. Instead, the overall compliance of the pads in an AFTB is demonstrated to be the essential reason for the superior behavior of AFTBs to rigid thrust bearings under misaligned conditions.

Conventional microheat sink design primarily focuses on the use of continuous fin arrays to optimally dissipate thermal energy from electronic components. By contrast, this paper experimentally measures the thermal and structural performance of two micro pin fin heat sinks designed for use in load bearing applications such as mechanical seals and thrust bearings. One pin fin array is of low porosity, which is more optimal for load bearing capacity, and the other is of high porosity, which is more optimal for heat dissipation. By using these two extreme cases, the thermal-structural tradeoff found in load bearing microheat sinks is demonstrated. The heat sinks are constructed of nickel, electrodeposited onto a stainless steel thrust ring using a modified LIGA technique. Under forced air cooling, the thermal performance of each is compared to a simple model based on a combination of macroscale pin fin heat sink results and classical correlations for fins in cross flow. The low porosity design is also tested under the application of a 44.5 N thrust load at 2500 rpm and found to be structurally sound. Experimental temperature profiles demonstrate a substantial benefit of the microheat sink in cooling the load bearing surface.

Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

Process fluid lubricated thrust bearings (TBs) in a turbomachine control rotor placement due to axial loads arising from pressure fields on the front shroud and back surface of impellers. To date, prediction of aerodynamic induced thrust loads is still largely empirical. Thus needs persist to design and operate proven thrust bearings and to validate predictions of performance derived from often too restrictive computational tools. This paper describes a test rig for measurement of the load performance of water lubricated hydrostatic/hydrodynamic thrust bearings operating under conditions typical of cryogenic turbo pumps. The test rig comprises of a rigid rotor composed of a thick shaft and two end collars. A pair of flexure-pivot hydrostatic journal bearings (38 mm in diameter) support the rotor and quill shaft connected to a drive motor. The test rig hosts two thrust bearings (8 pockets with inner diameter equal to 41 mm and outer diameter equal to 76 mm); one is a test bearing and the other is a slave bearing, both facing the outer side of the thrust collars on the rotor. The slave TB is affixed rigidly to a bearing support. A load system delivers an axial load to the test TB through a non-rotating shaft floating on two aerostatic radial bearings. The test TB displaces to impose a load on the rotor thrust collar and the slave TB reacts to the applied axial load. The paper presents measurements of the TB operating axial clearance, flow rate and pocket pressure for conditions of increasing static load (max. 3,600 N) and shaft speed to 17.5 krpm (tip speed 69.8 m/s) and for an increasing water supply pressure into the thrust bearings, max. 17.2 bar (250 psig). Predictions from a bulk flow model that accounts for both fluid inertia and turbulence flow effects agree well with recorded bearing flow rates (supply and exiting thru the inner diameter), pocket pressure and ensuing film clearance due to the imposed external load. The measurements and predictions show a film clearance decreasing exponentially as the applied load increases. The bearing flow rate also decreases, and at the highest rotor speed and lowest supply pressure, the bearing is starved of lubricant on its inner diameter side, as predicted. The measured bearing flow rate and pocket pressure aid to the empirical estimation of the orifice discharge coefficient for use in the predictive tool. The test data and validation of a predictive tool give confidence to the integration of fluid film thrust bearings in cryogenic turbo pumps as well as in other more conventional (commercial) machinery. The USAF Upper Stage Engine Technology (USET) program funded the work during the first decade of the 21st century.

The author brings together here for the first time important formulas and charts that have been offered by bearing analysts in this field during the past fifteen or twenty years. Some new material is added for completeness, and some references made to earlier fundamental work. Descriptive matter that accompanied the original publication of the charts and formulas has been eliminated as far as practicable. Improved charts derivable from earlier ones, and the rearrangement of others will, it is hoped, prove more useful to the designing engineer than the original publications. The net result is a concise summary of valuable information. In order that the reader at the beginning may have a fair idea of what is to be found and where in this paper, an explanation of the contents follows: The first section dealing with journal bearings begins with a concise illustrated description of their several kinds. The side-leakage chart is then explained because from its curves are obtained the correction factors that are necessary for the proper application of the subsequent material to the solving of journal-bearing problems. Optimum conditions for journal bearings of three classes are shown by charts, tables, and formulas. The titles, captions, and notes on these pages are intended to be sufficient explanation. General conditions for journal bearings of several classes are next shown by a series of charts which are accompanied by the necessary textual explanation. Thrust-bearing loading and friction data follow the charts for general conditions for journal bearings. They refer only to Kingsbury thrust bearings, which are made with freely pivoted shoes supporting a thrust collar having an unbroken flat surface. Data are given only for a single set of such surfaces having six pivoted shoes. The appendixes, of which there are five, contain descriptive matter, the reading of which will help the reader in understanding the first section of the paper. Appendix A contains the symbols and their explanation. Appendix B gives a number of examples together with their solutions, which explain applications of the charts. These are by no means exhaustive. Appendix C discusses viscous flow in general, the viscosity coefficient, the relation between viscosity and friction, and gives useful formulas for several kinds of viscous flow useful to those dealing with bearing problems. Conversion factors are given for several units of absolute viscosity. The symbols for these formulas differ in some respects from those in Appendix A. Appendix D contains an explanation of perfect lubrication as it occurs in bearings, and covers such headings as tapered oil film, side leakage, film thickness, viscosity change within film, the flat-wedge film, the curved-wedge film, optimum conditions, deviations from optimum. This is a valuable introduction to the charts in the body of this paper. Appendix E is a bibliography of the technical literature referred to in or forming parts of the paper.