Thermoelastohydrodynamic Analysis Research Articles

Investigation of Cavitated Flow in Water-Lubricated Bearings Considering Surface Roughness, Thermal, and Elastic Effects

Contrary to conventional journal bearings, which operate using oil-based substances, water-lubricated bearings (WLBs) utilize water and, thus, constitute a more environmentally responsible solution. The shipping industry, among others, as already been introduced to this technology with a lot of commercial ships using water-lubricated stern tube systems; in other cases, hydropower plants manage to keep up with the strict environmental regulations by implementing the use of WLBs in water turbines. However, there are a lot of challenges when it comes to transitioning from conventional bearings to water-based ones. Such challenges are caused by the low viscosity of water and lead to phenomena of high complexity. Such phenomena are related but not limited to cavitation and turbulent flow due to the interaction between the lubricating water and bearing surface. In this study, a numerical method will be used to simulate the fluid film and bearing geometries in order to perform a thermo-elastohydrodynamic (TEHD) analysis. The dynamic characteristics of the bearing will be calculated and the results will be discussed. The novelty of the study is evident in but not limited to the determination of the elastic deformation of a WLB during operation, as well as the effect of surface roughness, cavitation, and thermal effects on bearing characteristics.

Bi-directional misalignment effects on transient tribo-dynamics of offset-halves journal bearings subjected to step loading

This paper focuses on the nonlinear behaviors of offset-halves journal bearings (OHJBs), particularly under dynamic loading and journal misalignment. A new tribo-dynamic model is given to perform transient thermoelastohydrodynamic analysis in the crucial yet understudied domain of this novel structure. Bearing characteristics are compared among bi-directional misalignment, single-direction misalignment as well as alignment. The results demonstrate that the influence of bi-directional misalignment exerts dominance. Moreover, the evolution mechanisms of bi-directional misalignment and step loading on the time-varying stiffness and damping are evaluated. In addition, parametric analyses are done to emphasize key factors in the bearing design, including the horizontal offset and radial clearance, for better transient lubrication performance. This study enriches the structural optimum for dynamically loaded journal bearings.

Thermo-elastohydrodynamic analysis of the inhomogeneous foil bearing with misalignment

Purpose The misalignment is generally inevitable in the process of machining and assembly of rotor systems with gas foil bearings, but the exploration on this phenomenon is relatively less. Therefore, the purpose of this paper is to carry out the thermo-elastohydrodynamic analysis of the foil bearing with misalignment, especially the inhomogeneous foil bearing. Design/methodology/approach The rotor is allowed to misalign in two non-rotating directions. Then the static and dynamic performance of the inhomogeneous foil bearing is studied. The thermal-elastohydrodynamic analysis is realized by combining the Reynolds equation, foil deformation equation and energy equation. The small perturbation method is used to calculate the dynamic coefficients, then the critical whirl ratio is obtained. Findings The gas pressure, film thickness and temperature distribution distort when the misalignment appears. The rotor misalignment can improve the loading capacity but rise the gas temperature at the same time. Furthermore, the rotor misalignment can affect the critical whirl ratio which demonstrates that it is necessary to analyze the misalignment before the rotordynamic design. Originality/value The value of this paper is the exploration of the thermo-elastohydrodynamic performance of the inhomogeneous foil bearing with misalignment, the analysis procedure and the corresponding results are valuable for the design of turbo system with gas foil bearings.

Experimental and Numerical Investigation about Small Clearance Journal Bearings under Static Load Conditions

The aim of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., microgas turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed and the performance of its bearings was investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial rotor kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for thermoelasto-hydrodynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this paper, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RKs, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results.

A Computational Model for the Analysis of the Static Forced Performance of Self-Equalizing Tilting Pad Thrust Bearings

Abstract While failure analyses in the archival literature report thrust collar misalignment as a major cause of collapse in oil lubricated thrust bearings (TB), a self-equalizing tilting pad thrust bearing (TPTB) improves operation reliability by adjusting its pads to account for thrust collar tilt. This paper describes a kinematics model for the equalizing mechanism integrated into an existing thermo-elastohydrodynamic (TEHD) analysis tool to deliver load performance predictions for self-equalizing TPTBs. The analysis considers the actual leveling plates geometric model as obtained from a solids modeling commercial software and accounts for the sliding friction forces acting at the contact points of the leveling plates and the rolling friction at their pivots. Further, a Hertz contact analysis model uses the predicted forces to deliver a peak pressure and deformation over the contact area between the leveling plates. Next, this paper presents predictions for an example self-equalizing TPTB operating with a thrust collar static misalignment φ = 0.01 deg. The bearing 126 mm in outer diameter has six pads, operates at 4 krpm (26 m/s maximum surface speed) and under a specific load/pad ranging from 0.5 to 3.5 MPa. Compared to a nonequalizing TPTB, a self-equalizing TPTB operates with up to 50% larger minimum film thickness and about ½ largest elastic deformation. Friction forces acting at the contact points of the leveling plates show a significant effect on the performance of the pad leveling system as they reduce the film clearance and increase a pad peak pressure. Predictions from the Hertz contact analysis agree with those from a commercial finite element analysis tool and show a significantly large peak pressure at the contact points of the leveling plates (> 0.9 GPa) when the bearing supports a 3 MPa/pad specific load. This paper stresses the importance of conducting a comprehensive multiple-pad analysis to accurately evaluate the performance and reliable operation of self-equalizing TPTBs.

Thermo-Elastohydrodynamic Study on Textured Journal Bearing with High-Speed and High-Specific-Pressure

The performance of supporting journal bearing of the star gear transmission system in the geared turbo fan engine (GTF) is analyzed. A thermal-elastohydrodynamic analysis model was developed for textured journal bearing used in high-speed and high-specific-pressure conditions. The Navier-Stokes equation, energy equation, and viscosity-temperature equation were calculated by the computational fluid dynamics method. The influence of elastic deformation on bearing thermal hydrodynamic performance was studied in detail. The results indicate that the elastic deformation has an influence on the distribution of oil temperature and oil pressure. Besides, a comparative thermo-elastohydrodynamic analysis was conducted between the textured bearing and the un-textured bearing, and the discrepancies of maximum oil pressure, load carrying capacity and the maximum oil temperature are few. However, the textured bearing has a lower elastic deformation than the un-textured bearing.

Development of a new test rig for the analysis of hydrodynamic bearings for rotors of microGT

The aim of the present work is to design a test rig suited to investigate the dynamic interaction between rotor and hydrodynamic journal bearings in micro gas turbines (microGT), i.e. with reference to small bearings (diameter in the order of ten millimeters). Particularly, the device is capable of measuring the journal location. Therefore, the journal motion due to rotor vibrations can be displayed, in order to assess performance as well as stiffness and damping of the bearings. The new test rig is based on Bently Nevada Rotor Kit (RK), but substantial modifications are carried out. Indeed, the relative radial clearance of the original RK bearings is about 2/100, while it is in the order of 1/1000 in industrial bearings. Therefore, the same RK bearings are employed in the new test rig, but a new shaft has been designed in order to reduce the original clearance. The new shaft enables us to study the bearing behaviour for different clearances, as it is equipped with interchangeable journals. The experimental data yielded by the new test rig are compared with numerical results. These are obtained by means of a suitable finite element (FEM) code developed by our research group. It allows the Thermo Elasto-HydroDynamic (TEHD) analysis of the bearing in static and dynamic conditions. In the present paper, bearing static performances are analysed in order to assess the reliability of the journal location predictions by comparing numerical and experimental results. Such comparisons are presented for both large and small clearance bearings of original and modified RK, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance equal to 8/1000). Nevertheless, rotor alignment is quite difficult with small clearance bearings and a completely new test rig is designed for future experiments.

Behavior of a Two-Lobe Journal Bearing With a Scratched Shaft: Comparison Between Theory and Experiment

Using the experience acquired within our lab in terms of both thermohydrodynamic (THD) and thermoelastohydrodynamic (TEHD) numerical simulations, a new THD code has been improved by adding the possibility of taking into account geometrical defects, and particularly scratches, which are often discovered by turbine users during maintenance operations. To examine this issue, two numerical codes were coupled to provide the TEHD analysis presented in this work. To validate the numerical results, experimental tests were conducted using the Pprime Institute bearing test rig. The performance of the same two-lobe journal bearing (preload 0.524) as used in a previous study, lubricated with ISO VG 46 oil, was evaluated. Scratches of different depths (varying as a function of the radial clearance) were directly machined onto the shaft. TEHD solutions and experimental data were compared for various rotational speeds and applied loads. Pressure and temperature comparisons for the three scratch depths show good correlation, and give the expected results for cases with a scratch. It was also found that the asymmetry in the pressure field created by the presence of a scratch led to a slight misalignment. The comparisons were improved by taking into account this misalignment, using the balance of momentum.

A Thermoelastohydrodynamic Analysis for the Static Performance of High-Speed—Heavy Load Tilting-Pad Journal Bearing Operating in the Turbulent Flow Regime and Comparisons to Test Data

Abstract Tilting-pad journal bearings (TPJBs) ensure rotordynamic stability that could otherwise produce dangerously large amplitude rotor oil-whirl/whip motions in high-speed rotating machinery. Currently, highly efficient turbo compressors demand an ever increasing rotor surface speed and specific load on its support bearings. The accurate prediction of bearing performance is vital to guarantee reliable products, specifically with regard to reducing maximum bearing pad temperature and drag power losses, and operating with the least flow rate while still maximizing load capacity. The hydrodynamic pressure and heat generation in an oil film acting on a bearing pad produce significant mechanical and thermal deformations that change the oil film geometry (clearance and preload) to largely affect the bearing performance, static, and dynamic. In addition, a high surface speed bearing often operates in the turbulent flow regime that produces a notable increase in power loss and a drop in maximum pad temperature. This paper details a thermoelastohydrodynamic (TEHD) analysis model applied to TPJBs, presents predictions for their steady-load performance, and discusses comparisons with experimental results to validate the model. The test bearing has four pads with a load between pads configuration; its length L = 76.2 mm and shaft diameter D = 101.6 mm (L/D = 0.75). The rotor top speed is 22.6 krpm, i.e., 120 m/s surface speed, and the maximum specific load is 2.94 MPa for an applied load of 23 kN. The test procedure records shaft speed and applied load, oil supply pressure/temperature and flow rate, and also measures the pads' temperature and shaft temperature, as well as the discharge oil (sump) temperature. The TEHD model couples a generalized Reynolds equation for the hydrodynamic pressure generation with a three-dimensional energy transport equation for the film temperature. The pad mechanical deformation due to pressure utilizes the finite elemental method, whereas an analytical model estimates thermally induced pad crowning deformations. For operation beyond the laminar flow regime, the analysis incorporates the eddy viscosity concept for fully developed turbulent flow operation. Current predictions demonstrate the influence of pressure and temperature fields on the pads mechanical and thermally induced deformation fields and also show static performance characteristics such as bearing power loss, flow rate, and pad temperatures. The comparisons of test results and analysis results reveal that turbulent flow effects significantly reduce the pads' maximum temperature while increasing the bearing power loss. Turbulent flow mixing increases the diffusion of thermal energy and makes more uniform the temperature profile across the film.

Thermoelastohydrodynamic analysis of misaligned bearings with texture on journal surface under high-speed and heavy-load conditions

Hydrodynamic journal bearings are used to support the planetary gears in the transmission system of a Geared Turbo Fan engine, and they operate under severe working conditions, such as misalignment, high speed, and heavy load. Surface texture is regarded as an effective approach to improve mechanical properties under severe working conditions. However, the effects of surface texture on misaligned journal bearings under severe conditions have not been well studied. Therefore, a thermoelastohydrodynamic (TEHD) lubricating model with a textured and misaligned journal is presented in this study. Solid deformation, heat transfer between oil and the bearing, and heat convection between air and the bearing are considered in the model. The effects of cavitation and viscosity-temperature are also taken into account. The impacts of surface texture parameters and the misalignment angle on lubricating properties are investigated in the model. Results indicate that the bearing lubricating performance is greatly improved by optimal surface texture considering journal misalignment. The maximum oil film pressure and load-carrying capacity of a journal bearing increase with journal misalignment. Meanwhile, the oil film temperature increases sharply while considering misalignment.

Effect of temperature on wear and tribofilm formation in highly loaded DLC-steel line contacts

Abstract In the present study the tribological properties of DLC coatings are analysed by performing Stribeck experiments with a block on ring (BoR) configuration, developed for a rotational tribometer, under different temperatures operated with a conventional 5W30 engine oil. Both, block and ring are made of steel and surface hardened, whereby a-C:H coating with CrN adhesion and CrC gradient layer is deposited on the latter. Results reveal, that the amount of formed Zinc dialkyldithiophosphate (ZDDP) tribofilms can be linked directly to changes of wear volume and boundary friction coefficient (COF). Furthermore, wear and tribofilms can trigger topological surface adaptations, leading to a different frictional behaviour in the fluid lubrication regime as well. Optical, energy dispersive X-ray (EDX) and thermoelastohydrodynamic (TEHD) numerical analysis were carried out in order to gain a holistic understanding of phenomena taking place in DLC/steel tribosystems. Findings indicate, that anticipated positive effects of DLC coatings are partly suppressed due to the onset of these films under conditions relevant in automotive engines.

Contact and wear thermo-elastohydrodynamic model validation for engine bearings

Tribological machine components such as engine crankshaft bearings operating at high load or rotational speeds often experience very thin oil films leading to asperity contact between the bearing and crankshaft. When the oil film thickness drops below the peak asperity height there is an increase in contact, wear and asperity power loss leading to worsening severity factors and seizure risk. Key factors influencing the bearing lubrication performance are the surface characteristics of the materials at the contact interface. SABRE-TEHL is a software simulation tool used for performing thermo-elastohydrodynamic analysis of bearing applications. In this current study, the development of a combined contact and wear model is demonstrated. This includes a hard contact model giving a direct surface contact pressure in areas of zero oil film thickness, a surface yield model with yield limits and plastic gradient from measured stress–strain data, an asperity wear model using measured surface roughness data and an asperity contact model based on measured roughness, asperity density and tip radius. Input surface roughness data are measured using a white light interferometry method. The effects of surface characterization in terms of roughness and stiffness properties are demonstrated using simulation results comparing an aluminium bimetal bearing with a polymer coated bearing, showing a significant reduction in asperity friction for the bearing with a polymer coating. Simulation results are compared with experimental test results for a 1.5 l diesel engine, a 2.0 l diesel engine and for a bearing fatigue test rig. Generally good agreement is seen when comparing the wear contours and wear depth on the bearing surface.

Double Overhung Disk and Parameter Effect on Rotordynamic Synchronous Instability—Morton Effect—Part I: Theory and Modeling Approach

The Morton effect (ME) is a thermally induced instability problem that most commonly appears in rotating shafts with large overhung masses, outboard of the bearing span. The time-varying thermal bow due to the asymmetric journal temperature distribution may cause intolerable synchronous vibrations that exhibit a hysteresis behavior with respect to rotor speed. The fully nonlinear transient method designed for the ME prediction, in general, overhung rotors is proposed with the capability to perform the thermoelastohydrodynamic analysis for all the bearings and model the rotor thermal bow at both overhung ends with equivalent distributed unbalances. The more accurate nonlinear, coupled, double overhung approach is shown to provide significantly different response prediction relative to the more approximate linear method based using bearing coefficients and the single-overhung method, which assumes that the ME on both rotor ends can be decoupled. The flexibility of the bearing pad and pivot is investigated to demonstrate that the pivot flexibility can significantly affect the rotordynamics and ME, while the rigid pad model is generally a good approximation.

Effect of presence of lifting pocket on the THD performance of a large tilting-pad thrust bearing

Abstract Hydrostatic assistance is a commonly used method to improve limited load carrying ability of tiltingpad thrust bearings during transient states of operation of vertical shaft hydro-generators. Despite of special hydraulic equipment (as pumps, valves, etc.), it also requires manufacturing of special recesses/pockets at pad sliding surfaces, into which oil is injected under high pressure. It allows to lift the rotor before start-up of the machine and form a hydrostatic film between pads and collar. There is a quite wide variety of geometry of recesses (shape, depth, and size) met in practical large bearing applications. The presence of a hydrostatic pocket (usually located in the sliding surface above the pivot area, where thin film, high oil pressure and temperature are observed) affects bearing performance under hydrodynamic operation. In theoretical researches, there is an almost common practice not to include hydrostatic recess in thermohydrodynamic (THD) or thermoelastohydrodynamic (TEHD) analysis. This is probably due to the problems with obtaining solution for oil film geometry with pocket, the order of magnitude of the pocket depths being larger than gap thickness. In this paper, an attempt was taken to study the effect of lifting pocket on THD performance of a large tilting-pad thrust bearing of Itaipu power plant. Bearing performance was evaluated including recess shape for several cases of its depth. The results show that hydrostatic recess changes calculated bearing properties quite significantly, especially in vicinity of the pocket.

Metal Temperature Correlations in Tilting Pad Journal Bearings

The predicted and measured bearing metal temperatures of tilting-pad journal bearings are examined. All bearings are a five-pad design with load-between-pad orientation. The two loaded pads in each bearing are instrumented with a resistance temperature detector (RTD). The bearing pad metal temperatures are measured as a part of the ISO 10439 (API 617) mechanical test requirement. Bearing pad metal temperatures are predicted using the thermoelastohydrodynamic (TEHD) analysis method. One particular bearing size 4 in. (101.6 mm) in diameter and 1.54 in. (39.12 mm) in the axial length is examined with respect to the tolerance range influence on the predicted pad metal temperatures including the effect of bearing assembled clearance and preloads. A range of loads and speeds are investigated. The temperature variation observed for this bearing size is compared against the variation in the measured temperature data for three other bearing sizes (bearing sizes are denoted by diameter × axial length) 2.95 in. (74.9 mm) × 1.02 in. (25.9 mm), 6 in. (152.4 mm) × 3 in. (76.2 mm), and 8 in. (203.2 mm) × 7 in. (177.8 mm).

An engineering approach for the prediction of wear in mixed lubricated contacts

The continuum damage mechanics (CDM) approach in conjunction with the load sharing concept is applied to predict steady state lubricated line-contact wear. Empirical formula for the maximum contact pressure in dry rough contact is employed together with the lubricant film thickness equation to estimate the portions of the load carried by the asperities and the lubricant. Effect of contact temperature on wear is also included using a simplified thermo-elastohydrodynamic analysis in conjunction with fractional film defect concept. While most wear models require experimental calibration, current study attempts to predict wear purely based on numerical simulation. The proposed methodology is quite fast and easy to implement for practical engineering applications. Comparison of numerical calculations with available experimental wear data show very good agreement.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness, and Different Pad Preloads

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Thermoelastohydrodynamic analysis of auto water pump bearing seal

A numerical thermoelastohydrodynamic simulation method is proposed in this article with the considerations of the topography of sealing lip and shaft, interference of sealing lip, the elastic deformation of sealing lip and the influence of temperature on the viscosity of lubricant. The proposed method is applied to WR auto water pump bearing seal to study the lubrication and sealing property of lip seal, and the relationships between the lubrication property of lip seal and interference, rotation speed in given working condition are obtained.

Study on Elastohydrodynamic Lubrication of Transmission Gear in Fuel Cell Bus

The model of thermoelastohydrodynamic (TEHL) analysis of a transmission gear in a fuel cell bus was developed. The influence of rotating speed on the frictional pair was investigated numerically on the base of the mathematical model. The pressure field, the temperature field, the oil film thickness were calculated under different rotating speeds. It is shown that the worst lubrication in the tooth root occurs and the minimum film thickness increases with growth of the rotating speed. The temperature of lubricant is up to 140oC at 4000rpm.

Prediction of Steady State Adhesive Wear in Spur Gears Using the EHL Load Sharing Concept

The concept of load sharing between asperities and fluid film is applied in conjunction with lubricated sliding wear formulation proposed by Wu and Cheng (1991, “A Sliding Wear Model for Partial-EHL Contacts,” ASME J. Tribol., 113, pp. 134–141; 1993, “Sliding Wear Calculation in Spur Gears,” ASME J. Tribol., 115, pp. 493–500) to predict the steady state adhesive wear in gears. Thermal effects are included using a simplified thermoelastohydrodynamic analysis. The prediction of the model is verified by comparing simulation results with published experimental data pertinent to steady state wear rate. The main advantages of this method are the accuracy and the remarkable computational efficiency. The results of parametric simulation study are presented to investigate the effect of speed and surface roughness on a portion of load carried by asperities and wear rate.