Comparison with Thermo Hydrodynamic Lubrication between 2D and 3D Model in Thrust Bearing by Computing Simulation

Numerical analysis is performed to study the transient behavior of EHL finite line contact of a cylindrical roller and flat plane under load impulse. In the present work, effect of pressure on the density and viscosity of lubricant is considered. Finite difference method is used to discretize the governing equations. Multilevel Multi-integration method is used to calculate the elastic deformation. Moreover, Multigrid method is implemented to accelerate the convergence process. Uniqueness of this finite line contact analysis is that it provides an ability to determine the transient behavior of lubricated contact even at the edges of roller. Results show that the load impulse causes squeezing and separation movement within the contact that develops film dimple and pressure ripples at the inlet region, which propagate towards the exit region due to the entrainment motion. It is noticed that the time taken by oil film [Formula: see text] to travel the Hertzian contact width and the time period [Formula: see text] of load impulse decides the behavior of lubricated contacts. Firstly, under a relatively heavy load when the contact width is large enough so that [Formula: see text], then a significant rise in central film thickness (CFT), central minimum film thickness (CMFT) and minimum film thickness (MFT) occurs after the execution of load impulse. Further, under the light load generating a relatively small contact width such that [Formula: see text], then comparatively a small rise in CFT occurs right during the load impulse. Lastly, for a given load if the time period of impulse [Formula: see text] is large enough satisfying the condition [Formula: see text], then a considerable reduction in CFT, CMFT and MFT takes place during the application of load impulse. Moreover, as compare to other cases, for [Formula: see text] the steady state condition is reestablished after a relatively more number of time cycles. It is observed that the maximum pressure and MFT occurs at the contact edges of roller which can be controlled by a proper choice of the radius of end profile [Formula: see text].

The bidirectional thrust bearings are used to balance the thrust load of the entire shaft system which play an important role in the pumped storage units. The lubrication is usually analyzed by simultaneously solving the Reynolds equation, energy equation, film thickness equation of the film and the heat conduction equation, elastic equilibrium equation of the pad. However, in this method the assumptions for the inlet temperature of the film and the wall heat coefficients on the pad greatly affect the numerical accuracy. This study used fluid-solid-thermal interaction method, built three dimensional (3D) FEM model for the pad and collar and the 3D CFD model for the oil film, and then analyzed the influence of the thrust loads and the Babbitt layer on the bearing performance. The results show that increasing the thrust load will rapidly decrease the minimum film thickness, increase the maximum pressure and maximum temperature on the pad. Increasing the thickness of the Babbitt layer on the pad sliding surface will increase the minimum thickness of the film, decrease the maximum temperature on the pad which improve the bearing lubrication.

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.

Recently developed colorimetric interferometry technique was used for the study of both minimum and central film thicknesses for a wide range of operating parameters. Over 300 film thickness maps were obtained for the combination of four values of the materials parameter G, five values of the load parameter W and many values of the speed parameter U. The use of a spacer layer extended the range of film thickness measurement down to 5 nm. An excellent agreement was found between experimental values and data obtained from numerical solution presented by Venner and ten Napel, especially for thin lubrication films. An increase in a speed exponent with increasing material parameter G was observed for both central and minimum film thicknesses. The minimum film thickness and, thereby, the ratio between central and minimum film thickness was confirmed to be of a stronger dependence on material and load dimensionless parameters than Hamrock and Dowson equations predict. Presented at the 54th Annual Meeting Las Vegas, Nevada May 23–27, 1999

In this article, the problem of predicting the film thickness in so-called narrow or slender elliptic contacts is revisited. In particular, the variation of the minimum film and central film thickness and their ratio with load and ellipticity are studied. It is shown that the minimum film tends to decrease linearly with increasing ellipticity. The central film thickness, until a certain threshold, decreases very slowly, and then decreases linearly too, with a slope independent of the Hertzian pressure. The ratio central to minimum film thickness is not a constant and varies strongly with ellipticity and load conditions. In this article, it is shown that the ratio of central to minimum film thickness is a linear function of a single nondimensional parameter which has the physical meaning of the ratio of the length of the inlet pressure sweep to the relative width of the contact. Results for narrow contacts published in the engineering literature when represented as a function of this parameter exhibit the same trend. The behaviour is the consequence of the same unifying mechanism that, in the last decade, was discovered to determine aspects of behaviour in elasto-hydrodynamically lubricated (EHL) contacts under time varying conditions, such as surface waviness deformation. For these problems, the single parameter dependence facilitated the development of simple engineering tools (e.g. to predict the roughness deformation). The observation in this article that the ratio central to minimum film thickness is also governed by this parameter opens new perspectives to develop a simple computational engineering tool to predict central and minimum film thickness in EHL contacts.

The rollers and/or races in cylindrical and tapered roller bearings should be profiled to relieve high edge stress concentrations caused by their finite lengths and misalignment. In this study, a numerical analysis was performed to investigate the elastohydrodynamic lubrication (EHL) of a Lundberg profile-type cylindrical roller. A finite difference method with fully nonuniform grids and the Newton-Raphson method were used to present detailed EHL pressure distributions and film shapes, as well as the variations in the minimum and central film thicknesses with the profile modification coefficient. In the Lundberg profile, the maximum pressure and minimum film thickness always occurred near the edges. Proper modification of the Lundberg profile considerably increased the minimum film thickness.

With the application of the large capacity ESP in deep well and high temperature well, first to raise the submersible motor power, next also to improve thrust bearing load and temperature capability. This development tilted pad thrust bearing to replace the original fixed pad thrust bearing, because of oil film produced on the surface of tilted pad through adjusting the angle of tilted pad to ensure operation of motor at high temperature and load. While the tilted pad can not generate oil film, and locking burned. The operation problem of submersible motor at high temperature and load has been solved by adopting tilted pad thrust bearing, according to structural characteristics of submersible motor, The principle of oil film formed on surface of tilted pad is analyzed and all parameters such as oil film thickness, oil film pressure, friction resistance, motor oil flow rate and temperature rise and so on are calculated through the system model of tilted pad bearing, According to the data, this thrust bearing designed and manufactured has been tested in laboratory and field, test prove: the performance of tilted pad than the fixed pad thrust bearing has been greatly improved to meet demand of high-end ESP for long-term stable operation.

The surface quality of cold rolled strip is related to a greater extent on the rolling oil film thickness, and there are many factors that affect the oil film thickness. Considering the various factors comprehensively, an integrated mathematical model is established, such as roughness of rolls and strips, elastohydrodynamic lubrication, friction heat and plastic deformation heat in the rolling zone, viscosity varying with temperature and pressure, etc. A series of equations are developed, such as the Reynolds equation of partial membrane hydrodynamic lubrication based on average flow theory, equation of oil film thickness on rough elastic surface, the thermal interface equations between strip, oil film and roller surface, surface asperity contact pressure equation, lubricant viscosity and density equations, motion equation of the oil film, etc. This model is solved by finite difference method to get the film pressure, oil film thickness, and temperature distribution in the rolling zone. The average rolling pressure, the roll, and strip temperature calculated by the model are very close to the field test results. Comparing the minimum film thickness calculated by the model with the regression formula of other literature test, the error is less than 10%. The minimum oil film thickness is analyzed. It increases with the decrease of the rolling force and is approximately proportional to the rolling speed and lubricant viscosity.

An overshoot phenomenon of bearing temperature in hydrodynamic journal bearings may be observed during a sudden start-up experiment. This phenomenon implies that the maximum bearing temperature in acceleration operation may exceed the predicted one which can be predicted accurately by applying a state-of-the-art steady state thermohydrodynamic lubrication (THL) model. This paper presents the maximum bearing temperature including the one during acceleration operation by using a simplified THL model that is newly proposed for a transient THL analysis. It is found that the overshooted temperature can be qualitatively predicted by using the transient THL model that incorporates properly the interaction between the motion of journal center and the viscous dissipation, even if it is a simple model. Next, the transient temperature during slow acceleration operation and also those toward higher dimensional steady state journal rotational speed are calculated and they are found to be in qualitative agreement with the measurements. The oil film characteristics such as oil film pressure, temperature and thickness after reaching the steady state equilibrium do not depend on the value of initial journal eccentricity ratio in the transient analysis. However, when the values are different, the characteristics immediately after starting rotation change largely. In the case of the value 1.00, it is found to give a prediction that agrees qualitatively with the characteristics measured in the experiment.

The identification results for the static performance characteristics of a large tilting-pad bearing in load between pad configuration are presented for specific bearing loads between 1.0 and 2.5 MPa and for circumferential speeds up to 79 m/s. The bearing is lubricated by spray-bars and can be described by the following specifications: Five pads, 0.23 nominal preload, 60% offset, 56° pad arc angle, 500 mm inner diameter, 350 mm pad length and 1.28 per mille relative bearing clearance. The axial oil flow is reduced by a fixed seal on both bearing edges which has a nominal radial clearance of 1 mm. The film pressure and the gap width are determined in the whole area of the sliding surface by an axial shift of the shaft. The bearing temperatures are measured by means of 100 thermocouples located 5 mm behind the sliding surface. The experimental results indicate that significant pad deformation occurs in circumferential and in axial direction. Also the effective supply temperatures are much higher than the nominal ones. According to the lubricant flow the sensor temperatures close to the spray-bars at the sliding surface rise about 20 K for 7 l/s and 40 K for 3.5 l/s at 3000 rpm. The temperatures are nearly constant between all pads and depend only on speed and not on load. The theoretical analyses of the bearing performance was accomplished with the bearing calculation software COMBROS. This code models the transition between laminar and turbulent flow and solves an extended Reynolds equation, the three dimensional energy equation of the film and the heat conduction equations of the shaft and the pads considering various boundary conditions due to the judgment of the user. Concerning the minimum film thickness, the maximum temperature on the sliding surface and the maximum film pressure only poor agreement was reached if the influence of the axial pad deformation was neglected. In advanced analyses a co-simulation between COMBROS and a structural mechanics software shows that an improvement of the prediction was achieved. The comparison of the measurement data and the advanced simulation shows very good agreement for the characteristic bearing parameters as well as for the local distributions of film pressure, temperature and film thickness in the whole operating range of the bearing. Further, the applied inlet mixing model for the lubricant supply process proves to be very suitable.

This study numerically investigates the impact of optimal textures location on the performance of hydrodynamic porous self-lubricating journal bearings with sealed ends, subjected to a stationary load. The analysis employs a modified Reynolds equation coupled with Darcy’s law to model fluid flow in both the lubricating film and the porous matrix, considering the hydrodynamic self-lubrication problem. The governing nonlinear PDE systems were solved numerically using the finite difference method, combined with Reynolds boundary conditions and continuity conditions for velocity and pressure at the film-bush interface. A Binary Genetic Algorithm (BGA) is employed to optimize the topological distribution of square dimples in the textured porous layer to enhance bearing performance. The study investigates the influence of key parameters, including applied load, rotational speed, permeability, and texture depth, on bearing characteristics such as minimum film thickness and friction coefficient. Results show good agreement with benchmark data and indicate a positive enhancement in porous bearing performance. In addition, findings demonstrate that increasing the permeability of the porous structure reduces bearing performance (up to 25% in minimum film thickness and 8% in friction coefficient). However, the application of the optimization technique identified an optimal arrangement of textures that compensates for these performance losses, even under severe working conditions. Texturing the outlet region of the contact (beyond 180°) at the cavitation zone causes a micro-step bearing mechanism, generating localized pressure recovery within the textured area, significantly enhancing the minimum film thickness (up to 12%), reducing friction (up to 23%), and minimizing cavitation (up to 24%).

The paper considers vibration response of spinning shafts supported by flexible tilt pad journal bearings, to large mass imbalance (blade loss). A time transient study of the tilt pad journal bearing with thermal effects and without pad deformations, and with pad deformations and without thermal effects, is performed. Influence of the inclusion of thermal effects on the journal center’s orbit, the minimum film thickness, and the maximum film temperature is evaluated, and also the influence of pad deformations due to the fluid film forces on the journal center’s orbit and the minimum film thickness is studied. Inclusion of thermal effects had little effect on the orbit, while the inclusion of pad deformations had considerable effect on the journal orbit and the minimum film thickness. Three cases are studied in this paper; static load without imbalance, static load with low imbalance, and static load with high imbalance.

Thrust bearing coupling effects on the lateral dynamics of turbochargers

This part is a complimentary work to a previously published work on EHD lubrication behavior under pure sliding and combined rolling and sliding situations. In order to cover all aspects of EHD lubrication, the experimental work has been herein extended to present the results attained when two disks describe a pure rolling motion. A wide range of loads and speeds has been applied to the contacting disks under EHD regimes. The recorded pressure values and distribution confirm the existence of a second peak (spike) near the exit of the contact zone also under pure rolling situation. The spike has a value higher than maximum Hertzian pressure. A local constriction of oil film profile to identify the minimum EHD film thickness at trailing (exit) end of the film is observed to be nearby the location of the pressure spike. The results, compared to theoretical predictions, concluded that under pure rolling conditions, any increase in the applied load results in a corresponding increase in the developed pressure while a noticeable reduction in the minimum film thickness is recorded with decreasing rolling speeds.

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.