Nonlinear dynamic analysis of multiple grooved water-lubricated journal bearings using attenuation rate interpolation method

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 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.

Hydrodynamics of liquid-liquid two-phase flow accounting for the coupling of dean vortices and Poiseuille flow

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 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.

Minimum, central and average film thicknesses have been calculated for the isothermal E.H.L. point contact case, for a variety of load, rolling speed, and material parameters. The equations governing this problem were solved using a Multigrid method. This technique offers the possibility to work with a very fine grid, obtaining detailed and accurate solutions, at the cost of moderate cpu times and storage requirements, on medium size computers. Computations for low loads, requiring a large inlet zone, have been carried out using local grid refinements. The fluid in these calculations is assumed to be compressible and its viscosity-pressure behavior is described by either the Roelands equation, or the Barus equation. The ratio between the calculated minimum film thickness and the central value varied with the parameters governing the problem, but for low loads, a value of 3/4 was obtained. The film thickness behavior at these low loads can be accurately described in terms of the minimum film thickness. For higher loads, however, a description based on a film thickness, averaged over the Hertzian contact, is more appropriate to be compared with the asymptotic solution (Ertel, Grubin).

In response to the problem of lubrication failure of sliding bearings in circular arc gear pumps under variable operating conditions, this paper studies the lubrication characteristics of sliding bearings. Establish a fluid lubrication model for sliding bearings and introduce radial forces and Reynolds boundary conditions. Analyzing the influence of rotational speed and outlet pressure of circular arc gear pump on the lubrication characteristics of sliding bearings based on finite difference method. The research results indicate that as the rotational speed increases, the minimum film thickness gradually increases, the maximum film pressure gradually decreases, and the position of the dynamic pressure effect gradually shifts forward. The maximum film pressure position and the minimum film thickness position differ by about 0.4 rad in the circumferential direction. The acceleration curve has a significant impact on the lubrication characteristics of sliding bearings, and the greater the acceleration, the more obvious the changes in lubrication characteristics. Compared with the acceleration process, the changing trend of lubrication characteristics of sliding bearings during the boosting process is opposite.

Misalignment is an undesired phenomenon for all types of rotating machines because it decreases their performance and the lifespan. For the internal gear motor/pump, there are many elements that can cause misalignment; e.g. manufacturing or assembly errors, asymmetric load. Consequences of the misaligned ring gear leads to the metal-to-metal contact between the ring gear and the housing. An analytical and experimental study concerning the effect of misalignment on the performance of the internal motor/pump are presented in this paper. A new mathematical model has been governed to determine the eccentricity, the position angle, the minimum oil film as well as the misalignment angle around x- and y-axes. A test rig has been designed to evaluate experimentally the effects of operating parameters on the misaligned angle. The experimental results point out that the minimum oil film thickness can be reduced up to 18 % due to misalignment. This leads to the solid contact at one of two ring gear sides whereas at the mid-plane the minimum film thickness is not fallen below the permissible film thickness. Hence, for more accurate prediction of the performance and the lifespan of internal gear motor/pump, the effect of misalignment must be considered in calculation at the early design stage. After experiments, the inspection of the test motor was performed to prove the accuracy of the calculation.

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.

Hydrodynamic journal bearings supporting high mass rotating machinery are subjected to low rotational speeds during start-up or idling phases. These working conditions need a hydrostatic pressure contribution to ensure a correct load capacity when the hydrodynamic pressure is not established yet. This is possible by means of hydrostatic lift pockets. These pockets avoid mechanical damages via sufficient film thickness from start-up to hydrodynamic working conditions. In a first part, it is showed how an existing isothermal 3D hydrodynamic numerical modelling of tilting pad bearing has been adapted to take into account the lift pocket impact on static bearing performance. This approach is only valid for low rotational speeds, when inertia step pressure effects (rises or drops) at the film-pocket edge can be neglected compared to the total bearing pressure pattern. Then, numerical simulations have been performed, from 1 to 200 rpm with pockets and from 75 to 200 rpm without pockets. The results have been compared and discussed in terms of pressure fields and bearing static performance such minimum film thickness, friction torque or rotor center position. Therefore, the interest of such lift pockets has been highlighted. Finally, calculations with and without pockets have been carried out in case of a strong bearing misalignment. As a result, the benefits of the lift pockets in this configuration are also significant in terms of static performance.

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 purpose of this paper is to analyze dynamic behaviors of the oil film thickness and engine bearings in both aligned and misaligned operation conditions of a crankshaft using computer simulation techniques. A crankshaft as an elastic body is modeled for a misaligned crankshaft which is very important design parameter of the film thickness and engine bearings. In this analysis, a dynamic characteristic of a minimum oil film is analyzed based on the elastohydrodynamic lubrication theory. The boundary conditions for analyzing the film behaviors include non-linear constraint forces and bending moments in engine bearings. The more expedient model of an engine bearing is extended to consider the effect of crankshaft misalignment. The computed results indicate that the minimum oil film thickness that causes a major influence on the performance of engine bearings has showed a decrease of 16% to 24% for the misaligned crankshaft compared with an aligned crankshaft. The computed results show that the misalignment of a crankshaft inevitably brings the reduction of minimum oil film thickness and this may increase the failure of a bearing. These results as design parameters are very useful for a bearing designer as a firm reference data of an automotive engine.

Real-time fluid film modification technique is used in the active bearing technology to control the journal's equilibrium position for various operating conditions. This is achieved by the controlled movement of the flexible bearing element. The information of the minimum film thickness (MFT) is essential during the bearing element displacement to avoid the metal to metal contact. The bearing element-specific MFT develops in the multipad externally adjustable bearing with asymmetric combinations of adjustments. A single analytical expression fails to predict the multiple minimum film thickness for various bearing elements adjustment configurations. In this work, a neural network model is developed to predict the MFT in a multipad adjustable bearing having four adjustable bearing elements. Design of experiment and transformation technique is used to collect the data set between the eccentricity ratio 0.1 to 0.8. A feed-forward multilayer perceptron is used to model the MFT. The results show that an accurate estimation of the MFT is possible using a single neural network model.

This work presents a sensibility analysis for the journal bearings of combustion engines mass balancing systems. Applying it, it’s possible to improve the journal bearings and avoid possible failures. This analysis consists on studying the effects of the variation of the journal bearings main parameters (radial clearance, journal bearing diameter and journal bearing length) on the journal bearings operating conditions (minimum film thickness, maximum pressure and power loss). The analysis also includes the comparison and selection of the different metallic materials that can be used in these journal bearings, as well as the selection of the lubrication system groove suitable for the journal bearings used in this kind of application. This sensibility analysis shows that: increasing the radial clearance the minimum film thickness increases, the maximum pressure remains approximately the same and the power loss decreases; increasing the journal bearing length, the minimum film thickness and power loss increase and the maximum pressure decreases; increasing the journal bearing diameter, the minimum film thickness and power loss increase and the maximum pressure decreases. At last, it’s found that the white metals (Babbitts) are considered the most advantageous and indicated materials for these journal bearings, and that the lubrication system grooves should be circumferential.