A Demonstrably Optimum One Dimensional Journal Bearing

1972 ◽  
Vol 94 (2) ◽  
pp. 188-192 ◽  
Author(s):  
S. M. Rohde
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Journal Bearing ◽  
Infinite Length ◽  
Load Carrying Capacity ◽  
One Dimensional ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Constant Viscosity ◽  
Nonlocal Formulation

By the use of a new variational technique, the bearing profile which maximizes the load carrying capacity of an infinite length journal bearing is obtained. The lubricant is assumed to be incompressible and of constant viscosity. The flow is assumed to be laminar and the optimization is based upon a minimum film thickness. The solution obtained is a concentric step bearing with a film thickness ratio of 1.812 and a ridge to pad ratio of 0.328. It is mathematically shown by the use of the “nonlocal” formulation that this step profile does yield a maximum among all profiles sufficiently “close.”

The Performance of Hydrodynamic Lubricating Films With Viscosity Variations Perpendicular to the Direction of Motion

1972 ◽  
Vol 94 (1) ◽  
pp. 44-48 ◽  
Author(s):  
E. B. Qvale ◽  
F. R. Wiltshire
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Load Carrying Capacity ◽  
End Effects ◽  
Parametric Curves ◽  
One Dimensional ◽  
Lubricating Film ◽  
Families Of Curves ◽  
Load Carrying ◽  
The Coefficient Of Friction

The effects of prescribed viscosity variations across a hydrodynamic lubricating film are studied. The film is strictly one dimensional and end effects are neglected. The viscosity variations are given by three families of curves. The considerable decreases (in the limit 100 percent) and occasional increases in the coefficient of friction that can occur for constant film thickness and load-carrying capacity are evaluated and the results are presented in terms of parametric curves. Important physical situations where these viscosity variations may be observed or produced are described.

An Analytical Solution for the Normal Load Carrying Capacity of Lightly Loaded Cylinders in Combined Rolling, Sliding and Normal Motion

1981 ◽  
Vol 103 (3) ◽  
pp. 467-468 ◽  
Author(s):  
T. F. Conry
Keyword(s):  
Analytical Solution ◽  
Film Thickness ◽  
Exponential Function ◽  
Carrying Capacity ◽  
Normal Load ◽  
Load Capacity ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Minimum Film Thickness

The analytical solution for the normal load carrying capacity of lightly loaded cylinders in combined rolling, sliding and normal motion is obtained. It is shown that the load capacity is inversely proportional to the dimensionless minimum film thickness. The results are presented graphically and approximated in the form of an exponential function.

Increase of Operational Safety of Tilting-Pad Journal Bearings by Extraction of Hot Oil at the Trailing Edge

2015 ◽  
Author(s):  
Sebastian Kukla ◽  
Nico Buchhorn ◽  
Beate Bender
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Maximum Temperature ◽  
Load Carrying Capacity ◽  
Trailing Edge ◽  
Tilting Pad ◽  
Load Carrying ◽  
Operational Safety ◽  
Minimum Film Thickness ◽  
Safety Parameters

A theoretical study is presented with the main objective on the operational safety parameters (minimum film thickness and maximum pad temperature) and thermomechanical deformations of a ø500 mm rocker pad tilting-pad journal bearing (TPJB) for application in large turbo machinery. It can be described by the following specifications: Five pads, 0.23 nominal preload, 60% offset, 56° pad arc angle, 350 mm pad length and 1.28‰ relative bearing clearance. Theoretical investigations are carried out for circumferential speeds up to 78 m/s and static loads up to 3.60 MPa. The simulation tool simultaneously solves both Reynolds and energy equations for the oil film (3D temperature distribution) on the one hand and computes thermomechanical deformations of the pad on the other hand. The simulations are conducted for a single pad and are supported by boundary conditions taken from experiments. The results with regard to static bearing characteristics and pad deformation show good agreement with experiments. The impact of axial pad arching on operational safety parameters and load-carrying capacity are shown and compared to experimental results. It is shown that the axial deviation in film thickness Δh can be even higher than the minimum film thickness hmin. This leads to reduced hydrodynamic pressure build-up towards the axial edges and therefore significantly decreased safety parameters or load-carrying capacity. In order to reduce pad crowning, radial bores through the pad body are modelled to simulate the extraction of hot oil from the trailing edge. In the simulation, the hot oil is used to heat up the back of the pad for a decrease of radial temperature gradients and thus pad arching. It is shown that by extracting 0.4 l/s of hot oil, a decrease in axial pad crowning from Δh = 47μm to Δh = 26μm can be achieved and that this leads to a decrease of 7.8 K in maximum temperature and an increase of 5 μm in minimum film thickness respectively a gain of load-carrying capacity of 0.4–0.6 MPa.

Improvement of lubrication performance of water lubricated polymer bearing via enlarged axial end bearing diameter

2019 ◽  
Vol 71 (4) ◽  
pp. 564-572
Author(s):  
Fangrui Lv ◽  
Donglin Zou ◽  
Na Ta ◽  
Zhu-Shi Rao
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Load Carrying Capacity ◽  
Content Type ◽  
Lubrication Performance ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
The Impact ◽  
Polymer Bearing ◽  
Practical Implications

Purpose The purpose of this paper is to improve the lubrication performance of a water-lubricated polymer bearing with axial grooves, especially enlarge the minimum film thickness. Design/methodology/approach The bearing diameter is enlarged near the axial ends of the journal, with axial openings of a trumpet shape. A numerical model is developed which considers the proposed trumpet-shaped openings, bush deformation and grooves. The generatrix of the trumpet-shaped opening is assumed to be a paraboloid. Three different variations are covered, and the influences of the trumpet-shaped openings’ parameters on the bearing performance are analyzed. Findings The appropriate trumpet-shaped openings at the axial ends effectively increase the minimum film thickness, and the impact of trumpet-shaped openings on load carrying capacity is very small or even negligible. For the water-lubricated polymer bearing with axial grooves analyzed in this paper, the appropriate trumpet-shaped openings increase the minimum film thickness from 0.53 to 11.14 µm and decrease the load carrying capacity by 2.48 per cent. Practical implications The results of this study can be applied to marine propeller shaft systems and other systems with polymer bearings. Originality/value This paper has presented an approach for significantly increasing the minimum film thickness of a water-lubricated polymer bearing. A study on the performance improvement of water-lubricated polymer bearings with axial grooves is of significant interest to the research community.

Effect of journal misalignment on the static characteristics of an innovative journal bearing with adjustable elements in load-on-pad and load-between-pad configurations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
H. Girish ◽  
Raghuvir Pai
Keyword(s):  
Film Thickness ◽  
Journal Bearing ◽  
Load Carrying Capacity ◽  
Static Characteristics ◽  
Content Type ◽  
Load Carrying ◽  
Bearing Load ◽  
Minimum Film Thickness ◽  
Peak Pressures ◽  
Journal Misalignment

Purpose The purpose of this paper is to theoretically analyze an innovative form of variable bearing configuration having four pads with unique adjustability principle operated under journal misaligned conditions. The parameters such as load positions, degrees of misalignment (DM) and pad adjustment configurations influencing the steady-state performance of the four-pad adjustable bearing are detailed in this paper. Design/methodology/approach The proposed adjustable pad geometry possesses the ability to undergo radial and tilt motions in both inward and outward directions. Analysis is carried out by considering journal misalignment in vertical and horizontal planes with bearing modelled for load-on-pad and load-between-pad configurations. The film thickness equation derived to incorporate the radial and tilt adjustment parameters is further modified to accommodate the different load orientations and misaligned journal conditions. The pressure field equation is solved by applying finite-difference technique combined with Gauss Siedel iterative method. Findings At higher DM, peak pressures generated in the minimum film thickness region near the pad ends highly influences the bearing load carrying capacity. Results indicated that the adjustable four-pad bearing geometry is highly efficient in withstanding the journal misalignment by radially displacing and tilting the four pads in negative directions. Originality/value For bearing designers, this research highlights the importance of considering the misalignment factor during the design stages of an adjustable journal bearing. The proposed adjustability concept is proven to be effective enough to improve the bearing performance and, in turn, withstand the journal misalignment.

scholarly journals On the Design and Lubrication of Water-Lubricated, Rubber, Cutlass Bearings Operating in the Soft EHL Regime

Lubricants ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 75 ◽  
Author(s):  
Edward H. Smith
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Predictive Modelling ◽  
Load Carrying Capacity ◽  
Clearance Ratio ◽  
Surrounding Water ◽  
Load Carrying ◽  
Model Predictions ◽  
Design Guide ◽  
Minimum Film Thickness

All propeller-driven ships employ a drive shaft supported by journal bearings. To avoid water pollution, these bearings are generally lubricated by the surrounding water, removing the need for a rear seal. Such bearings, commonly referred to as Cutlass bearings, usually have an inner grooved nitrile rubber lining. The grooves (called flutes) allow debris to be flushed out and the bearing surface to be cooled. The remaining area is divided into a number of load-carrying areas called staves. At present, no rigorous design guide exists for these bearings. This paper presents a methodology to predict the minimum film thickness between the journal and the most heavily-loaded stave, an approach not hitherto reported in the literature. The method includes a new, 3D, finite element (FE) approach for soft elasto-hydrodynamic (EHL) predictive modelling of generated pressures in cutlass bearings. Model predictions compare favourably with experimental data. It is shown that the modulus of elasticity of the rubber has no influence on the minimum film thickness. An equation relating dimensionless film thickness to dimensionless load, clearance ratio and numbers of staves is presented. For a nominally circular bearing, increasing the clearance ratio or increasing the numbers of staves reduces load-carrying capacity. It is shown that distortion due to loading can increase load-carrying capacity.

Increased Load Carrying Capacity of Large Tilting-Pad Journal Bearings by Injection of Cold Oil

2016 ◽  
Author(s):  
Nico Buchhorn ◽  
Sebastian Kukla ◽  
Beate Bender
Keyword(s):  
Film Thickness ◽  
Carrying Capacity ◽  
Load Capacity ◽  
Maximum Temperature ◽  
Load Carrying Capacity ◽  
Tilting Pad ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Safety Parameters ◽  
The Impact

In this paper a theoretical study with the aim to achieve higher load capacity of large tilting-pad turbine bearings is presented. The main focus is set on the reduction of thermal gradients inside the pad and thus, of adverse thermomechanical deformations. This allows for the increase of either the load carrying capacity, minimum film thickness hmin, and/or decrease maximum pad temperature Tmax. Subject of the investigation is a 5-pad tilting-pad bearing with rocker pivots. Each pad arc measures 56° and the pivot is positioned at 60 %. By having a 500mm inner diameter the 350mm long bearing features a relative clearance of 1.28% and nominal preload of 0.23. It is shown that the axial pad bending Δh (crowning) has a major impact on film thickness and pressure distributions and thus on the operational safety parameters. In order to reduce this effect, radial bores through the pad supplying pressurized cold oil (Tinj = 50 °C) are simulated. Despite the evident increase in oil film pressure, the primary purpose of the injection is to rinse away the layer of hot oil sticking to the pad surface. The maximum pad temperature and the overall pad temperature gradients are thereby decreased. The code used for simulation solves Reynolds and energy equations and computes thermomechanical deformations simultaneously. However, the simulations are carried out for one single pad only and are therefore supported by boundary conditions taken from experiments. In order to determine the impact of the approach on the static bearing characteristics, diameter and location of the bores are varied (0.3mm ≤ db ≤ 0.5mm). It is shown that pad crowing can be reduced significantly: The axial deviation of the film thickness Δh can be decreased from Δh = 47 μm to Δh = 31 μm, while the maximum temperature Tmax can be decreased by 20 K. Further, the minimum film thickness hmin can be increased by 16 μm. Subsequently, allowing the same limits for hmin and Tmax for the new design, the load capacity can be raised by up to 1.21MPa ≙ 44 %.

The Maximum Principle Approach to the Optimum One-Dimensional Journal Bearing

1970 ◽  
Vol 92 (3) ◽  
pp. 482-487 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Maximum Principle ◽  
Film Thickness ◽  
Journal Bearing ◽  
Maximum Load ◽  
Load Direction ◽  
One Dimensional ◽  
The Maximum Principle ◽  
Minimum Film Thickness ◽  
Constant Viscosity ◽  
The One

Pontryagin’s Maximum Principle is used to determine the journal bearing which supports the maximum load for a given minimum film thickness and a specified load direction. The one-dimensional configuration which uses a constant-viscosity, incompressible lubricant is considered. Comparison shows that the optimum bearing carries a load about 13.5 percent greater than the maximum carried by the usual full-Sommerfeld bearing and about 121 percent greater than that carried by the half-Sommerfeld unit. The problem is formulated subject to the constraints of a fixed load direction and a specified minimum film thickness while the only boundary condition imposed is that the pressure must vanish at the inlet and at the outlet. The actual extent of the bearing is determined in the optimization process and it is shown that this extent is 360 deg. Further, the bearing is stepped with only two regions of different but constant film thickness.

Numerical Study on Load Carrying Mechanism of Two Parallel Lubricated Rough Surfaces With Relative Motion

2007 ◽  
Author(s):  
Hua-Ping Yao ◽  
Ping Huang
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Relative Motion ◽  
Carrying Capacity ◽  
Rough Surfaces ◽  
Peak Height ◽  
Load Carrying Capacity ◽  
Lubrication Film ◽  
Load Carrying ◽  
Minimum Film Thickness

In the present paper, the load carrying mechanism of two parallel lubricated rough surfaces with relative motion is numerically analyzed from the microscopic view. It is found that each asperity of the surface forms mini-type convergent and divergent wedge sliders. The convergent wedge can create positive hydrodynamic pressure and forms a hydrodynamic lubrication film so that pressure is produced to bear an outside load. The Reynolds equation is used to analyze the influence of the roughness on the performances such as the pressure distribution, the load carrying capacity, the shearing force, the friction force and etc. The varying rules of the load carrying capacity and friction coefficient with the peak height of roughness are discussed in detail, and the influence of the minimum film thickness on lubrication state is also analyzed. The results indicate that under a given lubrication film thickness the load carrying capacity can achieve the maximum value and then decrease slowly with the peak height increasing, while the friction coefficient can achieve the minimum value. Furthermore, under the given condition of the peak height and 1 μm⩽h0⩽100 μm of the minimum film thickness the load carrying capacity drops down gradually, while the friction coefficient increases gradually with increase of the minimum film thickness.

The Lubrication of Lightly Loaded Cylinders in Combined Rolling, Sliding, and Normal Motion—Part I: Theory

1976 ◽  
Vol 98 (4) ◽  
pp. 509-516 ◽  
Author(s):  
D. Dowson ◽  
P. H. Markho ◽  
D. A. Jones
Keyword(s):  
Boundary Condition ◽  
Steady State ◽  
Film Thickness ◽  
Carrying Capacity ◽  
Dimensionless Parameter ◽  
Load Carrying Capacity ◽  
State Problem ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Steady State Problem

The problem considered in this paper is that of the lubrication of rigid cylindrical solids by an isoviscous lubricant. The steady-state problem has been studied by several authors, but the present analysis explores the effect of non-steady-state conditions arising from combined ‘normal’ and ‘entraining’ motion. It is shown that the major bearing performance characteristics can be accounted for by means of a dimensionless parameter (q) involving the ‘normal’ and ‘entraining’ velocities, the minimum film thickness and the radius of a geometrically equivalent cylinder near a plane. The results are represented graphically and by a set of convenient polynomials in (q). The influence of the cavitation boundary condition is considered and it is shown that sinusoidal ‘normal’ motion superimposed upon ‘entraining’ action can lead to a substantial increase in the nett load carrying capacity.

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