A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

On the Analytical Evaluation of the Lubricant Pressure in the Finite Journal Bearing

2012 ◽  
Author(s):  
Athanasios Chasalevris ◽  
Dimitris Sfyris
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Closed Form Expression ◽  
Linear Ordinary Differential Equations ◽  
Definition Of

The Reynolds equation for the pressure distribution of the lubricant in a journal bearing with finite length is solved analytically. Using the method of the separation of variables in an additive and in a multiplicative form, a set of particular solutions of the Reynolds equation is added in the general solution of the homogenous Reynolds equation and a closed form expression for the definition of the lubricant pressure is presented. The Reynolds equation is split in four linear ordinary differential equations of second order with non constant coefficients and together with the boundary conditions they form four Sturm-Liouville problems with the three of them to have direct forms of solution and one of them to be confronted using the method of power series. The mathematical procedure is presented up to the point that the application of the boundaries for the pressure distribution yields the final definition of the solution with the calculation of the constants. The current work gives in detail the mathematical path with which the analytical solution is derived, and it ends with the pressure evaluation and a comparison with past numerical solutions and an approximate analytical solution for a finite bearing. Also the parameters of primary interest to the bearing designer, such as load capacity, attitude angle, and stiffness and damping coefficients are evaluated and compared with numerical results.

scholarly journals Improvement of Tilting-Pad Journal Bearing Operating Characteristics by Application of Eddy Grooves

Lubricants ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 18
Author(s):  
Eckhard Schüler ◽  
Olaf Berner
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Load Capacity ◽  
Fluid Film ◽  
Operating Characteristics ◽  
Fluid Film Bearings ◽  
Tilting Pad ◽  
Bearing Load ◽  
Bearing Loads ◽  
Tilting Pad Journal Bearing

In high speed, high load fluid-film bearings, the laminar-turbulent flow transition can lead to a considerable reduction of the maximum bearing temperatures, due to a homogenization of the fluid-film temperature in radial direction. Since this phenomenon only occurs significantly in large bearings or at very high sliding speeds, means to achieve the effect at lower speeds have been investigated in the past. This paper shows an experimental investigation of this effect and how it can be used for smaller bearings by optimized eddy grooves, machined into the bearing surface. The investigations were carried out on a Miba journal bearing test rig with Ø120 mm shaft diameter at speeds between 50 m/s–110 m/s and at specific bearing loads up to 4.0 MPa. To investigate the potential of this technology, additional temperature probes were installed at the crucial position directly in the sliding surface of an up-to-date tilting pad journal bearing. The results show that the achieved surface temperature reduction with the optimized eddy grooves is significant and represents a considerable enhancement of bearing load capacity. This increase in performance opens new options for the design of bearings and related turbomachinery applications.

An Approximate THD Theory for Journal Bearings

1990 ◽  
Vol 112 (2) ◽  
pp. 224-229 ◽  
Author(s):  
G. Gupta ◽  
C. R. Hammond ◽  
A. Z. Szeri
Keyword(s):  
Journal Bearing ◽  
Load Capacity ◽  
Pressure Coefficient ◽  
Journal Bearings ◽  
Maximum Pressure ◽  
Substantial Agreement ◽  
Interactive Mode ◽  
Lubricant Flow ◽  
Bearing Load ◽  
Sophisticated Model

The aim of this paper is to make available to the industrial designer results of the thermohydrodynamic theory of journal bearings, by providing a simplified, yet accurate model of journal bearing lubrication that can be implemented on a personal computer and be used in an interactive mode. The simplified THD theory we propose consists of two coupled ordinary differential equations for pressure and energy and an algebraic equation for viscosity, which are to be solved iteratively. Bearing load capacity, maximum bearing temperature, maximum pressure, coefficient of friction and lubricant flow rate calculated from this simplified theory compare well with results from a more sophisticated model. We also make comparisons with experimental data on full journal bearings, demonstrating substantial agreement between experiment and simplified theory.

Theoretical Study on Static Performance of Herringbone Grooved Aerodynamics Foil Bearing

2020 ◽  
Author(s):  
ZeDa Dong ◽  
Cheng Cheng ◽  
Fangcheng Xu
Keyword(s):  
Power Consumption ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Structural Parameters ◽  
Operational Parameters ◽  
Film Pressure ◽  
Friction Power ◽  
Foil Bearings ◽  
Bearing Load ◽  
Herringbone Grooves

Abstract In this paper, the mathematical model of herringbone grooved aerodynamic foil bearings is established, and the finite difference method is used to obtain the discretized form of Reynolds equation. The static characteristics of bearings, such as film pressure, film temperature, are obtained by solving the Reynolds equation and energy equation. The bearing load capacity and friction power consumption are obtained by calculating the film thickness and film pressure distribution in the bearing gap. The influence of the bearing operational parameters, such as eccentricity and rotation speed, and the bearing structural parameters, such as groove width, groove depth ratio, groove number and helix angle, on the bearing load capacity and friction power consumption of bearings are analyzed. The methods of improving bearing load capacity and reducing friction power consumption are obtained. Simultaneously, by comparing the bearing load capacity and friction power consumption of herringbone grooved gas foil bearings and gas foil bearings (GFBs) without herringbone grooves, the influence of herringbone grooves on the bearing performance is obtained.

A Radiometric Test to Determine the Lubricant Effect on Journal Bearing Load Capacity

1980 ◽  
Author(s):  
Arnold O. Dehart ◽  
Richard C. Rosenberg ◽  
Robert F. Hill ◽  
Eric W. Schneider
Keyword(s):  
Journal Bearing ◽  
Load Capacity ◽  
Bearing Load

Rayleigh Step Journal Bearing: Part 1—Compressible Fluid

1968 ◽  
Vol 90 (1) ◽  
pp. 271-280 ◽  
Author(s):  
B. J. Hamrock
Keyword(s):  
Compressible Fluid ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Pressure Profile ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Step Parameters ◽  
Bearing Part

A linearized PH solution to the Reynolds equation was obtained while neglecting side leakage. The analysis was divided into two parts—the step and ridge regions. The pressure profile across the step and ridge region of the various pads which are placed around the journal was obtained from the linearized PH Reynolds equation. Knowing the pressure, the load components and attitude angle were calculated. The resulting equations were found to be a function of the bearing parameters (the eccentricity and compressibility number) and the step parameters (ratio of the stepped clearance to the ridge clearance, ratio of the angle extended by the ridge to the angle extended by the pad, and number of pads placed around the journal). The maximum load capacity can be determined by numerically differentiating the load with respect to the step bearing parameters while finding where the slope is zero. A series of data was run while varying the bearing parameters. The attitude angle was calculated for the various cases which were run.

Empirical Treatment of Hydrodynamic Journal Bearing Performance in the Superlaminar Regime

1970 ◽  
Vol 12 (2) ◽  
pp. 116-122 ◽  
Author(s):  
H. F. Black
Keyword(s):  
Reynolds Number ◽  
Field Equation ◽  
Experimental Work ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Theoretical Treatment ◽  
Hydrodynamic Journal Bearing

The application of a perturbation in terms of simple correlations for friction in turbulent Couette and ‘screw’ flows, together with a further empirical assumption consonant with the experimental work of Smith and Fuller (1), leads to a pressure field equation identical in form with the Reynolds equation. The load capacity of journal bearings throughout most of the superlaminar range may be represented by a single curve, and existing laminar solutions may be applied with the parameters modified by Reynolds number. The theory is compared with published experimental results, and with the most successful theoretical treatment (4). The correlations obtained confirm the adequacy of the theory to predict performance in the superlaminar régime.

Measurement of Oil Aeration Effects in Journal Bearings

2002 ◽  
Author(s):  
J. L. Nikolajsen ◽  
D. Dong ◽  
M. J. Goodwin
Keyword(s):  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Damping Capacity ◽  
Bearing Load ◽  
Bearing Stiffness

Preliminary measurements have been conducted to determine the effect of oil aeration on journal bearing performance. Oil aeration was observed to reduce the bearing load capacity and to increase the bearing stiffness. Also, the bearing damping capacity was improved significantly by oil aeration.

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