Cavitation in mechanical face seals.
Gas cavities in mechanical face seals operating with hydrodynamic films, obtaining solutions to Reynolds equation for hydrodynamic lubrication
Findlay, J. A.↗
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Inward pumping in mechanical face seals.
Hydrodynamic characteristics producing inward pumping in mechanical face seals, solving Reynolds equation for hydrodynamic lubrication with short-bearing approximation and numerical iterative methods
Findlay, J. A.↗
Finite-element solution of the incompressible lubrication problem.
Finite element solution of incompressible lubrication problem by minimum principle for transient incompressible Reynolds equation with boundary conditions
Reddi, M. M.↗
Effect of surface asperity on elastohydrodynamic lubrication
The important aspects of elastohydrodynamic lubrication, with a single, one-dimensional asperity, have been found by solving numerically the coupled transient Reynolds equation and the elasticity equation. Even though the assumption of a single asperity is highly ideal, this study sheds some light on the effect of surface roughness on elastohydrodynamic lubrication. The results show that the film pressure tends to increase more than the steady state pressure, and in particular, the increase in pressure reaches a maximum as the asperity approaches the inlet of the contact region. The asperity height and the pressure increase above the steady state pressure are closely related to each other; the higher the asperity height, the larger the pressure increase. In the pure rolling case, it has been found that a local pressure peak is not developed. However, in the cases of sliding and rolling, a small, local pressure peak is developed on the pressure profile when the asperity moves into the contact region. In general, the overall film thickness profile increases with increasing asperity height, but is not significantly affected by the asperity width. Moreover, the slope of the overall film thickness profile for the transient cases is much greater than the steady state profile, which is approximately constant across the contact width. The increase in the center film thickness also depends upon the width and height of the asperity.
Lee, K.↗
An economical method of analyzing transient motion of gas-lubricated rotor-bearing systems.
A method of economically evaluating the hydrodynamic forces generated in a gas-lubricated tilting-pad bearing is presented. The numerical method consists of solving the case of the infinite width bearing and then converting this solution to the case of the finite bearing by accounting for end leakage. The approximate method is compared to the finite-difference solution of Reynolds equation and yields acceptable accuracy while running about one-hundred times faster. A mathematical model of a gas-lubricated tilting-pad vertical rotor systems is developed. The model is capable of analyzing a two-bearing-rotor system in which the rotor center of mass is not at midspan by accounting for gyroscopic moments. The numerical results from the model are compared to actual test data as well as analytical results of other investigators.
Falkenhagen, G. L.↗
Face-seal lubrication. 2: Theory of response to angular misalignement
A theoretical analysis was made of a hypothetical seal operating mode. The hypothetical seal model provides for three degrees of primary ring motion and includes the force and moments induced by primary ring response to seat angular misalignment. This ring response causes a relative angular misalignment between the faces of the primary seal. Hydrodynamic pressure generation is produced by this misalignment. The analysis is based on the Reynolds equation in short bearing form and on a balance of forces and moments that arise from hydrodynamic and secondary seal friction effects. A closed form solution was obtained that can be solved for film thickness and relative angular misalignment.
Ludwig, L. P.↗
Influence of surface roughness and waviness on film thickness and pressure distribution in elastohydrodynamic contacts
The Christensen theory of a stochastic model for hydrodynamic lubrication of rough surfaces was extended to elastohydrodynamic lubrication between two rollers. Solutions for the reduced pressure at the entrance as a function of the ratio of the average nominal film thickness to the rms surface roughness, were obtained numerically. Results were obtained for purely transverse as well as purely longitudinal surface roughness for cases with or without slip. The reduced pressure was shown to decrease slightly by considering longitudinal surface roughness. The same approach was used to study the effect of surface roughness on lubrication between rigid rollers and lubrication of an infinitely wide slider bearing. Using the flow balance concept, the perturbed Reynolds equation, was derived and solved for the perturbed pressure distribution. In addition, Cheng's numerical scheme was modified to incorporate a single two-dimensional elastic asperity on the stationary surface. The perturbed pressures obtained by these three different models were compared.
Chow, L. S. H.↗
Elastohydrodynamic lubrication of point contacts
A procedure for the numerical solution of the complete, isothermal, elastohydrodynamic lubrication problem for point contacts is given. This procedure calls for the simultaneous solution of the elasticity and Reynolds equations. By using this theory the influence of the ellipticity parameter and the dimensionless speed, load, and material parameters on the minimum and central film thicknesses was investigated. Thirty-four different cases were used in obtaining the fully flooded minimum- and central-film-thickness formulas. Lubricant starvation was also studied. From the results it was possible to express the minimum film thickness for a starved condition in terms of the minimum film thickness for a fully flooded condition, the speed parameter, and the inlet distance. Fifteen additional cases plus three fully flooded cases were used in obtaining this formula. Contour plots of pressure and film thickness in and around the contact have been presented for both fully flooded and starved lubrication conditions.
Hamrock, B. J.↗
Squeeze film dampers - Amplitude effects at low squeeze numbers
Gaseous squeeze film dampers are analyzed to determine the effect of periodic disturbance amplitude on the dynamic performance. Both circular and rectangular parallel surfaces are investigated. A solution of the nonlinear Reynolds equation is obtained by expanding the pressure in powers of the squeeze number, retaining up to and including terms of the order of the square of the squeeze number. The time dependent load characteristics are found. The effect of disturbance amplitude on the film stiffness and damping is given.
Sadd, M. H.↗
Pressure perturbation in EHD contacts due to an ellipsoidal asperity
The pressure fluctuations around an ellipsoidal asperity tip at the inlet region of an elastohydrodynamic contact is determined by solving a perturbed Reynolds equation assuming that the asperity shape is unaffected by the perturbed pressure. Results are presented as the amplitude of the perturbed pressure as a function of ellipticity ratio, maximum Hertzian pressure, nominal EHD film thickness, asperity size, asperity height, and pressure viscosity coefficient. For the case of simple sliding between a smooth surface and a stationary asperity, a comparison is also made between the results for large ellipticity ratios and the pressure fluctuations obtained by using a previous line contact EHD analysis for a two-dimensional asperity ridge. The agreement is found to be close for moderate Hertzian pressure and relatively thick EHD film thickness.
Chow, L. S. H.↗
Computer program for flat sector thrust bearing performance
A versatile computer program is presented which achieves a rapid, numerical solution of the Reynolds equation for a flat sector thrust pad bearing with either compressible or liquid lubricants. Program input includes a range in values of the geometric and operating parameters of the sector bearing. Performance characteristics are obtained from the calculated bearing pressure distribution. These are the load capacity, center of pressure coordinates, frictional energy dissipation, and flow rates of liquid lubricant across the bearing edges. Two sample problems are described.
Presler, A. F.↗
Theoretical and experimental study of the drag of multielement airfoils
The viscous/potential flow past single-element and multielement airfoils is studied theoretically and experimentally. A computerized analysis, based on iteratively coupled potential-flow and boundary-layer analysis, is used to predict the flow field of the airfoil. The method yields detailed characteristics of conventional laminar and turbulent boundary layers, turbulent wakes, and confluent boundary layers. The viscous flows are analyzed with a method that uses finite-difference solutions of the boundary-layer equations. Reynolds stress in the boundary layers and wakes is simulated with eddy viscosity models for the various flow zones. The viscous calculations are carried into the wake of the airfoil where the drag is found from the defect in the wake momentum.
Olson, L. E.↗
Amplitude effects on the dynamic performance of hydrostatic gas thrust bearings
A strip gas film bearing with inherently compensated inlets is analyzed to determine the effect of disturbance amplitude on its dynamic performance. The governing Reynolds' equation is solved using finite-difference techniques. The time dependent load capacity is represented by a Fourier series up to and including the third harmonics. For the range of amplitudes investigated the linear stiffness was independent of the amplitude, and the linear damping was inversely proportional to (1 - epsilon-squared) to the 1.5 power where epsilon is the amplitude relative to the film thickness.
Stiffler, A. K.↗
Performance of end-face seals with diametral tilt and coning - Hydrostatic effects
A face seal model is analyzed, taking into account both diametral tilt and coning of the primary seal ring. The Reynolds equation for incompressible fluid is solved analytically using the narrow seal approximation. The solution covers a wide range of tilt and coning angles, from complete alignment to touch-down. Seal performance like axial force, tilting moment, axial and angular stiffness, and leakage are analyzed. It is found that interaction between diametral tilt and coning strongly affects seal performance.
Etsion, I.↗
Squeeze effects in radial face seals
Squeeze effects in a liquid lubricated radial face seal are analyzed. The analysis considers face misalignment with both axial and angular vibrations of the primary seal ring. Translational, rotational, and cross-coupled damping coefficients of the fluid film are derived analytically from a solution of the Reynolds equation utilizing the narrow seal approximation. Results are given for a wide range of practical radius ratios. At each radius ratio, the complete range of angular misalignment - from parallel faces to touch down - is covered. It is shown that squeeze effects in face seals are usually larger than the more familiar hydrodynamic effects. These effects play an important role in the seal's mechanism of operation and therefore have to be considered in any realistic seal model.
Etsion, I.↗
Elastohydrodynamic lubrication of rectangular contacts
An isothermal elastohydrodynamically lubricated rectangular contact was evaluated numerically. This required the simultaneous solution of the elasticity and Reynolds equations. In the elasticity analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure was applied over each area. The elastohydrodynamic lubrication theory thus developed was used to investigate the influence of the dimensionless speed, load, and materials parameters on minimum film thickness. Ten cases were used in obtaining the minimum film thickness formula. Plots are shown that indicate the details of the pressure distribution, film shape, and flow. The characteristic pressure spike is clearly in evidence as is the parallel film shape through the central portion of the contact, with a minimum film thickness occurring near the outlet of the contact.
Hamrock, B. J.↗
Thermal elastohydrodynamic lubrication of line contacts
A numerical solution to the problem of thermal elastohydrodynamic lubrication of line contacts was obtained by using a finite difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter Q: H(min)/H(min,I) = 10/10+ Q(0.4). Plots of pressure distribution, film shape, temperature distribution, and flow are shown for some representative cases.
Ghosh, M. K.↗
Elastohydrodynamic lubrication of smooth surfaces
Fully flooded, elastohydrodynamically lubricated contacts are considered. Elastohydrodynamic lubrication (EHL) analysis requires the simultaneous solution of the elastically, viscosity, density, and Reynolds equations. The most important practical aspect of elastohydrodynamic lubrication theory is the determination of the minimum film thickness within the conjunction. The maintenance of a fluid film of adequate magnitude is an essential feature of the correct operation of lubricated machine elements. The results show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. Film thickness equations are developed for materials of high elastic modulus, such as metal, and for materials of low elastic modulus, such as rubber.
Hamrock, B. J.↗