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National Advisory Committee for Aeronautics, Technical Notes - Effects of Temporal Tangential Bearing Acceleration on Performance Characteristics of Slider and Journal Bearings

A theoretical analysis of the effects of temporal tangential
bearing acceleration on several performance characteristics of
slider and Journal bearings is presented. The derivations of the
mathenatical expressions for these effects begin with the laws of
classical hydrodynamics and conclude with modified versions of the
usual performce equations in lubrication. Equations are pre-
sented that establish flmdamental relations and show the effects of
this type of acceleration on pressure distribution and load capa-
city. Some emmples employing the results are presented along with
suggestions for other possible applications. Nomographs are
included to facilitate solution of practical problems.

The equations show that the factor which is most. important in
establishing the effect of acceleration on bearing performance
characteristics is the ratio of acceleration to speed. When this
ratio is high, theeffect of acceleration is large; when it'is low,
the effect is small. It was found that acceleration acts to
decrease load capacity of a bearing. In certain cases, the effects
of acceleration are as important as those due to lubricant
viscosity.

The present conventional hydrodynamic theory of lubrication is
based on a number of fundamental equations originally derived from
the laws of internal friction and motion of fluids. ferhaps the
most important expression on the subject is the basic differential
equation for pressure distribution put forth by Reynolds (refer-
ence 1). Several terms, such as those referring to the ccmpressi- .
bility of the fluid, eddy forces, variable visoosities, forces
from weight and inertia, and certain velocities, were disregarded
because their mgnitudes were considered to be of a second-order
nature.

These omissions are Justified as long as the excluded
quantities or their effects on performance characteristics rennin
small; however, if any one of them approaches first-order ungui-
tude, it should not be disregarded. Such may be the case with the
inertia toms. One possible reason why the calculated total
effect may be in error can be found in a statement by lamb (refer-
ence 2) in which he said, "Although the equations of motion of
viscous fluids are well established, the calculations basedcn
them are often subject to serious limitations. The reason is
partly to be sought in the omission, for the sake of mathem-
tical simplicity, of small terms of the second order in the
Eulerian expressions for the accelerations, which terms are often
at least as important as those due to viscosity.