On the Derivation of REYNOLDS EQUATION

Abstract

The complete Reynolds Equation in 3‐dimensions is derived by three methods which differ basically in the way in which the continuity condition is applied. The apparent divisions of the mechanisms of hydro‐dynamic lubrication which are suggested by these derivations, such as “wedge,” “squeeze” terms etc. are compared and it is shown that such a division is in every case somewhat arbitrary, since it merely depends on the volume to which the continuity condition is applied. A form of the Reynolds Equation is given for the case where both surfaces are curved (as in gears, for example), the x‐axis being taken along the common tangent at the contact zone. The reason for the differences in the forms of the equation derived in this paper and that given by Reynolds in his original paper, is pointed out to avoid possible confusion. The error involved in neglecting the variation in the horizontal surface velocity component of a journal bearing is considered. This is shown to be negligible under typical operating conditions.

Citation

CAMERON, A. and ROBERTSON, W.G. (1962), "On the Derivation of REYNOLDS EQUATION", Industrial Lubrication and Tribology, Vol. 14 No. 6, pp. 14-42. https://doi.org/10.1108/eb052697