A General Method for Calculating the Pressure Distribution and Load Capacity for Finite Hydrodynamic Bearings with Lubrication Films Curved in One Direction

Abstract

Reynolds' equation is separable into two single variable differential equations for the case of a hydrodynamic bearing with its lubrication film curved in one direction. One of the equations is not, in general, soluble analytically. A simple numerical solution of this equation is described. The solution depends only on the shape of the lubrication film and not on the ratio b/l where b is the pad breadth and l is its length. This means that a sequence of bearing parameters for a set of values of b/l can be calculated rapidly from the single numerical solution of the differential equation.

The method has been tested by calculating the dimensionless load capacity per unit width of an exponential bearing and comparing this capacity with the analytical solution which can be calculated for this particular bearing. The numerical and analytical results agree to better than 0.1 percent for the various cases considered.

No more than 10 terms are needed in the numerical solutions because analytical approximations which are given can be used for higher order terms.