When dealing with the lubrication of bearings, the governing equation describing pressure is the Reynolds equation, generally written in one dimension as

\[\frac{d}{d x}\left(\frac{h^{3}}{\mu} \frac{d p}{d x}\right)+6 U \frac{d h}{d x}=0\]

where \(h\) is the step height and \(U\) is the velocity of the lower surface. Step bearings have a relatively simple design and are used with lowviscosity fluids such as water, gasoline, and solvents. The minimum film thickness in these applications is quite small. The step height must be small enough for good load capacity, yet large enough for the bearing to accommodate some wear without losing its load capacity by becoming smooth and flat. Beginning with the 1D equation for fluid motion in the \(x\) direction, show that the pressure distribution in the step bearing is as shown, where

Transcribed Image Text:

12 h Ps= 6(h2-h1) hh L1 L2 h2 P Ps U P8.33 Li x