Exact Solution of Slip-Flow in Microbearings
Abstract
Macroscale journal bearings develop their load-bearing capacity from large pressure differences which are a consequence of the presence of a viscous fluid, an eccentricity between the shaft and its housing, a large surface speed of the shaft, and a small clearance-to-diameter ratio. Microbearings are different in the following aspects: being so small, it is difficult to manufacture them with a clearance that is much smaller than the diameter of the shaft; (2) because of the small shaft size, its surface speed is also small; (3) air bearings in particular may be small enough for non-continuum effects to become important. For these reasons the hydrodynamics of lubrication is very different at microscales. The lubrication approximation that is normally used is no longer directly applicable and other effects come into play. The present study analyzes microbearings represented as an eccentric cylinder rotating in a stationary housing. The two-dimensional governing equations are written in terms of the streamfunction in bipolar coordinates and an infinite-series solution is obtained. For high values of the eccentricity and low slip factors the flow may develop a recirculation region. The force and torque on the load-bearing inner cylinder increase with increasing eccentricity and decrease with increasing slip.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 1997
- Bibcode:
- 1997APS..DFD..De06G