This paper presents the first numerical study of self-acting grooveless, partial arc bearings under steady load and sinusoidal journal oscillation accounting for mass-conserving cavitation, with the objective of determining a range of bearing loads, oscillation speeds, and dimensional specifications under which a fully hydrodynamic lubrication regime can be achieved. A generalized Warner bearing (GWB) formulation is introduced to address the long computation times associated with this bearing application and to account for local flattening of the pressure region expected in very thin films. The computational speed of the GWB formulation is approximately 80 times faster than the complete formulation with comparable accuracy for the examples provided in the paper. Mixed or boundary lubrication is predicted for oscillation amplitudes less than π/4 radians regardless of load number, which concurs with experimental trends. Fully hydrodynamic lubrication is predicted over a large range of load numbers for minimum oscillation amplitudes of approximately π/2 radians.