Linearized ph Stability Theory for Translatory Half-Speed Whirl of Long, Self-Acting Gas-Lubricated Journal Bearings

The linearized ph approximation to the time dependent Reynolds equation is solved simultaneously with the equations of motion for a rotating journal shaft supported by a rigidly mounted bearing sleeve. Given the two bearing parameters and a critical operating eccentricity ratio is determined below which the bearing is unstable and above which the bearing is stable. Whirl frequency at the threshold point is computed to be equal to or slightly less than one-half rotor speed.