Gas foil bearing (GFB) technology has reached great maturity as per engineered design and construction and its system integration into rotating machinery. Empirical research has gone beyond showing a few instances of acceptable mechanical performance, to demonstrate GFB multiple-cycle repeatable performance in spite of persistent large amplitude sub synchronous whirl motions. A GFB is a forgiving mechanical element whose engineered resilient underspring structure contains and ameliorates large rotor excursions. Analyses, however, fail to distinguish the hardening stiffness from the FB underspring structure, which under conditions of large force excitations due to imbalance, produces a complex rotordynamic behavior, rich in sub harmonic motions when operating at super critical speeds. This paper extends an earlier analysis of a rigid rotor-GFB system that dispenses with the gas film component to predict the effect of shaft rotation acceleration/deceleration on rotor amplitudes of motion and whirl frequency content. For operation above the system critical speed and as the rotor accelerates, large amplitude whirl motions appear with a main subsynchronous frequency tracking rotor speed, first at 50% speed and later bifurcating into at 33% whirl frequency. Rotor imbalance awakens and exacerbates the system nonlinear response. Slow rotor accelerations result in responses with more abundant subsynchronous whirl patterns, increased amplitudes of whirl, and accompanied by a pronounced mechanical hysteresis when the rotor decelerates. Large rotor imbalances produce both jump phenomenon and a stronger hysteresis during slow acceleration and deceleration cases. Material damping (dry friction) in the FB aids to reduce and delay the nonlinear response, eventually eliminating the multiple frequency behavior. The results bring to attention rotordynamic issues during start up and shut down events that can result from an inadequate FB technology or an unacceptable rotor imbalance grade condition.

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