Dr. Green has inquired as to whether some theoretical explanation for the particular experimental observation that I have reported in my paper is available. We have for some time been investigating the observed phenomena in foil bearing systems both theoretically and experimentally. The program is fundamental in nature and is well underway. Once conclusive evidence and correlation is complete to the author’s satisfaction, it is our intention to publish the results. Incidentally, this peculiar phenomenon is most relevant to foil bearing systems. Investigators, skilled in the field of foil bearing technology, have been reporting similar situations for more than two decades; unfortunately such information has not been published, but privy to those intimately involved in foil bearing development.

Dr. Green’s discussion of rub phenomena and harmonic excitation is consistent with experience related to more conventional systems such as ball bearing supported rotors. However, I believe that this reviewer has misinterpreted the brief discussion referring to Fig. 19. First, it should be noted that we are talking about fractional subharmonic vibrations which lock onto the rigid body natural frequencies (a subharmonic resonance). The discussion states that in rub phenomena the harmonics will occur at integer multiples of the rotational speed. In contrast, the author has stated that the phenomena observed in gas foil bearing systems is strictly related to conditions when the operating speed is an odd multiple of a rigid body critical speed. If the reviewer would review Fig. 18 it can be seen that the subharmonic vibrations do not track or follow the operating speed as would be expected if this were a rub induced phenomena. To carry the discussion further and respond to the reviewer’s comments regarding the arc extent of the rub and potential heat generation in the bearing, the author totally disagrees with the reviewer’s hypothesis. The occurrence of even intermittent high speed rubs in a foil bearing can lead to major bearing performance degradation, if not outright bearing failure. Addressing first the potential for rub, it should be noted that the largest peak-to-peak amplitude of vibration occurred at approximately 570 Hz (34,200 rpm) as the rotor decelerated through the rotor bending critical speed. If a rub were to occur it would be expected during critical speed transition, not when overall vibrations were experienced at the operating speed of 747 Hz (44,820 rpm). Regardless of the vibration condition experienced, during post test examination of the bearings, no evidence of a high speed rub was detected.

The author next takes exception to the reviewer’s heat generation calculations and conclusion that “no major-system melt down” would be expected. The rough estimate of power generation does not include the dynamic force contribution which is often significantly higher than the static component. However, even assuming the reviewer’s value of 100 watts heat generation, and taking a typical high speed rub contact area as examined by the author in numerous other foil bearing systems, the expected power density for such a rub would be on the order of 1 Kilowatt/sq-cm. Clearly this localized heating would cause great distress to the very thin foil material and should be readily evident in post test examinations. Again no evidence of high speed rubs was detected which would lend credence to the reviewer’s contentions that the observed phenomena is rub induced.

In summary, the subsynchronous integer harmonics of rigid body critical speeds have been experimentally observed to occur when the rotor spin speed is seven times the rigid body critical speed. This author believes that it is related to nonlinear bearing system. No evidence of an intermittent rub has been detected as the reviewer contends. It is the author’s intention to bring to light this experimentally observed phenomena so that our understanding of foil bearing performance may be enhanced and to guide direction for future investigations.

Heshmat, Hooshang, 2000, “Operation of Foil Bearings Beyond the Bending Critical Mode,” ASME JOURNAL OF TRIBOLOGY, Vol. 122, pp. 192–198.