Discussion: “Operation of Foil Bearings Beyond the Bending Critical Mode” [ASME J. Tribol., 122, No. 1, pp. 192–198 (2000)]¹

The author associates the (integer multiple of) harmonics shown in Fig. 19 with rigid body frequencies. Would the author elaborate on this, and perhaps provide a theoretical foundation that supports such an association? It is our experience that integer multiple of harmonics may be present at any rotational frequency (unrelated to rigid body modes/frequencies) because of misalignment and deflection that cause intermittent rub between rotor and stator (see also Vance, 1 p. 356). In the author’s experiment the speed is supercritical and the harmonics shown are integer fractions of that speed. Rub will also cause the same phenomenon in subcritical speeds only that the harmonics will occur at integer multiples of the rotational speed. This has been observed by Lee and Green 2 in experiments of a flexibly mounted rotor face seal (the association with journal bearings and particularly trust bearings is, of course, trivial). The analysis by Lee and Green 2 reveals that the integer multiples result from a Fourier series expansion of signals that are contaminated with rubbing characteristics. That analysis also gives an explanation for the varying harmonics magnitudes (where some may not even show up). In fact there is a clear envelope in Figure 19 of the harmonic magnitudes which may disclose the arc extent of rub. Not only that this rubbing phenomenon can be monitored (Zou and Green 3) it can also be eliminated by either passive (Lee and Green 2) or active control (Zou et al. 4). It is worth of note that the power generated by such rubs is not high. Rough estimates of some of the parameters, and assuming a generous coefficient of friction of 0.2, reveals that the power generated in such a case would be fairly low (perhaps 50 Watts), which is insufficient to cause a “major system melt-down.” But rub over time has a detrimental effect on the bearing surfaces that would ultimately lead to their failure.