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## Section 3, Probability of "Foot-Related Resonance”

Update's courses have alerted many specialists for the first time to what Update now calls "Foot-Related Resonance (FRR)." Rather than resonating a specific part or span such as a length of skid, pipe or plate, the resonant "spring system" has instead been formed by several parts. For example, no one span or part of a gearbox may be resonant and, yet, a combination of such parts may result in resonance in a portion of the total structure. (For details on FRR see "Foot-Related Resonance".)

The usual methods for detecting resonance, such as plotting point-to-point amplitudes to determine curved modal shapes, or bump tests, most often do not reveal foot-related resonance. Instead, it is revealed by loosening and tightening hold-down bolts as described in that section. This is most often done while the machine is running and the resonant part of the structure is resonating. Or, it can be detected with a shut down machine by using a vibration shaker as a source for vibration at the resonant frequency. Bump tests can also work, but it may be difficult to determine if the resulting frequency is the natural frequency of the section bumped, or if it is the natural frequency of a total system combining several connected parts.

As reported, the results in decreased vibration when FRR is eliminated are usually phenomenal. But what percentage of machines are experiencing increased vibration due to foot-related resonance? The surprising answers have been supplied by many specialists who have tested several machines. Some did this on randomly selected running machines, whether their vibrations were higher than usual or not. For such, loosening the correct hold-down bolts lowered vibration levels in about 30 percent of all machines tested. Others reported 40 and 50 percent. Still others reported over 90 percent.

Why such a difference? Those who reported approximately 30 percent were working on a random selection of machines that were not necessarily vibrating excessively. Most of the machines were in the "good" range (and yet, during the test some of them had their vibration decrease appreciably). Those who reported the very high figure of approximately 90 percent, concentrated only on machines that were vibrating badly and had not responded to previous attempts at correction. Also very susceptible to FRR were badly vibrating vertical pumps. Mentally assume that on the average foot-related resonance or partial resonance magnifies vibration on about 40 percent of all machinery -- a number that should tell the serious specialist where there is an opportunity to further decrease vibration.

The following table is only a very rough guide, based not on extensive surveys but on the assimilation of many experiences.

 Estimated Probabilities for Magnification Due to Resonance Part Subject to Resonance Percent Rotors of constant speed machines (that have not had their speeds increased). less than 1 Lengths of pipes, sections of steel bases, plates, pedestals and lighter weight structural members, such as columns and beams. 20 Much heavier and larger cross-section columns, bases, beams and concrete decks. less than 1 Relatively rigid bearing housings and supports (most likely resonate to frequencies higher than running speed). 5 Foot-Related Resonance of portions of total framework or support system. 40

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