Bill Freeman wrote:

Paul,

The governing equation for vibration response frequency is:

         f = (K/M)^0.5

Where f = natural frequency
          K = system spring constant
          M = system mass

The stiffer springs (assuming they don't stack up and go solid)
will increase the natural frequency.  Most of the time this is
a good thing.  The 3mm wide tip seals will be about 50% heavier
than a 2 mm seal (if same material) and this will lower the
natural freq, generally a bad thing.  If the 3mm is a less dense
material, the freq could be unchanged or even increased.

Increasing the seal mass by 1.5X will lower the nat freq to 0.816 of
what it was before.  Assuming that three springs are 1.5X the stiffness
(I don't know enough about the config to know if this is true)
of the original 2 (is this right?) it will increase the nat freq to 1.22
times what it was before.

In many applications, a higher nat freq is either neutral or is good
since it moves the response freq above the (often fixed)
driving freq.  In some cases, it may move the response freq up
to coincide with a drive freq which was originally above the response
freq.  This may not apply to chatter since I'm not sure what
the driving freq is, or how it occurs.  Some driving freqs are clear
like once per rev for imbalance.

Designing for vibration response is non-trivial and often requires
substantial field testing with the right equipment to measure the
system driving freqs and do a fast fourier transform to extract all
the individual component freqs.  Then the design must be tested
to verify it has no modes (nat freqs) that are very close or on the
drive freq.  If you hit one, the whole thing may soon come apart
regardless of how strong it is in static calcs.  OTOH, I have seen
two of ten "identical" units fail from a torsional vibration problem,
and the other 8 ran for another year, 24/7.   Go figure.  Probably
tolerances.  Mostly science, but a tiny bit of voodoo.  Thats why
they hire test pilots.  :-)  That's also why the pay test pilots a lot.

Bill

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