Aaron and all -

Maybe more than you wanted to know................

That is an interesting site having a lot of the history of tuned
absorbers.

The bifilar aborber described makes the mass act like a simple one-axis
pendulum. If you look at any high school physics book, the resonant
frequency of a pendulum is inversely proportional to the square root of
gravity (remember the l/g term under the square root sign). On the
other hand the radial acceleration of a rotating mass is proportional
to the square of the rotational speed. Mathematics and good Karma make
the two effects cancel such that the tuned torsional natural frequency
of the so-called "counterweight" (a misnomer) becomes an integral
harmonic of the crankshaft rotating frequency - but only if the radius
of motion of the mass is held within very narrow limits.

For small motions, the effective radius of relative motion of the mass
on the pins is determined by the difference between the pin OD and the
wear bushing ID. That's why both wear limits are critical. Wear will
always make the hole bigger and the pins smaller. The net radius of
relative motion then becomes incorrect such that the resonant frequency
is no longer the exact desired harmonic of the crankshaft rpm. That's
when the back of the crankshaft starts vibrating a lot in torsion and
the propeller also sees a lot of torsional vibration.

The torsional natural frequency of most crankshaft-propeller
combinations is on the gross order of about 220 Hz (almost middle C on
a piano) so the pendulum length has to be very short to reduce the
crankshaft stress effectively. The torsional motions are small, but a
crank is so stiff that a lot of stress can be built up with even a
small amount of motion. The propellor will vibrate in a slight "S"
shape such that there are high stress excursions in the leading and
trailing edges of the prop.

One way to describe the vibration mode would be to imagine you are
sitting on the rotating spinner with X-ray vision. You will get a
reasonably smooth ride but the prop tips will seem to go to and fro
while the back of the crankshaft goes fro and to. (Read that again)

Obviously Piper was able to get by the need for RPM restrictions by
stiffening the crankshaft slightly (i. e. the solid crank version) so
that a damper wasn't needed on those 4 cyl installations. I'm
surprised that small amount of increase in stiffness of the whole
rotating structure could be enough, but at any rate, any field mixing
errors in prop-engine-tachometer combinations could create a bad
situation by not making original certification spec.

Some times more than one frequency is needed to be absorbed, especially
in 6 cyl engines. Hence the slightly different pin and bushing
requirements for say the 5th and a 6 th order damper.

The mass of the damper doesn't seriously enter into the tuning
parameters but it is very important that the pin and bushing diameters
don't become mixed up on assembly. Otherwise tuned absorbers (tuned
masss dampers) are a very powerful way to supress the damaging effects
of torsional vibration.

Tuned absorbers are a hobby of mine. I designed the ones used to
stabilize the John Hancock Tower in Boston and the CitiCorp Center in
NYC against wind induced vibration. My dampers are bigger than
yours..............!