I'm going to write out that equation for resonant frequency because the
symbols did not translate over properly.

It should read:

Omega sub-n (resonant frequency) = the square root of K (elasticity) divided
by m (mass)

If you plug any numbers into this equation you see that resonant frequency
goes down as stiffness goes up (elasticity goes down = stiffness going up).

We also see the same result if we increase mass: resonant frequency again
goes down.

This is important because we want to design an engine-gearbox-prop system
that resonates at an rpm below actual operation, if possible.

Regards,

Gordon.



"Gordon Arnaut" wrote in message
...
Bashir,

Actually, I spoke too quickly when I conceded a mistake.

Tautness and stiffness are two different things. A taut string will
vibrate at a higher frequency than a loose string, but we have not changed
its inherent stiffness or elasticity (e).

If you increase the stiffness (decrease the elasticity) of an object, you
will decrease its resonant frequency, as I first stated.

The resonant frequency of a system is symbolized by "w n"

and pronounced "Omega-sub-n". An object's mass and elasticity determines
its resonant frequency, and is expressed mathematically as:





wn = ?(k/m)





K is the value for elasticity, while m is the value for mass. So we see
that lower elasticity (greater stiffness) results in a lower frequency of
resonation.

So making a crankshaft stiffer does decrease the rpm at which it will
resonate. It also increases the value of restraining force acting against
excitaiton. So the benefits are cumulative.

We can see a real-world example of this in V-8 engines which would not
last very long without a harmonic damper, even though they have much
smoother torque pulses than a 4-cylinder. The reason is that the
crankshaft has to be much longer and thereby less stiff -- or more
elastic.

On most four-cylinder engines, dampers are not needed because the short,
stout crank actually resonates at a frequency below the oeprating range.
Hence resonance will never be encountered.

It's useful at this point to back up and define what resonant frequency of
an object -- or system -- really means. Stated most simply it is the
frequency at the object or system will vibrate if it is excited by a
single pulse.

The actual torsional resonance of an engine can be calculated if you know
the torsional rate of the crankshaft (which is its spring value) and its
mass moment of inertia, which is a function of crank stroke and weight,
number of journals, dimensions of the flywheel, torsional absorber,
accessories.

So now we know a little about resonance and how it affects a crankshaft.
But what happens when we attach a propeller or gearbox-propeller
combination to that engine?

Well, now we are dealing with not just an object but a system. And this
system has its own torsional resonance frequency, which is different from
that of the single object itself, like the crankshaft.

A key concept here is tranmissibility, which is the ratio between the
amplitude of the excitation torque, and the amplitude of the output
torque. In simple terms, this means that the gearbox and propeller can be
subjected to vibratory forces many times higher than the torque peaks
produced by the engine.

Here is where damping comes in. But even with damping there will be some
amplification of vibratory forces transmitted from the gearbox to the
gearbox and prop.

There is some good reading at this website, with specific info on how
torsional resonance is dealt with in designing aircraft PSRU systems:
http://www.epi-eng.com/BAS-VibBasics.htm

Regards,

Gordon.





"Bashir" wrote in message
oups.com...
He can be taught!! Who would have thought it!?