Torsional Vibration and PSRU Design

I hope ADK, who posted a question a few days ago on an interesting design
problem involving reduction gearing and a driveshaft got some insight from
the various postings.

The subject of torsional vibration quickly cam up and there was a lot of
stuff mentioned, but not really a simple and understandable explanation of
the forces at work.

Torsional vibration is not that hard to understand for the non-engineer, but
one must think of it in terms of excitation forces on one side of the
equation, and restraining forces on the other.

In a drivetrain system excitation forces come largely, but not solely, from
combustion firing events. Another contributor of excitation is imbalance in
a rotating or reciprocating mass. (Incidentally, it is impossible to
perfectly balance a reciprocating engine.)

Yet another source of excitation in airplanes is the spring effect of the
prop, where the blade tips whipsaw back and forth as they undergo
acceleration and deceleration due to the torque spikes of cylinder firing.

These various excitation forces work to induce vibration in the drivetrain
system and its various pieces.

Restraining forces counteract the tendency toward vibration. They consist of
three factors: stiffness, mass and dampening.

So what happens when torsional vibration starts to take place? First of all,
torsional vibration is a twisting vibration where the amplitude is measured
in degrees of rotation. It should not be confused with linear vibration,
which is the up and down and side to side shaking of an engine.

Torsional vibration in engines happens on a very small scale in terms of
overall movement. If a crankshaft were subjected to a twisting movement of
even a degree or two, it would not last more than a few minutes.

A large-diameter springy mass such a propeller will obviously be able to
exhibit considerably more twist at its tip, but there is still a limit to
how much it can twist before it will break.

Torsional vibration is simply the result of the various excitation forces
causing the drivetrain, or its constituent pieces to start twisting back and
forth.

The issue of frequency was brought up in the previous dicsussion, but there
were some misconceptions expressed.

As mentioned, every object in the engine -- or every other object for that
matter -- has its own natural "resonant" frequency. That is the frequency at
which a particular object will vibrate if it is acted upon by a single
excitation of sufficient force to displace it from its resting state.

Think of a diving board. If you jump on the diving board with enough force
to set it in motion, it will continue to vibrate at its natural resonant
frequency -- even if you depart the board after a single jump.

Just like the diving board, a crankshaft has its own natural resonant
frequency and will vibrate if it is disturbed with enough force. Where the
problem gets tricky is if that disturbing force is timed to exactly coincide
with the vibrational frequency. With each additional "push" coinciding
exactly with the oscillations, the amplitude starts to increase.

What that means in a twisting vibration is that the shaft will twist more
and more until it breaks.

So does this mean that frequency is somehow supremely important? That you
must make sure that your excitation frequency and your resonant frequency
must never coincide?

Quite simply, no. It is quite possible to have an engine with a resonant
frequency at a certain rpm and it will run all day at that rpm with no
problem.

How is that possible? This is where we go back to the basic equation of
excitation versus restraining forces.

If your excitation force is not strong enough to actually displace the
object, it cannot possibly set it vibrating. Think of a massive diving board
made for giants and a tiny person trying to jump on it. That litte
leprechaun is not going to set the board vibrating no matter how hard he
jumps on it. There are no worries about resonance or vibrations of any kind.

This is due to the restraining force of mass, which we mentioned at the
beginning. This shows that mass is important, unlike some erroneous comments
that mass doesn't matter. It should be intuitive that the mass of an object
and the force of the excitation must be proportional if there is going to be
any vibration created.

Stiffness is another restraining force. It acts similarly to mass in that it
makes it hard to disturb it from its natural state and therefore requires
that any excitation force will have to be much more powerful to produce any
kind of vibration. Think of a very stiff and rigid diving board. A small
child may not be able to deflect it at all.

And what happens if the excitation force is strong enough to overcome the
restrining forces of mass and stiffness? That's where damping comes in. If
the excitation force is strong enough to actually produce vibrations, you
can stop those vibrations if you apply enough dampening force.

Think again of the diving board. If you jump up and down on it to set it
vibrating, what happens if you then change your mind about jumping off and
use your knees as shock abosrbers to abort the jump? The board stops
vibrating.

It's the same with an engine. A flywheel is a simple example of a damping
device. It uses centrifugal force to counteract and overcome the twisting
acceleration imparted by the cylinder firing. The twisting force is not
strong enough to overcome the centrifugal force of the spinning flywheel so
vibrations can't get started.

It doesn't matter a whit that the frequency of of the engine at a particular
rpm may coincide exaclty with its resonant frequency. If the damping is
sufficient, frequency is meaningless.

Likewise for mass and stiffness. It doesn't matter if the frequency of the
excitations exactly coincides with the natural resonant frequency of the
engine if the engine is stiff and massive enough not to be disturbed.

Almost all four-cylinder engines operate perfectly well without any kind of
torsional damping device because of the simple fact that their short
crankshafts are quite stiff.

This despite the fact that they only have four cylinders so the torque
spikes are quite severe.

A six cylinder engine is actually more problematic because, while it has
smoother torque pulses, also has a longer and less stiff crankshaft.

A V-8 is even more of the same, but here the crankshaft is flexible enough
that it's natural frequency is now quite low and possibly even below idle
rpm.

So for the sake of ADK's question, he seems to have chosen the most
problematic configuration.

Also worth noting here is that when we talk about torsional vibration, we
are must examine the entire drivetrain system as a whole -- not just its
bits and pieces. As soon as you bolt anything to the engine, you have now
changed the vibrational characteristics of that engine, along with its
natural resonant frequencies. (Yes there can be more than one).

In the simplest aircraft propulsion system you have just the engine directly
driving a prop. That drivetrain will now have different vibration and
resonance issues than jsut the engine alone. And here is where it gets hard,
because it is almost impossible to predict what the vibrational
characteristics will be. The only way is to instrument and measure.

When you add a reduction drive, whether belt or gear, you have added an
additional component and have again changed the vibrational characteristics.
And then to add a driveshaft onto all that, well, you can certainly see that
this is adding layer upon layer of vibrational complexity.

So the simple conclusion is that this is a very problematic configuration.
That's not to say that it will be impossible to make work reliably, but it
is a considerable engineering challenge.

Some have made this kind of arrangement work. Taylor and the Mini-imp have
been mentioned and that's a good example. I don't know if this link was
already mentioned, but here it is:
http://www.mini-imp.com/index.htm

Dornier also created a very interesting axial thrust twin near the end of
WWII, the 335, which used a drivehsaft to turn the rear prop at the end of
the empennage. A marvelous design that performed exceptionally.
Incidentally, when Cessna came out with their axial-thrust Skymasters, they
gave it the 336 designation, followed by the 337, in an obvious nod to the
Dornier ancestry.

So these examples show that it can be done, but you will have to put your
thinking cap on and study up on those engineering texts.

Regards,

Gordon Arnaut.