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.

Gordon Arnaut wrote:
snip
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.
snip
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.

I'm going to have to disagree.

Stiffness, and mass are almost irrelevant to torsional vibration (and
any other sort).
Stiffness and mass change the resonant frequency.

I'd approach this from the 'Q' perspective. Q is 'quality factor', which
basically means how good something is at resonating.
A Q of 100 means that it will oscillate 100 times at its resonant
frequency before the oscilation decays to 27% of its original level (not
completely sure of the 27%).

Consider a mass on the end of a stiff wire hanging down from a fixed
point.
Twist and hold it.
There is now energy stored in the wire, in the form of deformation. If
you try to twist it too far, well, any structural element can only take so
much energy stored in it, and if you exceed that, it bends or breaks.

Let the weight go, and it'll spin clockwise, come to rest, then spin
back anticlockwise.
This is energy being traded from potential (stored in the wire) to
kinetic (movement) and back.
Let's call this amount of energy stored 'E'.

If the wire was a springy steel one, then the Q is probably quite high,
say 20.

In order to keep the mass spinning clockwise and anticlockwise, to the
same amount, you need to supply some energy.
Now, the higher the Q is, the less energy. E/Q, or E/20.
If you supply (at just the right times) 1 unit of torsional energy, the
system will build up so that it's storing 20 units in the vibration.

It's just like a swing - if it's got a heavy weight on it, but you push
it a little every time, it'll build up to a decent swing.

The other side to this is that as it's only storing 20 units of energy,
after a time, somewhere else that 1 unit is coming out, probably as heat,
maybe in another part of the system as vibration.

There are several ways to address this.

You can make sure that the resonant frequencies are never hit - which is
horribly hard in many cases, or make sure that the Q is very low, which
means low stored energy.

Adding mass, or stiffness does not alone change Q.

Taking the earlier posted example of the overheating clutch.

Let's say a 50Kw engine was pumping in 10KW of vibrational power, to a long
springy shaft, connected to a clutch.
Say the Q is 10, at the frequency that the engine is running at.

After a few moments, the vibrational power in the shaft is not 10Kw, but
100Kw, the vibrational torque stored in the shaft is 10 times higher than the
input torque, and the shaft is twisting back and forth much more than
expected.
But, the clutch is only rated for 70Kw maximum of torque, and starts to
slip back and forwards.
This damps the vibration in the shaft somewhat, but in the end, it ends
up with most of the 10Kw vibration output heating the clutch.

(I'm mixing power and energy, but I hope it's clear)

Now, you can fix this several ways.

Double the clutch size.
This will fix the immediate problem, but as the energy in the shaft now
is not being damped in the clutch, the vibration there will increase.
This may cause other things to break in the system, maybe the prop,
maybe the PSRU, maybe the pilot

Add a big sticker to the panel saying "Do not run for more than 10
seconds at between 2300 and 2400 RPM"
Maybe OK in some applications.

Make the shaft more or less stiff, or more or less massive.
This will change the resonant frequency, and may avoid the problem at
2340 RPM, but may add a new one at 3200.

Or, you add some sort of damping to the system, reducing the Q.

I need to go to bed, will add more tomorrow.

("Ian Stirling" wrote)
[snip]
Or, you add some sort of damping to the system, reducing the Q.

I need to go to bed, will add more tomorrow.


....and we'll read it.

Thanks for posting. And thanks to Gordon, too.


Montblack

Gordon Arnaut wrote:
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.

snipped out the juicy part

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.




Fabulous piece of work, Gordon.

Very well written, understandable, and agrees with what I think I understand of
the subject.

There is a difference between being able to understand the subject matter and
being able to explain it well.

I think you've done both here.

Don't know what more to add to that.


Richard Lamb

"cavelamb" wrote

Very well written, understandable, and agrees with what I think I
understand of
the subject.


There are parts, here and there that miss the mark, but mostly correct, and
well written.

Hopefully it will keep an unknowing experimenter from jumping in way too
deep, then finding out, far too late. It is a very tough subject, once you
actually start on the nuts and bolts part...
--
Jim in NC

"Gordon Arnaut" wrote

Cog belts are noisy, tend to fail more quickly and are expensive -- and
they are only needed in applications where synchronous operation is
required, such as in driving camshafts.

Today's multi-v belts -- the kind used to drive engine accessories on
newer cars -- are highly efficient and can handle huge amounts of power,
up to 1000 hp.

That is the first bad advice you have given.

It is interesting to note that the cog belt is the drive of choice, for
manufacturers of V-6 and V-8 redrives manufactured today. Perhaps they know
something that you don't?

Belts are lasting 200 hours with no sign of wear, BTW.
--
Jim in NC

Chain drives have the same effect.


Belt and chain drives do impose side loads on the front crankshaft journal,
however, so that is a negative point.


Another issue is packaging

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

Well written explanation but this is incorrect. The sideload is imposed
on the rearmain journal of the crank, not the front one. Most redrives
that use the cog belt also incorporate an idler bearing outboard of the
lower sprocket, that prevents the sideload forces on the crank. Also I
think a multivee belt will not transfer 1000 hp, I don't think it would
evem work on my 330 hp+ auto engine powered plane. I will stick with my
cog belt, thank you.

Ben
www.haaspowerair.com

Chain drives have the same effect.


Belt and chain drives do impose side loads on the front crankshaft journal,
however, so that is a negative point.


Another issue is packaging

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

Well written explanation but this is incorrect. The sideload is imposed
on the rearmain journal of the crank, not the front one. Most redrives
that use the cog belt also incorporate an idler bearing outboard of the
lower sprocket, that prevents the sideload forces on the crank. Also I
think a multivee belt will not transfer 1000 hp, I don't think it would
evem work on my 330 hp+ auto engine powered plane. I will stick with my
cog belt, thank you.

Ben
www.haaspowerair.com

Gordon Arnaut wrote:
Another contributor of excitation is imbalance in a rotating or
reciprocating mass.

True, but it has limited power compared to gas pressure
oscillation. I was trying to keep things simple.

Yet another source of excitation in airplanes is the spring effect of
the prop

Naaaa. Propellers in disturbed flow can excite the system, but
usually the concern is the opposite. Might be a few rare causes. For
example, I've seen (with telemetry) a variation in torsional vibration
due to a propeller-powerplant whirl mode.

a crankshaft has its own natural resonant frequency and will vibrate
if it is disturbed with enough force.

Actually a crank has N-1 natural frequencies, where N equals # of
inertias. That would be four frequencies for a typical 4 cyl with 90
degree throws (4 crankthrows plus flywheel, 5 minus 1). However, to be
fair, when designing a PSRU you can model the crank and flywheel
assembly as a single mass moment of inertia, IF the crank is short and
stiff. The inaccuracy in F1 prediction will be small, like 200-300
RPM.

A flywheel is a simple example of a damping device. It uses
centrifugal force to counteract and overcome the twisting.....

A flywheel is an inertia. A damper is a device that removes energy
from the system, usually as heat. Think slipping clutch, slipping
v-belt, or viscous ring damper. Designed a viscous disk damper and ran
it parallel with a soft element in a drive a few projects back. It
shed a lot of heat, and telemetry said it damped resonant amplitudes
very well. The successful Raven drive for the 3 and 4 cyl Suzukis uses
a dry frictional damper.

Ahhhh, I'll let you correct the part about centrifugal force g

This shows that mass is important, unlike some erroneous comments
that mass doesn't matter.

Who said anything about mass? For the record, please note that the
previous comment was "Shaft weight is not a factor", the context being
ship propulsion. Shoot, I'm all for careful use of terms. In the
context of torsional vibration, what IS important is "mass moment of
inertia". And that ain't the same as mass or weight.

Ok, you argue that torsional problems can be eliminated through the
use of flywheel mass and stiff shafting. I argue that your approach
has severe drawbacks when applied to the subject at hand, a long shaft
aircraft system.

I agree that a large-inertia flywheel (which is not necessarily a
large-mass flywheel) always reduces vibratory amplitude. It may not
be reasonable to incorporate a huge flywheel inertia in an airplane
because of effect on (1) handling (remember the Sopwith Camel), as well
as (2) aircraft empty weight. You must use a moderate flywheel, a
compromise, not the infinite inertia you describe.

As for stiffness in the shafting that connects the inertias, what
magic did you have in mind? All practical shaft materials exhibit a
stress-strain relationship. I know of only one practical PSRU concept
that meets your goal of near infinite stiffness; it has no shafts at
all other than the crankshaft. Hardly the long shaft system under
consideration. With a shaft several feet long, some degree of twist is
physical reality.

Given that infinite stiffness is impossible in the long shaft
system, I'll tell you what you'll really get. A stiff shaft will raise
the system F1 so that it intersects the gas pressure oscillation order
somewhere up in the operating range close to peak torque. The system
will resonate into junk. The classic solution then tried by the
uninformed is to make it "stronger" (the result being stiffer), which
makes the problem worse. Near idle or below idle is where you want the
intersection of F1 and gas pressure frequency, because gas pressure
oscillation isn't very powerful at idle. You do that with a soft shaft
or rubber element, and note that it doesn't take a huge inertia to
smooth a small near-idle-speed oscillation. By tailoring frequencies,
we can get a practical, lightweight system.

Nobody can teach this subject in RAH posts. Hell, "Practical
Solution" is several volumes. What we can do is (1) direct folks to
quality reference material, and (2) quit telling them it is impossible.
I think I'll puke if I see one more guy reference the Hessenaur
article and declare "torsional vibration even beat Rutan". If somebody
had handed Burt the right books or introduced him to J.P. Den Hartog,
you can bet you wouldn't be reading that crap.

Dan

Naaaa. Propellers in disturbed flow can excite the system, but
usually the concern is the opposite. Might be a few rare causes. For
example, I've seen (with telemetry) a variation in torsional vibration
due to a propeller-powerplant whirl mode.


Hi Dan,
Can you say a little more about the example of the whirl mode you saw?

Kent Felkins
Tulsa


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