# Torsional Vibration and Resonance - Basic Theory and Issues

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#### BBerson

##### Well-Known Member
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Is the odd firing 90° V-twin generally less problematic than a half VW opposed?
With compression reversals and all it seems too much to model (to my simple mind).
I always think of a father pushing his child on a swing with the exact forcing functions. If someone comes along and pushed at odd times almost certainly that would damp rather than force the swing.

#### wsimpso1

##### Super Moderator
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I can't compete with this on a phone with a 3.8" screen. I give up.
Uh, this is not supposed to be a competition...

#### wsimpso1

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The resultant will have zero 24 and 40Hz components. A cycle is a complete cycle. All the two rev cycles are identical. Therefore, the primary harmonic is at two revs, or half the frequency of rotation. Because you are adding two phased but identical waves full of harmonics, you will also have a strong component at the frequency of rotation. Depending on the phase and waveforms, this can be stronger or weaker than the primary harmonic.
Well, when you take apart the entire form with FFT, you will get 1x and 1/2x components, but if you let the software know it can take things apart into 1/4x order, it will find a couple really strong components because that is where the firing pulses are.

I am not so concerned with exactly what the pulse could be described as, I am concerned with designing a suitably low resonant frequency, which usually means a low enough spring rate and enough engine side inertia, to prevent amplification and destruction of the system.

Look at the last two spreadsheets in the attached file. The next to last spreadsheet is for an even fire twin with a sinusoid overlaid on it. If our engine - spring - prop system had the same frequency as the firing, as illustrated, it would resonate, amplitudes would quickly grow, and something is likely to break. This is not arguable... And if the engine was making firing pulses within 10-15% of the resonant mode frequency, it would still amplify, maybe enough to eventually tear the thing up in short order too. Get the resonant mode frequency 25% or more lower than firing, and it is isolating enough that it is likely to be safe...

The last spreadsheet is the same sinusoid overlaid on our 450-270 firing order twin. Look at it, that one will still amplify, just not as fast, because it does not perfectly line up. You might extend your time to failure to minutes instead of seconds. So, what do you do to keep it from amplifying? Is taking it down 25% from a nice match going to be enough? Using our 1800 rpm example with the shaft running at 30 Hz, that would require a spring that takes system resonance to 22.5 Hz. Hmm, every two turns of the engine we get a good solid pair of inputs at the spacing of 24 Hz. That is only a 6.66% mis-match and I am here to tell you, it will amplify. Better make sure you are 25% below the 24 Hz line. That is about 18 Hz. Now primary firing will not do any big amplifying. Going from 22.5 Hz to 18 Hz requires a reduction in (spring rate/inertia) of 36%. Maybe doable, maybe really hard to fit in.

If you really would prefer an engine that will run on one after a cylinder swallows a valve or holes a piston, you might need to get 25% below the 15 Hz line that this engine acting as a single will give you at 1800 rpm. Coincidentally, pictsidhe is arguing for being secure against 15 Hz in this example. 25% below 15 Hz is 11.25 Hz, and at that I know the twin flying as a single will not self destruct if you let the revs sag to 1800 rpm. Getting your resonant mode from 18 Hz to 11.5 Hz requires a further 61% reduction in (spring rate/inertia). I think that I would install a ballistic parachute first, as it can cover so many other failure modes besides sucking a valve. Then if the engine is barfing oil and running so rough you would swear it is going to depart the airplane, you can just yank the mixture knob, and if you do not like the looks of landing sites within your glide range, yank the parachute handle too.

Every time we ask for lower frequencies, we need either lower spring rates (and more travel on said springy devices plus some weight) or more engine side inertia (and more weight) or some of both. At some point it just becomes prohibitive, so be ready to draw the line sometime in this progression.

Bill

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#### wsimpso1

##### Super Moderator
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Is the odd firing 90° V-twin generally less problematic than a half VW opposed?
With compression reversals and all it seems too much to model (to my simple mind).
I always think of a father pushing his child on a swing with the exact forcing functions. If someone comes along and pushed at odd times almost certainly that would damp rather than force the swing.
Is the half VW crank two throws? One piston and rod on each like a BMW boxer twin? As i understand it, the half VW with direct drive works fine as a stiff system. It is only when you start putting gears or splines or other items with lash in (PSRU stuff) that you ought to be considering soft systems. If it is an even fire twin and the spreadsheets in the file I have stuck on here cover the soft system. Odd fire twin requires lower 1st mode resonance frequency than the even fire engine, but is otherwise similar.

Billski

#### Hot Wings

##### Grumpy Cynic
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Is the half VW crank two throws?
Billski
Yes, and very little engine side inertia. No flywheel, just a couple of counterweights.

#### BBerson

##### Well-Known Member
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Is the half VW crank two throws? One piston and rod on each like a BMW boxer twin? As i understand it, the half VW with direct drive works fine as a stiff system. It is only when you start putting gears or splines or other items with lash in (PSRU stuff) that you ought to be considering soft systems. If it is an even fire twin and the spreadsheets in the file I have stuck on here cover the soft system. Odd fire twin requires lower 1st mode resonance frequency than the even fire engine, but is otherwise similar.

Billski
Yes, two throws. I know several BMW boxer twins with PSRU are flying on trikes. Apparently none are successful with the half VW.

#### Vigilant1

##### Well-Known Member
Yes, two throws. I know several BMW boxer twins with PSRU are flying on trikes. Apparently none are successful with the half VW.
I don't know of any successful 1/2 VW PSRUs either, but I haven't heard about failures. Do we know the failure mode of previous attempts? Were they tearing up PSRUs, or were they breaking cranks?

#### BBerson

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Not sure, but I think shredding belts. Mostly repeated second hand comments on the 1/2VW forum.

#### wsimpso1

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Half VW with little engine side inertia and direct drive sounds like an already developed stiff system, like most conventional airplane engines. Highest firing frequency = max operational rpm*n/2/60 = rpmmax/60. In a flat twin, that is 1x rev. You will also have a significant 2 per rev. Sounds like the 1st resonant mode has to be at least 1/2 octave above max firing freq, and depending upon how much interaction you get from the 2 per rev, 1-1/4 octave above max firing freq.

Being as this type of conversion in direct drive is usually successful, it sounds like the modest prop size and crank/extension are plenty to drive 1st mode way high. If someone put speed sensors on engine and prop, I would sure like to see the FFT results from the data.

Half VW belt PSRU have a tendency to shread the belts? - that sure sounds like resonance within operating range. Is there any info on configuration? Type of belts (v, multi-v, cog, etc), overhung pulleys vs from and rear bearings, etc, and if they ran an idler/tensioner or not? Did they add a flywheel back in on the engine side? Just trying to gather some data if folks have it...

Billski

#### rv7charlie

##### Well-Known Member
I have heard that story... I doubt that the misfire tore things up at idle, as a misfiring rotor will look similar to one actually making idle level power. My bet is the pilot felt the and heard the misfire and pushed in the throttle in an attempt at clearing the misfire. That brought the power up on one rotor while the RPM stayed down (turning the prop on less than one half the nominal torque) which then gave big pulses ate one-half the nominal frequency, resonance, and BANG.

Neat thing is we have a model we can play with on that topic. When I have some time, I will mess with the model and simulate one cylinder misfire.

Billski
I knew the guy who had that experience. Unfortunately, he's no longer around to ask (cancer), but regardless of whether he advanced the throttle or not (likely he did), it sounds like something we should factor in. IIRC, the failure happened pretty quickly; almost instantly. After all, what's the 1st thing most of us do when an engine 'almost starts'?

After his transmission failure (he flew it safely for a couple of hundred hours prior to his startup incident), he replaced the trans with a RWS drive, and flew it in that configuration for quite a while until health issues did him in.

Charlie

#### wsimpso1

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I knew the guy who had that experience. Unfortunately, he's no longer around to ask (cancer), but regardless of whether he advanced the throttle or not (likely he did), it sounds like something we should factor in. IIRC, the failure happened pretty quickly; almost instantly. After all, what's the 1st thing most of us do when an engine 'almost starts'?

After his transmission failure (he flew it safely for a couple of hundred hours prior to his startup incident), he replaced the trans with a RWS drive, and flew it in that configuration for quite a while until health issues did him in.

Charlie
I did talk about this in post 149. While we can drive the resonance to 1-1/4 to 1-1/2 octaves below min normal firing, a twin on one cylinder is not going to idle at its usual speed - one one cylinder it is making maybe 35% as much torque as normal, and thus can only turn the prop about 60% as fast on that base idle setting. So it will be much closer to even a conservatively set 1st resonance.

The more I talk about failure mode management in twins with soft systems and PSRU's, the less I like them. Maybe if I get a bunch of free time, I will do some calcs to estimate belt stiffness...

Billski

#### Vigilant1

##### Well-Known Member
The more I talk about failure mode management in twins with soft systems and PSRU's, the less I like them. Maybe if I get a bunch of free time, I will do some calcs to estimate belt stiffness...
The more I read about it, the more I come to believe that there's no substitute for a lot of testing on a test rig with provisions for generating appropriste angular rotation speeds, across various RPM ranges, for many, many hours. A fleet of airboats logging a lot of hours under the right conditions would be a good adjunct testing environment similar to most types of flying.

#### rv7charlie

##### Well-Known Member
Bill,

From my layman's perspective, I agree. While I'm installing a Renesis (13B 2-rotor) on my RV-7, I consider the fact that there are only two power-producing elements (pistons, rotors, etc) one of the few downsides to the engine. There may be lessons to be learned from the old 7 & 9 cylinder radials, that can lose a cylinder and not only continue to run, but be returned to service by simply replacing the cylinder.

Charlie

#### BBerson

##### Well-Known Member
HBA Supporter
No good substitute for multiple cylinders. Just like no good substitute for displacement.
The twin usually won't run at idle speed, just quits.

##### Well-Known Member
Our current solution for reducing TV on an engine dyno is a custom soft coupling.
It's b__y expensive, and we had to specify capacity, torque, firing order, inertia of engine and load, etc., etc.

I know it's too heavy for aircraft use, but we're going to do some comparison tests using automotive dual-mass flywheels on our next engine dyno. Anything made in the millions is a fraction of the cost of a custom solution.

The test mule will probably be a 2.2l 4 cylinder, and I'll update when it happens (not for a couple of months at least).

Sorry if this is too far off topic.

#### pictsidhe

##### Well-Known Member
I did talk about this in post 149. While we can drive the resonance to 1-1/4 to 1-1/2 octaves below min normal firing, a twin on one cylinder is not going to idle at its usual speed - one one cylinder it is making maybe 35% as much torque as normal, and thus can only turn the prop about 60% as fast on that base idle setting. So it will be much closer to even a conservatively set 1st resonance.

The more I talk about failure mode management in twins with soft systems and PSRU's, the less I like them. Maybe if I get a bunch of free time, I will do some calcs to estimate belt stiffness...

Billski
Losing a cylinder is my biggest headache in my redrive design dabblings. Ill entertain something that would last an hour in the air by slipping a bit. If it misfires on the ground, don't fly! I'd like it to not instantly kill the belt, though. I'd like to use ribbed belts, they are cheap enough for precautionary changes if run on one cylinder more than a few seconds

#### pictsidhe

##### Well-Known Member
If you lose one cylinder on any engine, you get a strong harmonic at half rotation speed. It's begative torque at the firing frequency. Even a 9 cylinder radial will have that, though only 1/9 of the engine torque. But you still have to keep the redrive natural frequency away from that.

#### wsimpso1

##### Super Moderator
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If you lose one cylinder on any engine, you get a strong harmonic at half rotation speed. It's begative torque at the firing frequency. Even a 9 cylinder radial will have that, though only 1/9 of the engine torque. But you still have to keep the redrive natural frequency away from that.
Well, a lot depends upon how you lost the cylinder:

When either fuel or spark is interrupted the cylinder still has the same compression stroke and the firing stroke is a mirror image of the compression stroke. That does show up as some 1/2 order content but is not awful. Any tuning effects in the intake are roughly maintained, while exhaust tuning is disturbed, but not completely trashed. The torque drops to approximately the fraction of cylinders still running... A twin with one cylinder not firing will thus drop immediately to about 50% torque, which will only drive the prop at 70% of whatever rpm the the throttle setting would have it at with both running - you immediately go from having 100% power available down to 70%*50% = 35%... You might be able to hold altitude by opening the throttle and slowing down, and I suspect that the PSRU will be fine with the throttle open... Let it slow down, and you may be looking at a dead stick for the short balance of the flight.

Now a misfire at idle setting or modest throttle seems to have the most potential for resonance and immediate damage. Shoving the resonant frequency down is your main protection. That or go to more cylinders...

Hole a piston or drop a valve, and now you have all sorts of evil visited upon power production and vibration. The compression stroke becomes much lower negative torque and the firing stroke is virtually zero, giving much bigger half order content. All of the breathing can be messed up with air either going the wrong way in one of the ports or going into the crankcase. Power? Ugh. If you can keep a twin running on one, it is most likely a glide extender. Otherwise, it is dead stick time, which is what it also may be if you let the firing freq on one drift down into resonance...

Billski

#### Patrickh99

##### Member
Just saw another thread which might have a (future) solution to the TV issues for low-power low-speed applications: https://www.homebuiltairplanes.com/forums/threads/magnetic-gear-box.32055/

http://www.magnomatics.com/
They have an operational unit in a drill bore-hole running for two years, which implies good durability.

There is an applicability chart that seems to indicate 15HP and 1500RPM are their current limits, so they have a ways to go before anyone contemplates using this with a 200HP 2700RPM engine conversion on an aircraft.

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