# Torsional Vibration and Resonance - Basic Theory and Issues

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#### Vigilant1

##### Well-Known Member
Here's an odd bit: Some V-twins are set up to fire one cylinder immediately after another. So, if the Vee angle is 90 degrees, we'd have:
0 deg: Cyl1 Bang . . . 90 deg later: Cyl 2 bang . . . . .630 deg later: Cyl 1 bang.

The firing interval is called "twingling," and the intent is to make the engine produce power in a way much like a single. Apparently, an engine set up like this allows motorcyle dirt racers to better feel the limits of the available traction and this provides a competitive advantage. The most popular bike set up this way is the HD XR-750 (at least some of them). Since the Harleys have a 45 degree V, the firing sequence looks like: O deg Bang! . . . (45 deg rotation) . . . . Bang! . . . . . . . . . . . . . .(675 deg rotation) . . . .Back to zero and Bang!

So, a B&S with 270/450 may be "odd firing", but it could be still "odder." I suppose we should be thankful for that.
Back to the regularly scheduled back-and-forth.

Billski,
Thanks much for the spreadsheet with included graphs. It would sure be convenient if 30 HP lawnmower engines were horizontally opposed flat fours.

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#### Hot Wings

##### Grumpy Cynic
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When I look at that plot, I see big firing pulses with one starting at 0 degrees, next one at 450 degrees, next on 270 degrees later...
Billski
This is exactly what I was looking for, but I sure didn't expect you to do my work for me! Thanks! ... but it almost makes things too easy. How do you expect me to learn anything?

Yes, I know it's not a sine wave pattern. I just used that for a visual to hopefully illustrate what my question is/was. Online graphing site made the *.JPG easy too.

#### pictsidhe

##### Well-Known Member
First issue is that torque fluctuation in individual cylinders is most definitely NOT a Sine wave, and has a lot of dead space through the cycle. The big pulse starts at big pressure with the piston at TDC, and expands nearly adiabatically to near BDC, then the engine makes a whole revolution at near zero load during the exhaust and intake strokes, then a near adiabatic compression prior to ignition. Here is EPI's take on the whole issue.

http://www.epi-eng.com/piston_engine_technology/torsional_excitation_from_piston_engines.htm.

While this article does some combinations like even fire fours, sixes, eights and twelves, plus an odd fire V6 (90 degree V8 with two cylinders omitted and no offset crank pins), there is no 270-450 twin put together. You can see that the combined torques of even-firing eights and twelves do look sort of like a sine curve, and that is what I was talking about in earlier posts.

In order to show you what our 270-450 twin looks like, I ran an idealized Otto cycle - adiabatic compression, instantaneous fuel burn, adiabatic expansion. I included crank and rod geometry too. For a single cylinder, I got a very similar looking curve to the one in EPI and as listed in other sources. Then I offset a second copy by 540 degrees and ran four turns of the engine (1440 degrees) to illustrate the instantaneous torque curve for a 90 degree V-twin with a single crank pin and firing at 270-450 spacing.

When I look at that plot, I see big firing pulses with one starting at 0 degrees, next one at 450 degrees, next on 270 degrees later...

Just for reference, I also ran an even fire twin on the attached file, and firing occurs every 360 degrees.

The odd fire will, in this experienced powertrain engineer's opinion, require a somewhat lower spring rate to isolate a "soft" system from the rest of the driveline relative to the even fire engine. For a "stiff" system, the odd fire will require a somewhat higher resonant frequency to prevent resonance at high rpm.

Billski
I heard about a Mazda redrive using car gears. It worked great until the day that the engine only started on a single rotor, which stripped the gears.
It seems a good idea to factor misfires in, which means that any twin redrive should be able to run on a single cylinder without eating itself. That's what I plan to do, anyway. Failing that, detruction at startup and idle is a lot more acceptable than in flight.

#### pictsidhe

##### Well-Known Member
Here's an odd bit: Some V-twins are set up to fire one cylinder immediately after another. So, if the Vee angle is 90 degrees, we'd have:
0 deg: Cyl1 Bang . . . 90 deg later: Cyl 2 bang . . . . .630 deg later: Cyl 1 bang.

The firing interval is called "twingling," and the intent is to make the engine produce power in a way much like a single. Apparently, an engine set up like this allows motorcyle dirt racers to better feel the limits of the available traction and this provides a competitive advantage. The most popular bike set up this way is the HD XR-750 (at least some of them). Since the Harleys have a 45 degree V, the firing sequence looks like: O deg Bang! . . . (45 deg rotation) . . . . Bang! . . . . . . . . . . . . . .(675 deg rotation) . . . .Back to zero and Bang!

So, a B&S with 270/450 may be "odd firing", but it could be still "odder." I suppose we should be thankful for that.
Back to the regularly scheduled back-and-forth.

Billski,
Thanks much for the spreadsheet with included graphs. It would sure be convenient if 30 HP lawnmower engines were horizontally opposed flat fours.
I think all Harleys do that, Sir.

I had an XV750 to fix once. the owner had rebuilt the top end and it didn't want to start afterwards. I swapped the starter motor for one on the shelf, but it still barely turned. A squirt of ether and jumping from a car battery got it going.
"Did it sound like a Harley before you rebuilt it"
"No"
...

#### Vigilant1

##### Well-Known Member
I think all Harleys do that, Sir.
There are few engines that can't be made to run with a can of starting fluid and a strong battery.
I believe it is 315/405 for most of the Harleys, except for the "twingles" that are supposedly a bit of an oddity. But I am not an expert, I admit to preferring the Japanese bikes.

#### wsimpso1

##### Super Moderator
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I heard about a Mazda redrive using car gears. It worked great until the day that the engine only started on a single rotor, which stripped the gears.
It seems a good idea to factor misfires in, which means that any twin redrive should be able to run on a single cylinder without eating itself. That's what I plan to do, anyway. Failing that, detruction at startup and idle is a lot more acceptable than in flight.
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

#### wsimpso1

##### Super Moderator
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I think all Harleys do that, Sir.
After I once made this comment about H-D running 45-675 (on HBA), I was called out on it. The homologation models for dirt track racers definitely did that for controllability in power-on drifting, but the documentation I searched up showed 315-405 is normal production. Lots of documentation on it. In a large open pipe engine at low speed, the classic short-long exhaust report spacing still comes through.

#### pictsidhe

##### Well-Known Member
I will confess to have worked on enough Harleys to count them on the thumbs of one hand, but was told by a Harley guy they were close firing. That XV did sound uncannily like a Harley before its cams were rephased correctly, though.

#### wsimpso1

##### Super Moderator
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Modded the spreadsheet to include a look at what idle in V-twin looks like. Pulled the intake manifold pressure down to about where it would be at idle and lowered the pressure rise until I got close to five foot-pounds average torque.

Then I did a misfiring cylinder. Bumped the pressure rise on the good cylinder to get the engine to about 10 ft-lb, raised manifold pressure some with it (All guesses, but in the right neighborhood). The compression and power strokes look reversible on the dead cylinder. What you get is still four compression strokes and four power strokes, with every other power stroke being small. That would look to the damper system sort of like normal but with the biggest pulses at one half their normal frequency for any given rpm. If the resonance lined right up on the good power strokes, it could amplify and perhaps become destructive. How would it do this? Well, if you had 1st resonant mode a full octave below idle and you got the missing engine to your regular idle speed, they would coincide. Another way is if you only have a half octave of separation between firing and the mode and you ran the missing engine to 1.5 times normal idle, it could again amplify. Makes me want to drive 1st mode a lot more than a full octave below nominal idle for a twin or a two rotor Wankel.

Have a look.

Billski

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#### wsimpso1

##### Super Moderator
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Ummm, no.

Add two phased 15Hz waves you do not get any 24 or 40Hz components. Sine waves are actually a poor example to use here, you'll end up with a single sine wave...

With a pair of torque pulses, you'll end up with components at 15 and 30Hz with harmonics above that as they are not sine waves.

Spreadsheets have FFT functions, it may be informative to play with one.
OK, look at it this way. At 1800 rpm, we have 30 rev/s. In every second we get 30 turns and 30 power pulses. If we get one at t=0, and the next one is 450 degrees away, the interval is 1/30 * 450/360 = 0.04166 seconds between pulses. 1/0.04166 seconds is 24 Hz. The next power pulse comes early after only 270 degrees. 1/30 * 270/360 = 0.025 sec. 1/0.025 sec = 40 Hz. Those are the two repeat rates that we will see on firing. And it makes sense because if it were an even fire twin it would have one firing pulse per rev or 30 Hz. The odd fire twin straddles that rate...

Billski

#### Vigilant1

##### Well-Known Member
OK, look at it this way. At 1800 rpm, we have 30 rev/s. In every second we get 30 turns and 30 power pulses. If we get one at t=0, and the next one is 450 degrees away, the interval is 1/30 * 450/360 = 0.04166 seconds between pulses. 1/0.04166 seconds is 24 Hz. The next power pulse comes early after only 270 degrees. 1/30 * 270/360 = 0.025 sec. 1/0.025 sec = 40 Hz. Those are the two repeat rates that we will see on firing.
(Harkening way back to 12th grade physics and Slinkies on the floor)
So, if we had two tuning forks with frequencies of 24 Hz and 40 Hz, we'd expect a beat frequency of 40-24 = 16Hz. At that frequency (i.e. every 1/16th of a second), there would be constructive interference and a pulse of higher amplitude (the resultant of the two primary pulses).
Yet, that seems wrong/odd, since our little engine doesn't have a 24Hz tuning fork and a 40 Hz tuning fork. It physically has two cylinders that are the "tuning forks" and popping away at the same frequency of 1800rpm/60 (to get RPS)/2 (a "pop" every other cycle) = 15 Hz, though they are out of phase by an alternating interval.
I concede that the 24/40 hz approach is a LOT simpler to sketch out, and almost surely a more useful way to understand what is happening.

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#### Hot Wings

##### Grumpy Cynic
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Yet, that seems wrong since physically our little engine has two little "tuning forks" popping away at the same frequency of 1800rpm/60 (to get RPS)/2 (a "pop" every other cycle) = 15 Hz
Let me take a stab at this - and then someone that actually knows can correct. Best way to master a subject is to try to teach.......I'm a long way from a master at this point.

The engine is not 2 tuning forks. But if those 2 forks were attached to the engine the engine could excite each separately or as a pair depending on the rpm. The engine produces it's vibrations with a common zero point which is reset at each revolution, thus there is no phase shift as there can be with 2 independent systems. With the independent forks it doesn't matter when each started their cycle the resulting interference pattern will be the same shape, and at a rate of their least common denominator.
https://en.wikipedia.org/wiki/Beat_(acoustics)#/media/File:WaveInterference.gif

Per Hartog "All harmonic motions are periodic, but not every periodic motion is harmonic."

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#### pictsidhe

##### Well-Known Member
Hot wings has it.

#### Vigilant1

##### Well-Known Member
I think this is one of those topics that does a lot better with pictures.
The engine produces it's vibrations with a common zero point which is reset at each revolution, thus there is no phase shift as there can be with 2 independent systems.
So, you are saying we don't have 24 Hz wave and a 40Hz wave that constantly shift phase against each other and produce a 16 Hz "beat." Because the waves are re-synchronized with each 2 turns of the shaft, there's no opportunity for constructive (or destructive) interference to develop. Am I close?

#### pictsidhe

##### Well-Known Member
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.

#### wsimpso1

##### Super Moderator
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Hot Wings is way out front on this. Two things interact here:

The combustion chambers, pistons, connecting rods and crank throws make a highly intermittent set of pulses that are not sine waves. This is called the forcing function. There is no beat as the two big pulses and four smaller ones stay in sequence and timing on every pair of engine turns, from t=0 until the machine wears out;

The rest of any powertrain is a series of things that, once set into motion will vibrate at their set of characteristic frequencies. If we somehow come along with another push on these waves at the right time on each cycle, the amplitude will grow. This is the response of the system;

The forced vibration response of the vibratory system to the forcing function is the thing we want to manage in some way. To make the rest of the system reliable, you must, in some manner deal with the forcing function.

Specifically to the 450-270 Twin, we have a positive torque pulse followed by another at engine speed (in rev/s) times 5/4 followed by another pulse at 3/4, then another at 5/4 then another at 3/4, with the pairs repeating forever. We also have a another set, these are smaller negative pulses, and then there are all reflections, harmonics, etc that are of much smaller magnitude that I did not model. The smaller ones are usually not worried over.

If this was a pair of sine waves running each at their own pace we would get a beat that we can deduce from simply adding two waves and looking at the resultant. Our V-twin's two power pulses do not run each at their own pace and DO NOT HAVE A BEAT. They have something that looks very much like what I computed and plotted for you guys. It looks sort of like an even fire pair, but is a little more complicated...

Now our task is not to completely and totally define the input pulses, our task is to scheme out a system downstream of the crank throws that will not amplify this forcing function. Two approaches are known to be reliable:
• The first is to make everything downstream stiff enough that the lowest resonant torsional frequency of the downstream system is higher by at least half an octave (at least 50% higher frequency)than the highest firing pulse frequency that is input. This fully transmits the engine forcing function through the entire driveline including the prop and is called a "stiff" system;
• The second is to make at least one thing soft enough that the primary resonant torsional frequency is at least half an octave below (at least 25% lower frequency) than the lowest firing pulse frequency you can get. This mostly isolates the firing pulses from the rest of the system. The engine does what it does, a little bit of the firing pulses are transmitted to the rest of the system, and we call this a "soft" system.
The first usually requires a pretty stout system. That could mean heavy, but might be in an acceptable range. You get to decide what is good enough. There are V-Twin belt drives that look like they may very well be "stiff" systems. The ones that run with engines and props that you would use on your airplane and that either have good analysis and testing without failures, or lots of flight time without failures might be good candidates. Lycoming and Continentals with the prop bolted to the crank flange are "stiff" systems. The US Army and Navy figured out in the 1930's that with boosted high perf engines, stiff systems would fatigue the outer ends of prop blades right off the rest of the prop, and set the engine makers to work on preventing those big vibes at the prop.

That leads us to "soft" systems, which worked marvelously in all of the V-12's built and used by all combatants in WWII. The stiff systems worked marvelously with order tuned pendulums on the cranks of the big round engines designed in the US up through WWII.

In this case, our odd fire V-Twin forcing function looks sort of like the even fire forcing function, but with one pair closer together than the other. To get safely below the tighter pair, you need to know the frequency of the tighter pair at min operation speed and make sure that you soft system frequency is safely below it. 25% below that frequency is commonly thought to be enough. That automatically puts you more than 25% below the larger spacing too, and as revs increase and power pulses get bigger, you just isolate better and better.

Soft systems avoid resonant pumping by letting the forcing system part do what is doing with little interference. The soft spring deflects to position for average torque and then allows the small oscillating travel of firing pulses and such to run. The transmitted torque is the mean torque plus the spring rate times the firing pulse travel.

You have other fairly common problems to also worry over. Some folks have expressed concern over a misfiring cylinder. Well, we modeled it, and if either fuel or ignition is interrupted, the system still looks a lot like our regular V-Twin but with one power pulse as big as the compression pulse. I have done this work with fours and larger engines - misfires produce some weirdness, but they do not normally make for resonance. I suspect that we will have similar behaviour here too. But if you hole a piston or swallow a valve, your forcing function will immediately convert to that of a single with much lower frequency forcing function. If you are attempting to run at modest rpm above idle, this could coincide with your soft system resonance and be destructive, even within the frame of reference of getting to your precautionary landing. A V-twin with one cylinder dead is going to be pretty weak at turning your prop sized for both cylinders - you will be lucky to have 30% power with the throttle wide open. Do that until landing is assured, and the power train might hold together for a few minutes. I suspect that most of us running a V-Twin will either run it WOT to get to a decent field or shut it down to keep it from leaping off the the airplane. Nonetheless, you might want to make your soft element soft enough and with enough travel to push resonance a little more than 50% below your lowest nominal frequency, and then redline your tach for that min operating speed ...

While we have been focusing on the firing pulses, we have some more you might also be concerned about. If the airplane is driving the prop straight on through the air, the blades do not produce torsional pulses. But if you are flying with pitch or yaw angles to the relative wind, each blade gets at least one torque cycle per rev of the prop. 2 blades gives 2 nice sine waves per prop rev, with a 13/7 ratio (note they are both prime numbers making 1.86 speed reduction ratio) give 1.08 firing pulses per engine turn. Now that will go in and out of phase with each of the firing pulses, and may make a slight thrum-thrum, but will not coincide with both cylinders at the same time. But getting a little further away from 1 prop blade pulse per turn might make more sense. This is where a three blade prop might make more sense, as it would put our 1.86 ratio at 1.62 prop pulses per rev, the pulses will be a third smaller, and they will go in and out of synch with the firing pulses more rapidly. The really good thing about a soft system designed for a swallowed valve is it will also isolate the prop pulses from the engine, even at min operating rpm, so damaging resonance is made much more unlikely. In a stiff system, the interaction between prop and crank must be taken more seriously...

I hope that this helps...

Billski

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#### wsimpso1

##### Super Moderator
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I think this is one of those topics that does a lot better with pictures.

So, you are saying we don't have 24 Hz wave and a 40Hz wave that constantly shift phase against each other and produce a 16 Hz "beat." Because the waves are re-synchronized with each 2 turns of the shaft, there's no opportunity for constructive (or destructive) interference to develop. Am I close?
THERE WILL BE NO BEAT driven by the firing pulses. These are not free vibrations, they are forcing functions with fixed timing to each other. The can not drift into and then out of synch to give a beat. Understand that the beat we get from two waves is just the sum of the individual forms. See the attached file for the difference between them and then remember that these sine waves are NOT our forcing function with small numbers of cylinders.

Billski

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#### pictsidhe

##### Well-Known Member
I can't compete with this on a phone with a 3.8" screen. I give up.

#### Hot Wings

##### Grumpy Cynic
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I hope that this helps...
Billski
It does, and is very much appreciated.

Another kind of off the topic observation regarding beat .... I've seen it postulated that rogue waves might be a result of beat.
I suspect that this phenomena might explain some of the unexpected, one of a kind failures, in an otherwise well proven machine? And, there is no practical way to predict this kind of failure?