Torsional Vibration and Resonance - Basic Theory and Issues

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wsimpso1

Super Moderator
Staff member
The whole topic of PSRU's and drive shafts and torsional vibration has been talked around and I keep seeing the same difficulty in the thinking of the involved folks. Since we on HBA tend to be an intelligent bunch, I got to thinking about how much I had to work to get my arms around the whole issue. So, this little lecture was put up on a thread, and now we are trying to make it a sticky to help everyone who is interested get a grip on the basics.​
Let's start off by saying that the science of vibration control and management has lots of smart people working at achieving the goal of the dead smooth system, and at minimum weight. And there are still new things happening out there, but mostly, it is exploration of existing knowledge.​
Every field has its nomenclature. Let's define a few words so that we all know what we are talking about.​
Components - Masses are things that resist changes in speed and require forces to accomplish those changes in speed. Springs are things that store energy and have a force associated with them when deflected. For our purposes, let's assume that our deflections are all elastic, meaning that load and deflection are related by a fixed spring rate, and that when the load is removed, the spring goes back to its original length. Spring rate is k, mass is m.​
Frequency - this is the rate at which a component or system is vibrating, usually in whole cycles per second.​
Orders - this is the number of times per rotation of a device that something occurs. A single cylinder four stroke engine has firing at one-half order (a firing pulse every other rotation), and a V8 has firing at fourth order. In addition to the firing order, we also have other vibrations at twice the firing order (from the pistons going up and down in the cylinders), three times and four times the firing order from other imbalanced movements, and fractions of the firing order because the various cylinders do not have exactly the same firing pulses.​
Systems - This is everything in a chain of structure that is connected together. Usually, these structures have a purpose, like transmitting power, and the power does not come through dead smooth. If you have a system with masses (not springy) connected by springs (no mass), you have the easiest schemes to conceive of and model. Think two masses with a spring between them. They also pretty neatly describe a lot of what is out there as many parts are relatively light and springy or relatively massive and stiff. The other end of the scale is systems made up entirely of components that have significant mass and are springy. They are a little more difficult to manage mathematically. Think of a conventional radio antenna on a car, vibrating in the wind or a strings on a musical instrument. Understand that generally, most systems have six degrees of freedom - three linear and three rotational. Yes, motion in some degrees of freedom is more limited than in others, but it still exists. For simplicity, we will work in rotation along the intended rotation axis. If it helps you to think in terms of linear motion, go ahead, the theory works the same.​
Mode - This is the shape of each of the vibrations that a system can do. In the case of a string of masses and springs, there is one mode (in each degree of freedom) for each pair of masses in the system. Two masses on a spring has one mode, where the two masses vibrate towards each other and then away from each other, and the frequency is set by the ratio of mass to spring rate. Three masses and two springs have three primary modes - M1 vs M2, M1 vs M3, M2 vs M3, and the frequency that each runs at is dependant upon the ratio of the mass to spring rates of each set. That same set of three masses will also have a modes where two masses will move together vs the other mass. More masses means more modes to manage and the number of modes go up faster than the number of masses.​
Resonance - If you have a forcing function (firing pulses from the engine, imbalance, universal joints running at even small angles, gear teeth engaging/disengaging, turbine blade passing frequency, bearing defects, propeller blade/wake interference, and more) that occurs at the same frequency as one of the modes, you will amplify the mode, and there is no theoretical upper bound on how much. This is how a swing can go so high - we pump its oscillation with inputs timed to the oscillation. It does not have to be every stroke, and it does not have to be strong, just repeated.​
Amplification - When the mass vibrates more than the forcing function does, the vibration is being amplified. The system will amplify when the forcing frequency is "near" a resonant mode.​
Damping - Let's stick with the engineering version. Damping is energy removed from the motion of the system and is generally converted to heat. Elastic structures have very little damping. In metal structures, it is generally below 1%. Strike and hold a key on a piano, and it takes a while for the note to die out. Composites are also very low on damping. Wood is a little better. Rubber does even better. If you want to take out energy faster than you can dissipate energy to the environment, your damper will increase in temperature. And air, well, it will only develop much energy loss if the speed of the motion is high. Yes, the prop is moving fast, but even destructive vibration is at tiny distances and equally small speeds. Usually, we can ignore damping of a device vibrating at small displacements in air without significant errors.​
Absorbers - Three types, those that are tuned to a frequency, those that are tuned to an order, and those that are actually dampers.​
Frequency tuned absorbers are a free mass on a spring attached to a vibrating part of a system. To be effective they have to be as close as possible to the vibrating mass that we are attempting to tame, and they have to be tuned to vibrate at the frequency that the mass is vibrating at. When sized and tuned and located correctly, they will prevent the resonance, but at frequencies near the resonance, they will cause modest increases in response of the system. Neat if they work.​
Order tuned absorber are devices that will respond to a particular order regardless of speed. Torsional pendulums have been in aircraft engines since the 1930's. The device is a short pendulum that is mounted on a rotating machine, and its natural frequency is dependant upon the speed it is spinning, so you can tune them to any order of rotation you want. Neat. And they are noted for being able to pick off as much as 95% of vibration in a particular order... There are others.​
Dampers, well, you make an energy sink and hope that you do not need the energy thrown away. Rubber elements can convert quite a bit of energy, but are difficult to cool. Hydrodynamic devices do similar things and exist for many engines. You can put in a clutch or use belts to drive something, and then let them slip enough to take off the peaks of the forcing function, but you will be able to measure this loss in airplane performance, and you will have significant cooling needs here too.​
So, if you have a resonant mode in the range of the forcing functions, you will amplify. If you match a resonant mode with a forcing function, it will amplify hugely. If you apply much damping to the motion, you will have to cool the damping device. If you can pick off the resonance with a tuned absorber, you will still have amplification at frequencies near the resonance that you have to be able to handle. Best solution is to adjust your resonance modes to be out of the range of your forcing functions. Next best is to at least drive the resonance modes to an area where you have little exposure AND little energy to drive the resonance.​
We change the resonant frequency of a mode by changing mass or changing spring rates. Each mode's resonant frequency varies directly with the square root of k/m. If you want to double the resonant frequency, well, you have to quadruple the ratio of spring rate to mass. While it is easy to increase mass of something, it is undesirable in airplanes so you have to consider the big picture while you do it. Spring rates, well, if you were weight conscious in the first place, you started near minimum spring rate too. Increasing spring rate requires adding diameter or thickness or both.​
If you really need to drop spring rate somewhere and can not do it with a component that already exists, you can put in a spring deliberately. This is called a spring isolator and they are widely used. Get this, they are called dampers - misnomers exist. While they do have some damping, springs rubbing on their housings and the like, they are primarily soft springs in the system. Ground vehicles and stationary engines use them between the engine and the shaft going to powered device. We use them in manual transmissions, automatic transmissions, and even hybrid powertrains. The biggest single reason for using them behind engines is to avoid exposing the downstream components to the full fury of the firing pulses. The gadget sucks up the energy of the pulse and distributes it later as the pulse eases. You still get the firing pulse at the firing order, but the peak is greatly reduced, and the valley is not as low... Putting a really big flywheel on the engine would do the same thing, but a spring isolator is so much more compact and lighter. And you had better believe that their rates and travels matter. I have made a big portion of my living since 1996 working with these guys to make our ground vehicles smoother and more fuel efficient.​
So, on to common discussion topics:​
If you change one spring rate or inertia in your system, you will change not only the resonance frequency of the pair of inertias attached to the spring, but you also influence all of the modes that those two inertias participate in. You fundamentally can not isolate one vibrating element and let the others do their thing. Changing one shifts many of the others;​
You can put in more flywheel effect to reduce the amplitude of a forcing function and to move the resonance downscale, but the forcing function is still there and still at its original frequency. Just understand that while you drive down one mode's frequency, you drove down some others too. Common to get one mode out of the way and drag in another mode (or two). Also remember that your biggest rotating inertia (by far) is your propeller in most airplanes. In boats, the propeller may also have significant inertia, but it will usually be much smaller.​
You can change the spring rate or put in spring devices to shift things, but just remember that shifting one mode out of the way does drag other modes too.​
Airplanes have very little damping in their systems unless you put it in there, so much of base resonance theory holds in airplanes. The things we get away with in cars looks like murder by comparison. We have so much compliance (low spring rate elements), and so much energy absorption (rubber and hydraulic mounts, isolator hysteresis, torque converter losses, tuned absorbers with rubber in them, tires, suspension components with rubber and hydraulic mounts). If you put in damping, remember to find a way to cool it adequately.​
Motorcycle systems - wow, completely different from cars and planes. Generally they can have very low order forcing functions (H-D racing v-twins run 45-645 degree firing spacing, so they behave like a really big single, the production ones use 315-405 spacing), and so would require a positively huge isolator. Instead they go for hanging a rubber isolator at the back wheel. And they recognize that the back tire is slipping at high torques, and the high perf end is in active engine management due to tractive limits until way up in the speed range. Yeah, they cut back on power to keep the back tire from running away.​
Billski​

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Staff member
Thank you Bill!

pwood66889

Well-Known Member
Five Stars, Billski. I'll try to catch the rest of this lecture series.
Percy in SE Bama

Himat

Well-Known Member
Very nice Bill!

A few points that I would like to add.

Lumped systems. A lumped system is a system where each component can be described as discrete part such as a mass, a spring or a damper.

Distributed systems. A system where each component is described with their mass, stiffness and damping.

Wavelength, the spatial length of one period of vibration. A function of frequency and speed of sound in the material.

If the system can be analyzed as a lumped system or distributed system is down to the wavelength. If each part of the system is “small”, less than a fraction of a wavelength, in wavelengths the system can be analyzed as a lumped system. If each part of the system is “large” in wavelengths, larger than one wavelength, the system is better analyzed as a distributed system. To tie it the definitions listed in the first post, if each component has vibrating modes on its own, then we have a distributed system.

Autodidact

Well-Known Member
Excellent Billski, thank you!

Glastar1

New Member
Dear Billski: Very fine article. Glastar1

aboazeaz

Well-Known Member
hi Bill:
what is the most basic and common way to cope with TV, thrust, bending and gyroscopic loads(i have no idea what that even means) from the prop ?
and do these problems exist in the helicopters in the same way?

Aircar

Banned
Drive shaft resonance (even crankshaft resonance) is well known and needs expert attention to not be a catastrophic or long term problem but IS soluble . No mention of devices that slip to allow avoidance of resonance during power up or down has been made and these constitute a large part of the 'prevention' part of the solution . Avoidance by simply bolting a propeller directly to a crankshaft comes with many drawbacks of it's own and puts lightplane design in a sort of cul de sac with no prospect of much improvement.

After studying more than forty shaft drive aircraft (not counting helicopters or VTOL ) I concluded that the reason for non adoption of remote driven propellers was NOT because they all failed catastrophically as described, from torsional resonance (only one had driveline failure due to aged rubber components -the WACO Aristocraft ) --in fact, after normal development, NONE suffered torsional failure . Plenty of propeller failures and even engine tear outs from directly driven bolted on props in comparison .

We know that cantilever wings are trying to 'fold up' all the time and are much less weight efficient than externally braced biplanes --the English air force actually banned monoplanes at one point due to the concern over structural failure (and structural resonance -flutter) --despite this, development persisted and the unbraced wing has come to be accepted. With road vehicles it is almost impossible to find one that is not shaft driven and shafts are not seen as a special problem area. The reason for the 'bad name' of tailprop shaft driven aircraft is more related to the basic configuration rather than anything to do with what was going on inside the aircraft --and repetition of the 'impossibilities' of shaft drive.

N

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pictsidhe

Well-Known Member
Hmmm.. the 1000+hp V12's of the 1940s never dealt with this issue. And just about every water cooled engine in use at the time was gear driven.

https://en.wikipedia.org/wiki/Packard_V-1650_Merlin#/media/File:Packard_V1650.jpg

But now any V type motor is magically suffering from torsional resonance???

What's changed??

It's my understanding that the v12s used a quill shaft. The large number of cylinders meant that it didn't need to be too torsionally soft. Wright had huge TV issues on one of their big radials.

wsimpso1

Super Moderator
Staff member
Hmmm.. the 1000+hp V12's of the 1940s never dealt with this issue. And just about every water cooled engine in use at the time was gear driven.

https://en.wikipedia.org/wiki/Packard_V-1650_Merlin#/media/File:Packard_V1650.jpg

But now any V type motor is magically suffering from torsional resonance???

What's changed??

Nothing. The Army and Navy specified maximum torsional vibration in the 1930's originally to protect their props. The V-12's and the geared round engines all had issues with torsional vibration during development. The engineering teams designed the engines with layouts that facilitated torsional isolation and then added features that dealt with torsional vibration. Quill shafts and a variety of dampers made their way into the big V-12's.

http://www.enginehistory.org/NoShortDays/Introduction.pdf

Here is the pic for work on the R2800 geared round engine. The pic is intro, the rest of the story follows on that site. By the time they got to service use, the issues had been solved and in service, they worked fine. Crankshaft mounted torsional pendulums (order absorbers) are commonplace in 6 cylinder Continentals and in some four cylinder engines as well.

Torsional vibration is real and can be significant. If you choose to ignore it in engine-PSRU design, you may get lucky or you may have sudden serious problems with your power delivery.

Billski

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wsimpso1

Super Moderator
Staff member
hi Bill:
what is the most basic and common way to cope with TV, thrust, bending and gyroscopic loads(i have no idea what that even means) from the prop ?
and do these problems exist in the helicopters in the same way?

TV is torsional vibration, and is the topic of this thread. You can make the whole system really stiff and drive resonance above the range of input vibration frequencies, selectively add soft elements to take nasty modes below the range of input vibration frequencies, add order tuned absorbers (torsional pendulums are good examples) to remove vibrations at certain orders of rotation, add frequency absorbers (crankshaft harmonic balancers and driveshaft dampers are good examples) to absorb specific frequency vibrations, selectively add inertia (rotary mass) to drive noxious modes to lower frequencies, selectively reduce inertia to drive noxious modes to high frequencies, and so on. With so many modes possible over huge range of frequency and so many fixes that might be used, this sort of system should be designed with torsional analysis as a major part of the design process. FEA works nicely for this...

Thrust comes from propellors and helical gears and form other design features, and can be present on any shaft. It is axial load on the shaft. Generally there are either separate thrust elements (direct drive airplane engines and automotive engines have these features on their crankshafts and crankcases) or bearings selected have adequate axial and radial load carrying ability for long bearing life. Most ball and tapered roller bearings have load ratings for axial and radial directions in anticipation of mixed loading. Other types of bearings (straight roller bearings and journal bearings) have virtually zero axial capability - if axial loads are to be carried, they must be handled separately with thrust bearings.

Bending is also possible on any shaft. Two gears running on parallel shafts will generally have forces pushing on the middle of the shafts, while they are supported at their ends, which produces bending moments in the shafts. The prop spinning in front of the airplane is a huge gyroscope - push on either rudder or the elevator and the airplane (and prop) is briefly rotating at right angles to the axis of prop rotation. Gyroscopes resist this motion with a force called a gyroscopic moment. The end of the prop shaft sees this moment as trying to bend the shaft. All of these moments can be resolved into loads at the bearings, and bearings selected or designed to handle the loads for long product life. Likewise the linear and rotational loads on the shafts can be figured out and the shafts designed to live a very long time too.

Do these issues exist in helos? You **** betcha they do! The main rotor is a big gyroscope, with immense reaction moments to pitch and roll rotation, while the tail rotor has similar big reactions in roll and yaw rotation. These rotors make thrust too. And the bearings and shaft must be designed to stand all of that. And the torsional vibe guys are busy during the design evolution and test of these systems. Look at a Bell 47 (useful because you can see lots of stuff without pulling panels) when you get a chance. Find the main gearbox, then the shaft that goes aft to the tail rotor gearbox. Long slender shaft with a bunch of bearings along it. This shaft is a nice soft spring in the middle of the system, making the lowest frequency between engine and tail rotor much lower than any of the forcing vibrations and effectively isolating any vibration at one end form going to the other end. All of the bearings are there to drive the resonant frequency of whirl mode above rotational speed, which is another resonant phenomena. Some main rotors have torsional pendulums on them, right out in the open, easily visible if you know what to look for...

Basically a long soft shaft will fly around like a jump rope when spun in the right speed range. Put bearings along the shaft and frequencies at which it will do this go up. Driveshafts on many road vehicles will have two or more shafts and three or more Hooke joints to drive critical rpm for those shafts above operating speeds...

The engineering teams solved these issues and now a lot of folks, even mechanics who work on the stuff, never have to think about the "why". And folks who think that they can just hang a box with a couple gears on the RFOB and bolt a prop to it may be in for surprises if they do not cover all of the things that can happen when they are laying it out, designing the shafts, picking flywheel inertia, bearings and rubber isolator elements. There are PSRU where gyroscopics were never thought about... Now just maybe these guys were lucky and the shafts and bearings were already beefy enough that the reactions from the gyroscopics were small compared to capability, and thus no matter. And maybe the bearings are close to limits, and a pilot aggressively oscillating the stick or the rudder pedals (clearing the envelope for flutter) will over load the bearings and cause bearings and gears to tear up in flight. How good are you at dead stick landings?

Billski

pfarber

Well-Known Member
Nothing. The Army and Navy specified maximum torsional vibration in the 1930's originally to protect their props. The V-12's and the geared round engines all had issues with torsional vibration during development. The engineering teams designed the engines with layouts that facilitated torsional isolation and then added features that dealt with torsional vibration. Quill shafts and a variety of dampers made their way into the big V-12's.

Here is the pic for work on the R2800 geared round engine. The pic is intro, the rest of the story follows on that site. By the time they got to service use, the issues had been solved and in service, they worked fine. Crankshaft mounted torsional pendulums (order absorbers) are commonplace in 6 cylinder Continentals and in some four cylinder engines as well.

Torsional vibration is real and can be significant. If you choose to ignore it in engine-PSRU design, you may get lucky or you may have sudden serious problems with your power delivery.

Billski
I'd like to know where this spec is. Do you have a contract number or reference?

I understand the general TV issue but I don't think it's anywhere near the crisis you make it out to be. Do you own and engineering firm???

I've followed PSRUs and auto engines for decades (back when Kitplanes actually was a usefull magazine).

What are some crashed directly caused by tv?

wsimpso1

Super Moderator
Staff member
I'd like to know where this spec is. Do you have a contract number or reference?

I understand the general TV issue but I don't think it's anywhere near the crisis you make it out to be. Do you own and engineering firm???

I've followed PSRUs and auto engines for decades (back when Kitplanes actually was a usefull magazine).

What are some crashed directly caused by tv?

Contract number? From 1937? Hit the pic I put in and read the whole article. This is no made up story. Specification cited in the articles is AN-9504. Have fun...

Then know a few things:

Bifilar torsional pendulums were invented and played with in multiple forms in the 1930's because the big engines were capable of fatiguing the tips off of aluminum propellor blades, among other things. They became standard items on many radial engines and are commonplace in six and in larger four cylinder opposed engines'

Alan Tolle did several dead stick landings in the Powersport RV3 while he and Everitt Hatch figured out that the "standard" approach and several others to building PSRU for Mazda rotary engines may not be adequate. All PSRU failures. That Alan was both talented and lucky is shown by the fact that he deadsticked that ship seven times IIRC;

Jan Egenfellner produced a line of airplane engines based upon 6 cylinder Subaru engines that included a PSRU. Among other things, the PSRU had noise and vibration issues that resulted in most of these engine-psru packages being removed from service or having the PSRU removed and replaced with other units. You might have some trouble documenting this one, as Jan himself is reputed to have been quite active about clensing the internet of bad things said about his engines. For several years, the internet community was abuzz over the various engine failures, before Engenfellner abandoned his customers, closed up that company, and started a new one around other engines and with a new line of PSRU to go with them;

BD5 had a series of ongoing issues with torsional vibration caused powertrain failures that contributed to the ruin of that project. http://ibis.experimentals.de/downloads/torsionalvibration.pdf is an article written by fellow who worked on the BD5 and some other projects, all of which had torsional vibe issues;

I worked on a small airplane company called Teton Aircraft in 2010 in which a 44" driveshaft extended between the engine and the prop. Powertrain resonance resulted in several spectacular failures on their test rig prior to my involvement. My postings on hba.com were what brought me to their attention in late 2009. I was brought on board, performed appropriate analyses and identified a suitable change to the system, and vibration issues were resolved. I resumed employment in the auto industry after helping them for three months.

There have been others. TV is real, and it must be designed for in PSRU. Crashes? There must be some. Alan Tolle should have had at least one, but he did not.

Crisis? Who said anything about a crisis? I wrote this in 2012. I am pointing out that designing PSRU without proper attention to torsional vibe can result in mysterious failure modes, sometimes resulting in complete loss of power and a forced landing. A number of PSRU have been built with nicely made isolators. Some last fine, some do not. I cited the Eggenfellner boxes, and I am afraid others being offered may be problematic too. Ross at Simple Digital Systems (www.sdsefi.com) has considerable discussion on he website over his Subaru EJ22 turbo and his work to understand and then reduce vibration in his bird.

Do I own an engineering firm? What are you accusing me of? Nope, after a successful career, I am comfortably retired, flying airplanes and building one. Oh, and concerned that folks who do not understand their products are letting homebuilders do their durabilty runs.

Big issue from me is always "how many are flying?", "how many hours on the fleet?", "what is the mean time between failures on them?". If your engine looks like theirs and you think the risks are low enough, have at it.

Billski

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Vigilant1

Well-Known Member
I've followed PSRUs and auto engines for decades (back when Kitplanes actually was a usefull magazine).
And regarding this swipe: People can differ in their opinions. Mine is that today's Kitplanes is a good magazine for the HBA community. There are many people knocking it who may not be fully aware of what has been in it for the last 2 years or so. It is (IMO) much more focused on info useful to people building airplanes than it was in the recent past. It is as good as it was on the "good old days" (the Roncz articles, etc).

BJC

ScaleBirdsScott

Well-Known Member
The apparent lack of issues in the past is that we tend not to remember the failures this far out unless they were spectacular and catastrophic. Most all of the engines back in the day were designed with what, hundreds of engineers doing the work, pouring over every detail, with many years if not decades of experience on engines by the time WWII pushed them to make ever more and more powerful engines? So we don't hear about it, but obviously they were large teams with vast resources behind them. (P51 designed in weeks, etc etc.)

Now for most us here, we're dealing with completely different regimes, with one or two people responsible for an entire system, and not all of them with many years dedicated to any specific issue. They can do a pretty good job covering all the bases and for the most part that's probably enough to get them close enough to make a safe product. But sometimes it seems problems could and have come up. So what are the risks? How close is close enough? How many decades of experience do you really need to really know the last piece of the puzzle? What does that last few percentage points of assurance get you?

There's no single answer here, but I'd wager some are wrong.