# Torsional Vibration and Resonance - Basic Theory and Issues

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#### pictsidhe

##### Well-Known Member
The RR Merlin had some major developmental issues. Even the early production models were a bit fragile. I'd be very surprised if other engines from that era didn't take some effort till they came good.

#### Toobuilder

##### Well-Known Member
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I read somewhere that the contractual TBO of the fighter Merlin was 75 hours. Pretty unimpressive.

#### pictsidhe

##### Well-Known Member
75 hours would have been plenty. Early ones were built for very high performance and tended to have a much shorter life for other reasons... After the Mark X, they held up very well in service, being known for their reliability. Earlier ones were not so good. An early developmental Merlin failed its military 100 hour test. By the end of production, civil versions had a TBO of up to 800 hours.

#### Toobuilder

##### Well-Known Member
Log Member
"plenty" in the context of combat with an established supply chain, sure. But in the context of this thread (post 10, specifically) the big V-12 engines were far from reliable.

#### Vigilant1

##### Well-Known Member
To take a step back: If we consider the case of an individual homebuilder who is considering designing his/her own PSRU or buying one from a vendor, what is it practical to engineer/check? Let's consider belt drives for now.
Propeller and engine pulley loadings: The side loadings from belt tension and prop gyroscopic forces can be calculated in a straightforward manner, and the manufacturers of the bearings provide applicable information for assuring things are okay. Likewise for bearing speeds. Likewise for axial loadings (esp from the prop).
Belt strength/suitablity: probably can be worked through with manufacturer info and knowledge of the belt speed and forces on the "working side" of the PSRU.
TV: (belt, crankshaft, prop): Is the problem even practical to address for a homebuilder? It would seem that the vibrational attributes of the most important moving parts are not easily known by a homebuilder, and the results of interactions between them would require tools and techniques that are not available, either.
1) Have I got that about right?
2) Is there a "prudent approach" that can be taken, absent a complete TV analysis, that can get us into a likely safe window? For example:
a) If successful PSRUs are known (based on field experience), can we determine the applicability of that history to another (new) PSRU/engine/prop combination? What attributes would need to the same to make that previous history a good guide?
b) Avoiding first-order prop/crank/PSRU resonance: as this often occurs below "usable for flight" engine RPMs, can we achieve usable improvements through use of belt slip/idler pulleys, etc, or are sprag clutches, Guibo "donut" dampers, or other measures required?
c) Assuming that even a thorough analysis will require testing, what would a thorough test program for a one-off PSRU look like? Tricks (e.g. strobe photography useful for belt/torsional dampers? Can commercial "knock sensors" be used to tell us something about gear lash issues?)

I know this goes outside the treatment billski probably intended with his (very handy) tutorial. Maybe it can be discussed in another thread, if useful.

Mark

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#### pictsidhe

##### Well-Known Member
There are numerous and sensible reasons that many people opt to buy a redrive from someone who has already done the engineering...

Now, while I do now have a day job hitting million dollar machines with a hammer, I do not have Billski's luxurious experience with million dollar test gear. So my approach to problems can sometimes be a little different...

If you can estimate or measure the stiffness of the crankshaft and the MOI of parts, you can calculate resonant frequencies.
Somewhere, I saw that a very rough guide for the stiffness of a crankshaft is to assume that it is a straight shaft with diameters of the journals. Yeah, rough, but it puts you in the ballpark and lets you know if you need to work a bit harder, or can risk the jump to testing.

For masochists, like myself:

#### wsimpso1

##### Super Moderator
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There are numerous and sensible reasons that many people opt to buy a redrive from someone who has already done the engineering...

Now, while I do now have a day job hitting million dollar machines with a hammer, I do not have Billski's luxurious experience with million dollar test gear. So my approach to problems can sometimes be a little different...

If you can estimate or measure the stiffness of the crankshaft and the MOI of parts, you can calculate resonant frequencies.
Somewhere, I saw that a very rough guide for the stiffness of a crankshaft is to assume that it is a straight shaft with diameters of the journals. Yeah, rough, but it puts you in the ballpark and lets you know if you need to work a bit harder, or can risk the jump to testing.

For masochists, like myself:
Buy a good book. I recently acquired Den Hartog's 'Mechnaical Vibrations', but haven't read it yet. I expect it to be very useful. Maybe Billski could suggest one or two from his library, but not a $500 one Some ideas I've had that I may use when testing my redrive. If it's a ribbed belt, it will slip if there is appreciable TV. That will heat it up. That can be measured with a laser thermometer. Run the engine with a club at all RPMs from idle to full power. Preferably a little higher, and see what the laser thermometer says. Do this with a range of tensions. Toothed belts may warm up too, but they have an annoying habit of breaking things, too. It's also occured to me that TV harmonics are going to be audio frequency. There are a lot of handy little sensors and transmitters that could be used to build a battery power transmitter to be mounted to spinning parts to sense and transmit torsional vibrations to a radio then your PC for analysis. Clever. Hmm, taking them in sequence: I am concerned that the belt drives are NOT engineered. Somebody tried it and it seemed to work, somebody else tried it, and so on. Maybe it is OK for your engine, prop, mounts, etc, maybe it is not... which is why I am concerned when they sy they have never analyzed it and do not keep up with their customers on installed hardware, hours, etc. While the Rotec equipment was no more affordable for you and me, it was$70k, not a million. In fairness, the powertrains were running in million dollar dyno cells or \$300k prototype vehicles.

The straightline journal estimate might be pretty good. All EAA members can get Student Version of SolidWorks, which will allow you to model up any single part that you have drawings for or is on the table in front of you. Once its major features are modeled, and it looks like the part in question, you can set the material from the library of materials, get its mass, inertia, fix it at places and load it in others to get its torsional stiffness or you can run the Eigen solver to get its resonant shapes and frequencies. With the Student Version, you can not do this with assemblies, so be clever - build things that you will analyze together as one piece.

Hertog is on my shelf. Lots of stuff in there. PM when you have specific questions.

You are proposing a vibe survey, and watching for the temp to rise on the belt is great if it is slipping the belt. I agree that is a likely spot for vibe to show up, but may not be the only one. If it does show up at low enough rpm, you can yellow band the tachometer, but what are you going to do if it shows up in the flying range? If it is close to max rpm, you might be able to substantially stiffen the softest components in torsion and get there. If it is low but not quite low enough, you might be able to increase torsional compliance in the system. I think you understand that Increasing belt tension in a resonant regime won't help much as the resonance will still be there but will then be hammering other stuff harder, and the belt will still slip - you have to move the resonance point further away from the operating range.

Good luck with audio. Engines and props are noisy things. Divining the resonance noises from the rest will be hard but might be possible. I can download a frequency analyzer for my phone that shows the frequency content, perhaps you can get one for a laptop and a suitable microphone that connects to the laptop. if you get the frequency content of your just your exhaust note you are likely to determine that it is composed of order based content (follows engine speed) and the resonance of the pipes (is always the same frequencies). You can do the same thing with the prop. Perhaps you can take the readings for each close to the them but far from the redrive to isolate each. Then when taking data with the mic at the redrive, you can find and digitally remove the engine and prop to see the redrive content, and run a vibe survey. I am skeptical...

One other possibility is if you can get an accelerometer with either onboard storage or wireless transmission and a high enough frequency response (at least 8 times firing frequency at max operating rpm) you can attach it to the prop hub, take the data for speed sweeps, download it and FFT it to look for resonance. This too can work, but can be difficult to debug. In the auto industry we use such things on running vehicles...

Billski

#### wsimpso1

##### Super Moderator
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TV: (belt, crankshaft, prop): Is the problem even practical to address for a homebuilder? It would seem that the vibrational attributes of the most important moving parts are not easily known by a homebuilder, and the results of interactions between them would require tools and techniques that are not available, either.
1) Have I got that about right?
Close. You can as an EAA'er get SolidWorks for free and model individual parts, get mass, inertia, and even resonant modes and frequencies for the individual parts, but you can not just assemble the parts and run them on the free version. There are ways to mimic the assembly in a single part and run the Eigen solver, but you have to be clever...

2) Is there a "prudent approach" that can be taken, absent a complete TV analysis, that can get us into a likely safe window? For example:
a) If successful PSRUs are known (based on field experience), can we determine the applicability of that history to another (new) PSRU/engine/prop combination? What attributes would need to the same to make that previous history a good guide?
I call this monkey-see monkey-do engineering and it can work. You have to closely imitate the big inertias, the primary spring rates, and the architecture as these set the Eigen modes and the frequencies. Architecture includes support of shafts - length between supports, diameters, if cantilevered or not, etc. You also have to avoid adding any new big inertia or new soft springs as these will change things. This is why I find it so important that each drive maker track the engine side and prop side inertia of their successful applications and their unsuccessful ones, then plot the inertia against each other noting which are which, and showing good and bad regimes.

b) Avoiding first-order prop/crank/PSRU resonance: as this often occurs below "usable for flight" engine RPMs, can we achieve usable improvements through use of belt slip/idler pulleys, etc, or are sprag clutches, Guibo "donut" dampers, or other measures required?
BIG TOPIC. I will get into this in a separate reply

c) Assuming that even a thorough analysis will require testing, what would a thorough test program for a one-off PSRU look like? Tricks (e.g. strobe photography useful for belt/torsional dampers? Can commercial "knock sensors" be used to tell us something about gear lash issues?)

I know this goes outside the treatment billski probably intended with his (very handy) tutorial. Maybe it can be discussed in another thread, if useful.
I covered this in other posts on this thread. Possibilities exist for the clever. The only ones that I KNOW will be successful likely cost more than the engine and drive will (Rotec used by a torsional vibe guy for a couple days). Not reasonable for a one-off, but definitely in range for somebody producing and selling the things...

Billski

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#### Hot Wings

##### Well-Known Member
HBA Supporter
Log Member
I'm wondering if all of this recent posting should be moved to a separate thread rather than loading up a sticky?

Since this is wsimpso1's domain I'd suggest that he and the moderators separate the basics and the discussion - then leave the basics here and reference the new discussion thread with a link?

Might also be a good idea for the other stickies as well?

#### pictsidhe

##### Well-Known Member
My audio idea is not to use a microphone, it's to use either a pair of accelerometers (to cancel linear vibrations), or a rotating weight on a strain gauged spring, then use cheap and available audio electronics to get the signal to a PC. Small FM transmitters can be had in small sizes for peanuts and seem ideal for this. A modern version of torsiograph used to diagnose Wrights woes.
Rotec is out of my budget. But, if I get far enough to consider selling stuff, I would definitely consider a professional test to check for things that my improvised methods may have missed.

#### BBerson

##### Well-Known Member
HBA Supporter
There is a YouTube video where the late Gene Smith explains the one way clutch effect of his belt idler tightener.
I watched him fly year after year at Oshkosh, which was impressive to me.
The redrive is no longer available, as far as I know.

#### markaeric

##### Well-Known Member
My audio idea is not to use a microphone, it's to use either a pair of accelerometers (to cancel linear vibrations), or a rotating weight on a strain gauged spring, then use cheap and available audio electronics to get the signal to a PC. Small FM transmitters can be had in small sizes for peanuts and seem ideal for this. A modern version of torsiograph used to diagnose Wrights woes.
Rotec is out of my budget. But, if I get far enough to consider selling stuff, I would definitely consider a professional test to check for things that my improvised methods may have missed.
I wasn't suggesting using a microphone, but a microphone interface (preamp + analog to digital converter + pc interface like USB). Check out those links I posted if you haven't already, and you will see that many of the sensing techniques are pretty simple and can potentially be done on a small budget. Though I don't know how well audio equipment would work for something that outputs a square wave, at least not without some additional signal processing before going through an [F]FT.

#### Vigilant1

##### Well-Known Member
I'm wondering if all of this recent posting should be moved to a separate thread rather than loading up a sticky?

Since this is wsimpso1's domain I'd suggest that he and the moderators separate the basics and the discussion - then leave the basics here and reference the new discussion thread with a link?

Might also be a good idea for the other stickies as well?
FWIW, as someone who is responsible for taking this discussion off the original "sticky-worth" path, I have >no< objection to moving my posts elsewhere, or to deleting them entirely if that serves the greater interest.
There is a YouTube video where the late Gene Smith explains the one way clutch effect of his belt idler tightener.
I watched him fly year after year at Oshkosh, which was impressive to me.
The redrive is no longer available, as far as I know.
I wasn't able to find that video. I understand in concept how that might work (since the idler is on the "slack" side of the belt, it would allow the prop to smoothly "overrun" the engine's drive pulley in between torque pulses of the engine). But (and this is just "gut engineering", take it for what it is worth) that these pulses would be of such high frequency that it would seem improbable that the idler actually displaces appreciably in the time available. And the idler would not serve to disconnect the prop hub/pulley from excitation by the engine during the periods of increasing torque.
From the "field experience" side: How did the Big Twin redrives perform in practice? I haven't heard of problems, but I don't now how many they sold, how many hours were put on them, what types of props they were mated to, and what type of service they saw.

This is the whole thing of figuring out if the first torsional mode frequency is significantly above max firing frequency, significantly below idle firing frequency, or within the range of firing frequency. Here's why you might need to know this:

If you have a "stiff" system, where first torsional mode is above the operating range, the entire system accelerates and decelerates with the crank, in phase and somewhat amplified. The amount of prop shaft acceleration is decreased relative to the engine side shaft, but it still cycles with the engine and is somewhat amplified, so you have to design everything to stand the firing order accels and thus torques, including the bearings. Firing torques are much larger than the mean torque of the engine. Props and flywheels bolted directly to the crankshaft flange are really beefy for exactly this reason - there has to be enough torque capacity in the joint to keep the parts from slipping;

If you have a "soft" system, where first torsional mode is below the operating range, everything from the crank to the springy element is accelerating and decelerating with the crank, while everything downstream is seeing a small fraction of the firing oscillation, and can thus be designed to a level modestly above the mean torque in the system. This is why transmission components and driveshafts with big gear ratios can get by with bolted joints that are lighter than the crank to flywheel or prop bolts;
Just from what I've read about the rigor needed to assure a geared redrive stays in the "stiff" mode (strict attention to gear lash reduction, etc), is it conceivable that a poly-v belt system could be stiff for our present purposes? I would guess (and that's what it would be), that any poly-v belt system would be "soft" forour purposes.

And if your firing frequency coincides with any of your resonant mode frequencies, well, it is likely to tear itself apart;
This seems to be the very toughest nut for a homebuilder thinking of designing his/her own "soft" system. And when we throw in the uneven firing pattern of a V-twin (boom- 270 deg - boom - 450 deg - boom . . .), the potential system resonances get yet more complex.

If someone has the spring rates and inertia of the parts and sends them to me, I will find a way to run it and get the modes and frequencies. I might even be able to calculate spring rates and inertia with enough detail on the parts...
That's very generous--thanks.

Related note: Flexidyne couplings. I knew that Molt Taylor used this type of "dry fluid coupling" in some of his designs. I also toured the operational Wright B Flyer replica a few years ago and they use a similar coupling in this design (the plane looks like a Wright B Flyer, but uses a modern engine and materials. I guess it is a "standoff replica"). These Flexidyne couplings seemed an interesting way to isolate an engine from a driveline/prop. Simple in concept, but not especially light. A 50 HP unit would use about 6 lbs of steel shot as the "fluid." Engine starts under zero load, there is zero slip at full RPM and torque output.

#### pictsidhe

##### Well-Known Member
Optibelt got back to me. They do not disclose the spring constant of their belts to customers :/
I did find it for gates polychain gt 8M toothed belts, but not from Gates. I was looking at largish pulleys and a 63mm belt for a stiff 627 redrive. I would be able to dispense with the flywheel entirely, saving lots of lbs, but thats a big and expensive set of pulleys and belts.
The uneven firing of V-twins would give some extra higher harmonics, which would be no trouble for a soft system. They may bother a stiff system, though.

#### BBerson

##### Well-Known Member
HBA Supporter
The Big Twin was sold as a tested package, engine/belt drive/prop, demonstrated in flight year after year.
I haven't seen any others, such as Ace.

#### Hot Wings

##### Well-Known Member
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Log Member
I recently acquired Den Hartog's 'Mechnaical Vibrations', but haven't read it yet. I expect it to be very useful.
Related to this, I had not heard of a mechanical harmonic analyzer until I read it in this book.
You may find this interesting. I did.

#### BBerson

##### Well-Known Member
HBA Supporter
Gene explains the over running action some here (about 5:00 minute point)

#### Vigilant1

##### Well-Known Member
Optibelt got back to me. They do not disclose the spring constant of their belts to customers :/
I did find it for gates polychain gt 8M toothed belts, but not from Gates. I was looking at largish pulleys and a 63mm belt for a stiff 627 redrive. I would be able to dispense with the flywheel entirely, saving lots of lbs, but thats a big and expensive set of pulleys and belts.
You may have already been down this road, but this spring rate info may be of interest, even if it is not tech info for the belt you are looking for:
Gatesfacts pdf on synchronous belts--see pg 7 (14mm belt).
Stiffness. The dynamic elongation of a belt, as well as the stiffness, can be best quantified by the use of EA or spring rate charts. Simply stated, the EA product is Young’s Modulus (E) times the Cross Sectional Area (A). A 1-inch-wide belt is placed on a test apparatus and its elongation is measured under various tension loads. Several belts of the same size and construction are tested and the average elongation is plotted on the EA chart, Figure 9.[in the PDF] The deviation from this curve by any single belt can be as great as ±30% due to normal material variations
Now, that info sheet is almost 30years old. It is likely that newer belts (esp those with Aramid fibers) have tighter tolerances.

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