# Belt Drives and design

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#### wsimpso1

##### Super Moderator
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Pendulum dampers were invented for use on the big radials. read a first person account of that here:

Piston Engines

The hockey puck type has been completely eclipsed by the the roller-weight type. Hockey puck type was actually available as The Rattler for Detroit V-8's, it replaced the front pulley/ harmonic damper. Story was it worked at higher rpm, had rollers tuned to 4th and 8th order of rotation (the biggies in V-8's), but is no longer available.
Roller-weight type have been applied to airplane piston engines since the late 1930's, and are currently in use in some cars, mostly diesels, supplied by ZF-Sachs and LuK. LuK holds the patents, so ZF-Sachs sells under license. There are even multiples of them hung on some large helicopter rotor sets. These gadgets must be designed and developed to rather precisely match the vibe orders you are after, one swing radius per order attacked. Where they are designed/developed to work, they work extremely well, sucking off firing pulses very nicely on diesel engines. I have seen data indicating 95% reduction of tuned order. But if you need 2x engine order and yours absorbs 2.25x engine order, it is doing just about zero for you. So the design has to be adjusted to be very close to what you need. And once you suck off the biggest order, what used to be the second biggest vibe order now becomes the biggest vibration. It is like the light under the door... LOL.

On the crankshaft, they have small radius and so these tuned counterweights have to be pretty big to be effective. For vehicles with transmissions, these gadgets can go on at larger radius on a flywheel or inside a torque converter and so can be lighter. In automatic transmission vehicles, they actually work better on the wheel downstream of the spring element. Tuning to run in air (manual trans flywheel mounted) is different from tuning in oil (mounted inside torque converter), so be careful to run in the intended fluid or it simply won't work. Also, know that cars and trucks make their big firing pulses during accel, so the manufacturers actually tune the tracks to be ever so slightly above the intended firing order - you get better isolation during accels that way. Buying car systems to attach to your airplane may not be an effective strategy.

Now how would this apply to our problem? Order Tuned Torsional Pendulums will reduce the order attacked. but not eliminate it. In cars and trucks, they are used to reduce firing order vibration through the drivetrain because the customers can feel that vibe. Turbocharged diesels are particularly bad, so more effort is applied there. They are not being used to suck off driveline resonance in cars and trucks. Resonance is handled by driving resonant frequencies low with arrangement of inertia and springs, adding soft elements, then applying frequency tuned absorbers where needed.

To have value in Engine-PSRU-Prop arrangement, the pendulum could be applied to reduce engine firing pulses, but they are still there and so damaging amplification can still occur. The other engine orders are also still there with all their damaging potential should they line up with system vibe modes. Even fire four cylinder engines have 2x (compression-firing), 4x (pistons accelerating back and forth in the bores), and a bunch of others due to all sorts of issues that no one has been able to control. So maybe you put the gadget between engine and prop and tune it to absorb the natural frequency between engine and prop. That absorber might have to be big indeed. Maybe you tune the order of the gadget coincide with the vibe on frequency and rpm. OK, that gets one. Ross and his buddies have already experienced more than one rpm range - these vibes may be the same mode but with a different order coming from engine or the same order from the engine but a different mode. We do not know without more involved modeling and/or instrumentation.

Instead of an order tuned absorber, would not a frequency tuned absorber work better on beating something that happens at a particular frequency? They too exist and are way simpler. Steel sleeve on a rubber sleeve pressed over a shaft, used on front crankshaft pulleys (called harmonic dampener) and driveshafts/halfshafts on some vehicles. But you only get one frequency per gadget, and with a poor scheme, you might have more than one mode you need to beat. Be careful which ones you beat, and which ones you leave.

The really big trick in managing vibration is not in knowing the gadgets that can handle any one mode and forcing function combination, but in having a strategy of knowing all of the vibe modes and exciters of each layout so that you can pick a layout that can then have gadgets added to handle the modes. In road vehicles, we put the clutch or torque converter at the engine with a soft element there to isolate the engine firing order from everything else, then add the gearbox. Layouts with the clutch elsewhere, gearbox remote, etc have way more troublesome situations than what is common in cars and trucks. AWD racecars have been built using unusual configurations and had problems no one ever solved.

Much more complicated schemes exist. A standard helo is one with a piston engine, transmission, flexible shafting to one big rotor, even more flexible shafting to another gearbox and rotor. Turbines appear to have made part of it simpler - no firing pulses - but there are still a bunch of other vibe forcing functions out of the engine, accessories, gearboxes, shafts, and rotor sets). Then there are multiple engine sets, double main rotor helos, and then tilt-rotors - an engine and gearbox on each wing, a rotor on each wing, a shaft system with clutches between the engines for cross driving in an engine-out situation, and tilting the whole thing so it can fly as an airplane and as a helo. And all of these have ground resonance as significant modes too. Ugh.

By comparison we have it easy - put the firing frequency well below idle but safely above cranking speed with a soft element, make everything else stiff enough so the remaining modes are off range high, then see if anything else is hiding, and handle them. Keep your torsional vibe analyst and instrumentation geek in the loop, as you will still need their help at any stage of the process.

Billski

#### dog

##### Well-Known Member
Found this as another comarison of TV "dampers",mentions various types.

Also the "rattler" apears to be in production still.

#### DanH

##### Well-Known Member
Umm, guys, you have a world class mentor who has written endlessly for your education. You have a small bibliography of good textbooks, and simple, effective software tools keyed to being educational. I humbly suggest that you skip the gadgets and magazine ads masked as articles. Work on the basics, just as Bill writes.

Pincraze, you out there? I assume you have now established inertia values for your basic components (with ratio adjustment for the driven side parts), and stiffness for any shafting you have in mind. That's enough for a few first pass Holzers of component arrangements. Reduce it to a three or four element model. Run two, in which you move the soft element location from the flywheel to the upper sprocket. Tell us what you learn.

#### dog

##### Well-Known Member
Umm, guys, you have a world class mentor who has written endlessly for your education. You have a small bibliography of good textbooks, and simple, effective software tools keyed to being educational. I humbly suggest that you skip the gadgets and magazine ads masked as articles. Work on the basics, just as Bill writes.
Well well.
Dan.
My post was on topic, and in good faith.

The "rattler" appears to be directly relevant to the discussion insomuch as it is a type of pendulum damper, is in production, and therefore may be familiar, and also may have relevant engineering data available. The other "ad" linked to is also directly relevant as the whole thing relates to devices of the types being discussed here and while not academic in nature does point to a variety of engineered solutions (gadgets) again perhaps familiar, or useful as illustrative talking points. What I was thinking when I dug into what Billski posted about the "rattler" was that this is the thread that all the other threads want to be, that we have 100 pages to go and that I was bang on topic.

Still do.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Found this as another comarison of TV "dampers",mentions various types.

Also the "rattler" apears to be in production still.
These are all front end accessory devices intended primarily to protect the crank, cam, and accessories on high revving race engines. Believe me when I tell you, racers run up toward and into crankshaft resonance. 2x firing is usually the forcing function that approaches crank resonance, which is 4x rotation in I-4, 6x rotation in V-6, and 8x rotation in V-8. This is fundamental frequency of the crankshaft by itself that firing is approaching. Virtually all durable engines are designed with the crank fundamental frequency set at least 2-1/2 octaves above max firing frequency - this is to put resonance out of reach of both firing frequency (biggest at WOT) and 2x firing frequency (second biggest and always big). Now make a race car out of that basic architecture, the crank and block are still about that size and resonant frequency, but they tune the engine to run the revs up (More engine turns is more air is more power), and now the 2x firing goes through the resonance frequency. OK, we upgrade the block to four bolt mains or full girdle blocks to make the cases stiffer, then change from cast iron to forged steel crankshaft, then folks make the journals a little bigger, so it can go to higher revs before it self destructs, but it is only a little higher, and you are still getting into crankshaft resonance. Ugh. That is where these guys are trying to give them a little more headroom for revs.

The elastomeric ones work the same way stock does, but tend to be beefier and survive longer as racers. They also tend to hold balance better. They are frequency tuned absorbers, a weight on a spring. They will very nicely pick off a vibration of their tuned frequency and of vibrations at multiples of that frequency. They will also tend to pick off some energy at 1/2 the tuned frequency. Usually they are tuned to a resonant frequencies of the most sensitive gadgets on the front end - Cam drive and alternator are favorites. They have little impact on transmitted vibration at the other end of the crank. If you had a particular resonance in the FEAD, you can drive its amplitude down by tuning the proportions of rubber and inertia to match it.

The fluid filled ones work great for letting drag cars get through runs without broken cranks, and they have a following in circle track racing too. They have this neat effect of taking off the most energy where the most energy is. Good for crank survival, not so good for picking out a resonance between crank and prop and suppressing it. I question their ability to help much when we start talking about the crank/flywheel oscillating opposite the prop and gears. We are talking a couple order of magnitude more energy in the oscillation than in a crankshaft singing at its natural frequency.

The Rattler is a hockey puck style order tuned absorber. Nice gadget, glad to see it is back on the market. The problem with hockey puck style absorbers is the radius is small and so is the roller mass, which limits their effectiveness. That was why the big counterweight type came to predominate in big radials and a number of Lyc and Cont boxer engine models - they needed more mass at that radius to pick off most of the vibe. The ones listed are tuned for V-8, V-6, and I-4 and set up for install on GM engines only. The tuning for a number of firing pulses per rev will work for any engine with that same number of cylinders. If one were industrious enough, one could buy the one for the I-4, reverse engineer your way to installing it on an even firing four, and suck off a chunk of the torsional vibration at firing and 2x firing (2x and 4x rotation) at all speeds. Thing is that if you have a natural frequency in your operating range, you will still have some a big fraction of the original forcing function exciting it, which can still be amplified and break things.

Then there is the fundamental issue that these guys are the wrong end of the crank shaft. They are for taming some sort of twisting of the front end of the crankshaft. So even if it does make the front end dead smooth in rotation, the back end still winds up and unwinds for every power stroke and the other torsional orders too. And these gadgets do little for vibration at this end of the crankshaft.

Nope, the fundamental is still to isolate firing from the downstream components with a tuned soft element, then put all of the other orders at or above 2.5x max firing frequency with short stiff shafts, stout housings, and beefy bearings.

Billski

#### dog

##### Well-Known Member
As soon as I saw the picture of the "rattler" I thought I can learn the math for that AND build one as part of a flywheel.
Slugs in holes,of a certain mass,as a certain
radius,with a specific amount of movement.
Trying to visualise what happens with the "rattler", the crank accelerates on a combustion event,and leaves the mass of the rattler behind,
reducing the twisting moment on everything up and downstream,then as it decelerates the
rattlers catch up and add there momentum and again reduce the reverse twisting moment.
All of the other pendulum dampers look ultra
gadgety and of the not happening in a shop near me variety.

#### plncraze

##### Well-Known Member
HBA Supporter
I am still reading this thread and will post some pictures, drawings and revised Holzer numbers soon.

#### wsimpso1

##### Super Moderator
Staff member
Log Member
As soon as I saw the picture of the "rattler" I thought I can learn the math for that AND build one as part of a flywheel.
Slugs in holes, of a certain mass, as a certain radius, with a specific amount of movement. Trying to visualize what happens with the "rattler", the crank accelerates on a combustion event, and leaves the mass of the rattler behind, reducing the twisting moment on everything up and downstream, then as it decelerates the rattlers catch up and add there momentum and again reduce the reverse twisting moment. All of the other pendulum dampers look ultra gadgety and of the not happening in a shop near me variety.
I searched on "bifilar order absorber pendulum" and got a bunch of stuff right away. It is all pendulum theory when the gravity running the pendulum is from the gadget spinning at engine speed. The more massive the rollers, the more reduction in vibe your get. There is a minimum to make the things effective. Have fun. Oh, PM me if you want me to check your work.

I never designed these, we had two suppliers competing for the business, LuK owned the patents, ZF-Sachs was paying licensing fees for building on LuK's patents. Looking at the patents might help you. LuK is in Buhl, ZF-Sachs is in Schwienfurt. Some of the history is covered in the the "No Short Days" article and in the PhD theses...

Billski

#### Lendo

##### Well-Known Member
Thanks Billski, you certainly know your subject welI - I wish I did, but your explanations did cover a lot of detail.

The attached by Dog also gave good information. I notice the Rattler is suggested to eliminate all vibrations, are you suggesting this is misleading.

The Rattler to my mind is a Pendulum Damper, that must be tuned to an engine for best results and why I suggested bearings for easy adjustment of weight for the novice experimenter. Bearing slap can also be softened with light springs between them and lever arms can be adjusted with making the retainers a bigger diameter, grooved on a Lathe to retain the bearings and springs - all contained with a cover plate.

I'm trying to think simple, adjustable and low cost.
George

#### Lendo

##### Well-Known Member
Dog, If you do any experimentation with my suggestions using bearings, there's some things to consider, Pendulum travel, Lever arm (Radius) and weights naturally. On Pendulum Travel I would split the retainer into sections maybe 4 for smaller radius more for larger radius, if that makes sense to you.
George

#### wsimpso1

##### Super Moderator
Staff member
Log Member
The Rattler to my mind is a Pendulum Damper, that must be tuned to an engine for best results and why I suggested bearings for easy adjustment of weight for the novice experimenter.
Not they way they work George.

Two values determine the order that is smoothed out - the swing radius of the pendulum and the radius from crankshaft centerline to the center of pendulum swing. The ratio of these two is adjusted to get the order right, and there is an exact formulation out there that works. Once you have it set to say 2x rotation, you get 2nd order absorption. You can attach that package to any four banger you want and it will absorb 2nd order just fine.

The other major variable is pendulum mass. If it is too small the absorber is not effective. Make it big enough and it works great. There is also a formula for this out there someplace. So, if you have an absorber that works fine on one gasoline four banger, to make it work on a much bigger four banger or a diesel four banger, you will probably need bigger weights.

If you want to smooth out an even fire four cylinder, you will need pendulums tuned to 2x to get firing pulses. The next biggest pulses occur at twice firing, so maybe you want one pendulum out of four tuned to 4x. Usual application in cars and trucks is all four masses at 2x, but folks are continuously on the lookout for an application needing 4x.

Go up to an even fire V6, and you will need tuned to 3rd order. Maybe one out of four should be tuned to 6x, maybe not.

V8 require 4x and maybe 8x. The Rattler for V8s appears to have pucks tuned for both orders.

Billski

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#### DanH

##### Well-Known Member
Well well.
Dan.
My post was on topic, and in good faith.
Belt drives?

The "rattler" appears to be directly relevant to the discussion insomuch as it is a type of pendulum damper, is in production, and therefore may be familiar, and also may have relevant engineering data available.
Be serious. The original paper on the application of pendulum absorbers to aircraft engines was written by E.S Taylor of MIT, published in SAE Transactions, March 1936, Vol 38, #3. You'll find pendulum absorbers beginning on page 219 of Mechanical Vibrations, and you can have your very own copy for a whopping $14. You'll find an entire chapter on them in the 1958 edition of A Handbook On Torsional Vibration, plus a foldout with equations for all the different types. I'm sure there are many, many more good reference works available at your local university library. Any of them beat magazine filler...but none have much to do with belt drives. Focus on fundamentals. #### dog ##### Well-Known Member Belt drives? Be serious. Focus on fundamentals. Thats more like it. Dan. Critisism WITH suggested reading. I am focusing on fundamentals. Honestly. I need a picture in my head to hang the math on. And even more fundamental for me is to have a physical end goal. The rattler is an excellent example of something to hang fundimental math on,and as a rank beginer it answers another fundimental need which is to have something to hang the terminology on. University?An hour drive in good weather.Thats two hrs fuel, food in town, parking, oops, then double all that to return the books. Call it$100 plus time.
My phone has brought me the world, cranky profesors and all, book recomendations, and Machinery's Handbook is finding its way to me right now, slightly dinged copy, landed for \$25 ca. It will just be here one day when I get home.
And speaking of cranky professors,I know just how lucky I am to be taking any part in this disscusion.
Very lucky indeed.
Thank you all.

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#### DanH

##### Well-Known Member
Thats more like it. Dan. Critisism WITH suggested reading.
Let's skip the sensitivity training. I'm incorrigible, and happy about it.

I am focusing on fundamentals.
No, you're not. Re-read this from Bill, just a few posts back...

The really big trick in managing vibration is not in knowing the gadgets that can handle any one mode and forcing function combination, but in having a strategy of knowing all of the vibe modes and exciters of each layout so that you can pick a layout that can then have gadgets added to handle the modes.
"Knowing all the vibe modes and exciters". Start with layouts and frequency prediction. When you have those well in hand, then maybe you come back to pendulums. Until then, it's just a distraction.

University?An hour drive in good weather.
Been there, done that. There's no shortcut.

#### AdrianS

##### Well-Known Member
I assume someone has tried a sprung belt tensioner to make it a soft coupling.

And that it didn't really work well enough.

#### dog

##### Well-Known Member
Let's skip the sensitivity training. I'm incorrigible, and happy about it.

No, you're not. Re-read this from Bill, just a few posts back...

"Knowing all the vibe modes and exciters". Start with layouts and frequency prediction. When you have those well in hand, then maybe you come back to pendulums. Until then, it's just a distraction.

Been there, done that. There's no shortcut.
Dan.

I agree with much of what you say, not quite all though. Having a complete picture in my head is the starting place, I was stuck trying to build an image of complete system, the" gadget" closed the circle for me, it isn't central, and is exciting only in that it helped me SEE how the inertial and spring elements react with each other and how, one way or the other, we must manage that in a real machine.

I get it, there is no difference between an individual crank throw and any other "gadget". For me this process is the first and steepest part of the learning curve. AND the reason "my" process is pertinent is that there must be others who have floundered around WANTING to do stuff and failed over and over because they have not learned or been TAUGHT to build a picture in there head, hang words(terminology) on that, and then, and only then assign symbols to those real things, acquire numerical inputs and run the equations.
While not incorrigible, I am violently obstreperous on occasion.

Cheers.

#### Lendo

##### Well-Known Member
Certainly can't knock some who is well educated and trained to think and understand in a certain way - then there's the rest of us who must struggle with concepts and try to think outside the Box, striving for simplicity - where just maybe there's none. I know that feeling well.
George

#### DanH

##### Well-Known Member
Is anyone here actually designing and building a belt drive?

#### wsimpso1

##### Super Moderator
Staff member
Log Member
I assume someone has tried a sprung belt tensioner to make it a soft coupling.

And that it didn't really work well enough.
Belt tensioners, where they are used, are mostly there to take up the slack that starts small and increases with use in these systems from wear.

In chain and cog belt drives, there is no tension needed on the undriven side of the system. Engine torque divided by engine side sprocket radius is belt tension, which then is multiplied by prop side sprocket radius to get prop torque. Rpm sees a commensurate decrease in speed. The belt on the drive side of the sprockets is slightly stretched by this force in proportion to the steady state engine torque. That describes the steady state situation.

Superimpose upon that the oscillations from firing pulses and other parts being accelerated about as the engine spins, and we have the behaviour. How big are the oscillations? Not big at all, but pretty fast, such that the tensioner will have a tough time keeping up with it.

I just put together a little spread sheet and calculated the approximate swing due to 2x and 4x vibe - the big orders made in a four cylinder engine. I get about half a degree of total swing maximum, and it gets smaller as your rpm goes up. In a road vehicle or a machine spinning a hydraulic pump, you can get full engine torque at any speed, so the numbers at low to medium rpm do get bigger, but even then, you are on the order of 3-4 degrees maximum.

How did I do the calculation? 2x is firing pulses and this basically varies with engine torque. Engine mean torque while driving a fixed pitch prop basically goes with prop speed squared. At peak engine torque a naturally aspirated gasoline engine makes about 2500 rad/s/s of firing accel, called alpha. Peak amplitude of this firing pulse is alpha/omega^2 where alpha is in rad/s/s, and omega is firing frequency in rad/s. Turn that into degrees peak by multiplying by 180/PI(), and you know the one-way amplitude. Total for the whole cycle is twice that. Then we have 4x, which has about the same alpha all the time, about one quarter as big as peak at 2x. Again this is all for a four cylinder engine. Add them up, and we know how far to expect the crank sprocket to cycle.

Back to the swing - if the engine side sprocket is only swinging 0.5 degrees and the sprocket radius is 2", that is 0.018" of total swing. Let's also remember that this firing cycle is repeating at 33 times a second (four banger, 1000 rpm). If the prop were spinning at an absolutely smooth speed, the belt would lengthen and shorten 0.018" on the drive side and the slack on the other side would change 0.018" with each firing pulse. This is superimposed upon whatever the stretch in the belt is due to steady state torque. The belt is sort of like a drive shaft in that it deforms to take the mean torque and then the forcing function is added to it. Then tensioner can keep the slop on the non-driven side from flopping around, but otherwise, it is not doing much, and it sure can have a hard time keeping up with the firing rate.

So far, we have been assuming isolation - the prop spins pretty steady compared to the engine. Now let's say we put the whole thing in resonance... The prop and engine are turning together in steady state, but the vibe is engine and prop moving opposite each other. Every firing stroke the engine tries to go faster than the prop and between firing strokes the engine tries to go slower, and little bit more energy gets added to the vibration on every cycle. Even at say 8 times the nominal , we are still only talking a little over 1/8" of swing. And you are at break the drive level forces... Now, the belt tensioner can not do much for this problem here.

Go to v-belts... The V-belt requires off side tension to make it carry torque and it slips when overloaded. When operated in isolation mode, the analysis looks about the same, except that you have static tension in the belt from mean torque plus the oscillating component. If you get to the point of belt slip, whether from static overload (not enough preload, too much mean torque) or from cyclic overload (firing pulses, resonance) the belt and sheaves get hot, and thermal failure follows shortly. If you get clever enough to make the tensioner fast enough to follow firing pulses, you can avoid the negative accel between firing pulses from being added to the resonant energy, but the positive side will still be there. As long as you have resonance, it will still amplify up to damaging levels. Make the belt slip during resonance, and only do it for a few firing strokes after engine lightoff and you might be able to tolerate the belt life impact. Run there steadily, and you will fail belts.

So either way, to have an unconditionally safe design, you still have to run resonance either an octave or more below idle firing or 2.5 octaves above max firing. Taking a bit more risk, but in a manner that the world has sometimes found acceptable when spinning fans, props, centrifugal pumps, etc, we can have prohibited bands that are above idle but below all nominal flight speeds that has a resonance, and we try hard to pass through those bands quickly. Maybe at power settings above idle and above taxi power, they are OK. Putting it around 50% power is much scarier.

That is my story and I am sticking to it.

Billski

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#### dog

##### Well-Known Member
Is anyone here actually designing and building a belt drive?
Yup,and @ home even.
Working my ass off lining everything up
and ditching/selling non aviation projects/distractions.