Propeller Inertia vs Torsional Amplitude

A few months back Ross asked a very good question; why did he observe a significant increase in torsional vibration when he swapped to a heavier propeller on a test subject? In retrospect, I didn't do a good job answering his question. At the time my mind was focused on change of natural frequency with a change of inertia or a change in a connecting stiffness. The question really dealt with amplitude, ie, an angular measurement of shaft twist between opposing inertias.

Not all bad however; we did explore some very simple math to demonstrate that a change in inertia did not shift frequency very much, a good rule of thumb to remember. We also looked at a change in connecting stiffness and established a similar rule; it has a larger effect on frequency than a change in inertia. You can find the the discussion here:
http://www.vansairforce.com/community/showthread.php?t=19030&page=2

Anyway, I was left with a nagging question. Could I establish a simple rule-of-thumb for change in amplitude with a change of prop inertia? I am a student of vibration, not an expert. Such questions are how I learn, so it made my list of things to do in spare moments; bedtime reading if you will.

Well, I think I've got it. The nice thing is that understanding it requires practically no math at all, but it does assume you understand the concept of mode shape.

When inertias are connected to shafts (each shaft having a stiffness value) and set to oscillating torsionally, the direction of rotation for the inertias opposes each other; some rotate one way, some the opposite. The degree of rotation of each inertia (amplitude) is predictable (a function of the relative size of the inetias and the magnitude of the connecting stiffnesses); big ones rotate less, small ones rotate more. The number of available natural frequencies is equal to the number of inertias minus one; thus for a system with three inertias there are two natural frequencies. Terms vary depending on who you're reading, but I'll refer to them as F1 and F2. Another way to say F1 and F2 would be the "first mode of vibration" and the "second mode of vibration". Here's a drawing to illustrate:



It is important to establish the actual relative amplitude (the relative degree of rotation) for the inertias, and the classic way of doing so is called a "Holzer table". One inertia is assigned an angular displacement value of 1 and the others are compared to it. The results of a Holzer are often graphed for illustration, and that graph is called a mode shape. Here's an example from Den Hartog:



From left to right, you're looking at a seven-inertia model; a large-inertia generator, a flywheel, four diesel crankthrows and the accessory drive. The horizontal line is zero twist. If you wish, think of the curve below the line as being clockwise rotation and the curve above the line as being counterclockwise, although it really just means "in opposition". The little circle where the curve crosses the zero twist line is called the "node". The numbers are expressed in proportion to the amplitude of the accessory inertia. It tells you in the first mode (natural frequency 5300 VPM, or 88.33 hz) the generator oscillates with an amplitude 5 times less than the other end of the system. The second mode is kinda scary, because the curve is steep between the flywheel and the accessory end, meaning that if the system resonates (if its natural frequency of 10,950 VPM or 182.5 hz is matched by a driver of the same frequency), the crank will be very highly stressed in torsion.

So much for mode shape. Now here's the rule-of-thumb.

I ran some 3-inertia Holzer numbers (software, easy to do) for a purely theoretical system with inertia and stiffness values like we might find in the small engine-propeller systems we use. I picked 0.5 Kg-m^2 for the prop, 4500 Nm/radian for a rubber coupler or torsion spring forward of the flywheel, a flywheel inertia of 0.05 (1/10 of the prop inertia), 45000 Nm/rad (10x the rubber coupler) for the crank stub and again 0.05 for the crank inertia. The first mode result is +1 for the prop, -4.849 for the flywheel and -5.151 for the crank. Put another way, the flywheel-crank assembly has roughly five times as much amplitude as the prop.

Re-ran the Holzer, this time with double the prop inertia, 1.0 Kg-m^2. The new values were +1 for the prop, -9.725 for the flywheel, and -10.28 for the crank. Notice the amplitude almost exactly doubled.

Again, this time with 3x prop inertia; 1.5 Kg-m^2. Values were +1, -14.6, and -15.4. Three times the prop inertia resulted in three times the shaft twist.

The rule-of-thumb is obvious; shaft stress increases in almost direct proportion to propeller inertia.

Imagine a mode shape plot of the above. The curve would cross the zero line between the prop and the flywheel, then run almost flat between the flywheel and the crank inertia. This is good; it says almost all the twist is taking place in the rubber coupler, with very little torsional stress in the crank stub.

I also ran Holzer values for the same three prop inertias, but this time with 45,000 Nm/radian forward of the flywheel to simulate a "hard" system, ie, no soft coupler, just a steel shaft equal in stiffness to the crank stub. New values were:

0.5 prop: +1, -3.534, -6.466
1.0 prop: +1, -7.358, -12.64
1.5 prop: +1, -11.18, -18.82

Again, the rule-of-thumb holds true, but note the change in the mode shape. No surprise; with equal stiffness on both sides of the flywheel, the crank is now getting twisted much harder. Not only is the curve steep between the flywheel and the crank, but the maximum value is higher compared to the "soft", rubber-coupled system.

Comments welcome. As always, I appreciate "professional supervision" <g>

OH, Dan you make my head hurt------------

propeller inertia and tortional amplitude--

Dan, after reading your dissertation on the above subjects, I really decided I had to jump in here and try to see where you obviously were on the wrong track, and how I might enlighten you as to the real causes and effects of tortional amplitudes as well as propeller inertia and vibrations, and their effects on airframes and engine parts, such as crankshafts, camshafts, and all other moving parts. However, after deep deliberation and my best efforts, I am humbled to admit I have to agree with everything you said.

Interesting Article on Torsional Vibration

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

Dan, very interesting topic.

I am wondering if the importance on the relative amplitudes is interesting, but not telling much of the story. The amplitude that matters is the total amplitude between masses (stick to a two mass system for now....). The relative amplitudes do not tell that story. They really only tell you where the node is, which has no real physical significance (it might be the one location on the shaft which is rotating at a constant angular velocity). For example, the actual twist total between the masses could be the same for both cases, where the prop's moment doubles or triples, even though the node has moved a lot. The movement of the node alone is not something that will be externally noticed, at least in a two mass system.

The equation defining the resonant frequency for a two torsional mass system with no damping is:

W=(Kt/(I1*I2)*(I1 + I2)^.5,

where W= omega, circular frequency, radians per second (2*pi*f), f being frequency
I's are the mass moments of inertia (mmi)
and Kt the torsional spring constant between the masses.

If we put your example values in this equation to examine the natural frequency shift, we get:

W1 = 314 rad/s (.5, .05, 4500)
W2 = 307 rad/s (1.0, .05, 4500)
W3 = 304 rad/s (1.5, .05, 4500)

W4 = 994 rad/s (.5, .05, 45000)
W5 = 972 rad/s (1.0, .05, 45000)
W6 = 964 rad/s (1.5, .05, 45000)

These changes to resonant frequency aren't much, due to the 10:1 minimum ratio of the large mmi to the small mmi.

The vibration that could be greatly affected by the props mmi is the engine on the mounts. Each cylinder's firing torque pulse may impart more angular acceleration to the engine with a larger mmi prop. In other words, a lighter prop may have been the component undergoing relatively large swings in angular velocity with each firing, while the heavy one is varying less (which causes higher peak torques on the crank, which in turn pushes on the motor mounts). I think we would be in deep trouble if we could actually sense the torsional vibrations of the crankshaft itself. I suspect the problem is more "macro". I'm not sure about this concept yet, but will think further...

It would be interesting to compare the mmi of the props in your example to the mmi of the engine around the axis of the crank.

Man, vibrations are a difficult subject!

Hi Alex,
<<The amplitude that matters is the total amplitude between masses (stick to a two mass system for now....).>>

Correct, for any number of inertias. I'm not sure what you mean by a distinction between "relative amplitudes" and "total amplitude between masses".

Ahhh, wait......are you thinking about shaft twist during resonant operation, in degrees? Perhaps an example to illustrate (terminology in this game is often a problem). See if this fits what you had in mind:

Assume F1 (first mode) is at 35hz. The system will start resonating when excited at about 0.8 of 35, or 28hz, but it won't have significant amplitude. When excited at 32 hz it will have more amplitude, at 35 it will reach peak amplitude (which can be very high), at 38 it will again have less amplitude, and at about 42 hz (1.2 x 35) things will be almost back to normal. A mode shape won't tell us the actual amplitudes reached at any of these conditions, but in every one of them the relative amplitudes will be identical. Using a two mass system with a prop inertia 10 times the engine, the opposing rotation for the two masses may be 0.1 degree and 1 degree at 28 hz, 0.2 and 2 at 32 hz, 0.5 and 5 at 35, 0.2 and 2 at 38, and 0.1 and 1 at 42 hz.....but in all cases the relative amplitude is 10 to 1....the mode shape.

A Holzer table is an intermediate step in the process of determining resonant amplitude.

<<..node....(it might be the one location on the shaft which is rotating at a constant angular velocity).>>

It is.

<< For example, the actual twist total between the masses could be the same for both cases, where the prop's moment doubles or triples, even though the node has moved a lot.>>

No, the total twist will double or triple.

<< The equation defining the resonant frequency for a two torsional mass system....>>

Right. That was the discussion from the previous thread.

<<Each cylinder's firing torque pulse may impart more angular acceleration to the engine with a larger mmi prop.>>

Sure, but with a conceptual tweak. It is true for every point in the RPM range, just not the resonant periods. It doesn't have much to do with the mode shapes of F1, F2, F(etc). Remember, the F's are natural frequencies. If they're not matched by an exciting frequency, the corresponding mode shape angular deflections don't happen. When matched and resonating, the first mode shakes the block very hard via reaction to the cylinder walls. However, take a look at the example for the 2nd mode shape in the previous post. It will shake the block far less than the 1st mode (hmm, maybe not, needs some thinking) but crank stress is higher. Mode shape does tell interesting things.

<<It would be interesting to compare the mmi of the props in your example to the mmi of the engine around the axis of the crank.>>

Yes indeed. I'll bet total engine inertia is quite large. And I suspect the wet-dog shake of a Lyc when it fires up is at least partially a matter of firing impulses matching the natural frequency of the engine assembly on it's mounts.

<<Man, vibrations are a difficult subject!>>

Careful, you'll get hooked too. <g>

The relative amplitudes in eigenfrequency analysis don't mean much when looking for the real amplitudes. One exception (sort of) is when damping is included, and your results are in complex mumbers with non-zero imaginary values.

The actual amplitude at ressonance is directly related to energy dissipation due to friction in bearings, internal (material) damping and viscous effects (propeller rotating in air for instance). The damping due to the propeller is large, but also very complicated because it is dependent on many factors that are unrelated to the initial problem (actual pitch, rpm, velocity of the aircraft and so on).

Let's take a very simple example. Consider everything equal, except that one of two propellers have more mass than the other. They are mounted on torsional springs, and for simplicity let's assume they are not rotating, only oscillating (easier to visualize when they have zero mean rpm). The driving force is a constant power torsional shaker. The one with most mass will have a ressonant frequency below the other one, but what about the amplitude? The one with a small mass will oscillate faster, and this creates more dissipation than the heavier one, and so it will need smaller amplitudes for the same dissipation rate. If the ressonant frequencies were 2:1, then the amplitdes would typically be 1:4.

Hello Bjørnar,
<<The actual amplitude at resonance is directly related to energy dissipation due to friction in bearings, internal (material) damping and viscous effects (propeller rotating in air for instance).>>

True; the Holzer calculation does not consider damping.

<<The damping due to the propeller is large, but also very complicated because it is dependent on many factors that are unrelated to the initial problem (actual pitch, rpm, velocity of the aircraft and so on).>>

That goes back to a question David asked a few months ago (change in propeller pitch quieted a gear rattle). At the time I could find little about the damping value of an air propeller. I'd love to have more information; is there an available reference specific to the subject?

<<The one with a small mass will oscillate faster, and this creates more dissipation than the heavier one, and so it will need smaller amplitudes for the same dissipation rate. If the resonant frequencies were 2:1, then the amplitudes would typically be 1:4.>>

For clarity (remember, I'm a student) let's explore inertia first, then damping.

The goal here was to develop a practical rule-of-thumb specific to our practical application; change in amplitude due to change in propeller inertia. So, is it possible to get a 2:1 shift in frequency using only a change in propeller inertia?

Using a Holzer code and not considering damping, it looks like the propeller inertia change required to shift first mode frequency by a factor of 2 would be impossible in the practical world.

With the more-or-less realistic values from the three-inertia example in the first post:

0.5 Kg-m^2, 4500 Nm/radian, 0.05 Kg-m^2, 45000 Nm/rad, 0.05 Kg-m^2

......frequency would be 230 radians per second (36.6 hz).

Recalculating with higher and lower prop inertias, a first mode frequency half of 230 (115 rad/sec) is impossible even with an infinite prop inertia. Reducing prop inertia in order to double the first mode frequency (460 rad/sec) would require a prop inertia of 0.026 Kg-m^2. That would be a tiny little toothpick, about 5% of the 0.5 Kg-m^2 inertia for the example MT-7.

Clearly you can't change the frequency by a factor of 2 by changing prop inertia, at least not within the practical constraints of our application.

So, that leaves us with damping. I have no values for damping in our practical application, nor any software to explore the frequency effects of damping. At my student level I tend to do simple frequency calculations to find resonant intersections, then assume the actual natural frequencies found in operation will be a bit lower. So far, limited field experience has found them to be a few hundred RPM lower, in the range of 5 to 10 hz, perhaps a 25% shift at most, and I've attributed it to damping. I've never seen a 2:1 shift, and I have to wonder if there can be enough damping to drive frequency down by a factor that large. I'm happy to accept your 2:1/1:4 frequency-to-amplitude statement; I'm still too uneducated to really consider the point. However, what might it look like if the frequency reduction due to damping was more like 15%?

Later:

I was driving down the road thinking, and I may have been a bit brain dead about your comment:

<<If the resonant frequencies were 2:1, then the amplitudes would typically be 1:4.>>

In the above, does the "2:1" mean double or half the previous frequency? And what does the "1:4" represent?

I'm sorry, I was a bit brain dead myself when my cat woke me up much too early this morning I was just illustrating the general effect of dissipation of energy vs amplitude. If the frequency of the small inertia prop vs large inertia prop was a factor 2 (2 to 1 or 2:1), then the amplitude of the oscillations at ressonance for would be a (roughly) factor 1 to 4 (small vs large inertia). So if the small inertia prop oscillates twice as fast, it's amplitude would only be 1/4 of the large inertia prop. But, this was on a prop mounted on a torsional rod that is fixed in the other end, not a system of masses where the prop is the one with largest inertia, making this a very poor example in this thread.

Reading your post again, you are very correct about the relative angular displacements. The problem is that you have no real (actual) displacement to relate your system to. If you can measure the actual displacement or amplitude at one spot, then the other ones will be relative to that one for that system at that frequency. If you now change the inertia on the prop, you have created a new system, and you cannot relate the amplitudes of the old system to the new system, not without a new measurement on the new system. For instance, the example from Hartog shows the first two frequencies and the amplitudes are scaled using the right most node. If you measured the actual (real) amplitude at that node, I would believe that for the highest frequency, the amplitude would be only 1/2 or less compared with the amplitude of the lowest frequency. So even though the higher frequency oscillation looks worse in terms of stress looking only at the mode shapes, it most probably is much better than the low frequency when looking at the actual amplitudes.

What these results tells you:
0.5 prop: +1, -3.534, -6.466
1.0 prop: +1, -7.358, -12.64
1.5 prop: +1, -11.18, -18.82
is that the more inertia is put in the prop, the less the prop will oscillate relative to the other masses. But it is also natural that a large inertia prop is much more stable, you have to use a lot more of energy to accelerate it, so the amplitude of +1 for the 1.0 prop, is probably only 1/2 measured in actual displacement, and the +1 for the 1.5 prop is probablu closer to 1/3.

Added:
This can be seen more easely when looking at the energy is the system. Considering the dissipation is the same regardless of inertia on the prop, then the max energy must be the same regardless of inertia in the prop. For the 0.5 prop, the strain energy is 0.5*K1*(1 + 3.534)^2 between the prop and the first mass and 0.5*K2*(6.466 - 3.534)^2 between the last two masses. Obviously this is much less than for the 1.5 prop which is 0.5*K1*(1.0 + 11.18)^2 + 0.5*K2*(18.82 - 11.18)^2. So the comparison between the props cannot be correct energy-vise. For a rough comparison with similar frequencies you can scale the results using the strain energies, but this will not be 100% correct because it is the dissipation energy you have to compare, and this will be dependant on the frequencies, and you have to know the damping in the system.

Strain energy

Ok, this is not entirely correct, but nevertheless without numbers for the damping it gives a clue. When the total strain energies are equal for the vareous props the results will be:

0.5 prop: +1.000, -3.534, -6.466
1.0 prop: +0.507, -3.727, -6.403
1.5 prop: +0.339, -3.791, -6.382

All in all a larger prop doesn't really do that much. Probably because it is so much larger than the other masses to start with. What is does is to move some strain energy in the shaft between the prop and the first mass to the shaft between the two last masses.

<<So if the small inertia prop oscillates twice as fast, it's amplitude would only be 1/4 of the large inertia prop. But, this was on a prop mounted on a torsional rod that is fixed in the other end, not a system of masses where the prop is the one with largest inertia....>>

Ahhhhh, ok, I'm with you now. Since the amplitude of a large mass prop on the multiple small-mass system would be low, propeller aero damping would also be be quite low, yes?

<<If you now change the inertia on the prop, you have created a new system, and you cannot relate the amplitudes of the old system to the new system...>>

Good point. Ok, I'm back to the books. Sounds like we must consider a rule-of-thumb based strictly on mode shape to be suspect. Can anyone suggest an alternate rule, equation or relationship for amplitude vs prop inertia?

I don't think there are any easy way to do what you want. There are several engineering software specialized in the dynamics of shafts for ships, generators and so on, maybe one of those can be used? The damping in engine and bearings can be rather accurately predicted, but as far as I can se, an appropriate (dynamic) model for the propeller at different loads, airspeeds and pitch is something that will be very hard to do and get it right regardless of what software you have.

More Data

I've got a couple more data points here from two other users who have recently made first flights with Subaru EJ22 engines and light props:

EJ22T with RAF cog belt drive, no damper or soft coupling, aluminum flywheel and 27 lb. IVO Magnum prop- 800-1100 rpm has a pretty serious vibration. Again, idle had to be turned up to about 1300 to smooth things out. Heavy vibration at about 4200-4800 rpm also. Reasonably smooth 3500-4000 rpm.

EJ22 with Marcotte M-200 drive, std pin and rubber bushing coupler, aluminum flywheel and Quinti lightweight prop. Noticeable vibration below 1100 rpm and another period at 2200-2400 rpm.

My EJ22T with Marcotte M-300 drive, same coupler and flywheel as above and 27 lb. IVO prop as first example. 400-950 rpm results in a serious vibration, 1000 rpm is smooth, 1050- 1500 has another less serious but very noticeable period. I'm smooth from there to 5200 rpm which is as high as I've taken this combo.

Interestingly, these all have "unhappy zones" below 1000 rpm.

I hope to try a heavier flywheel on example 1 in the coming months and example 2 may try this as well. Will be interesting to see what changes this makes.

Strain energy would seem important.

Guys,
I was reading the paper written by Donald Hessenaur about taming the BD5 prop and drive TV issues again in light of what you were talking about Dan. (doubling the prop mass) One of the comments just jumps out at me all the time. "Clearly it could be seen that the resonance could be excited by the compression strokes alone. The thing that blew our minds was that even when the input energy was low, the output loads were still as destructive to the airframe as when the input energy was high."
"When we started to look into torsional resonance theory we found an explaination. Without any damping in the system, theoretically the peak load at resonance approaches infinity."

The correllation is that when we put on one of these heavy props we will be moving the system towards the "soft system" that Don was describing in the paper. We really need some dampening in the system to prevent the high angle to the curve Dan mentioned earlier. Without dampening the system can just "hang up" at one of the low frequency harmonics and just shake the plane apart! Thankfully few of the systems we use will be that soft. Most of the systems we design will have some dampening. Those factors will usually allow us to power through the low RPM harmonic area without ripping the engine off the firewall! Best idea is to tune F1 completely below the operating range. The BD-5 guys used a sprag to help solve their problem, but as you mentioned Dan the number of cycles can really wear out a sprag fast in higher output situations. The BD-5 was originally designed for 40 HP.
Gear drives have the lash to contend with as well. I believe we really need the prop to load the system enough areodynamically to have a continous low level of strain on the drive system. That would allow some of that energy to be dissipated. So I'm I accurate here or missing the point entirely?
Bill Jepson

Bjørnar,
<<I don't think there are any easy way to do what you want.>>

Yes, but it is an interesting exercise. I've not yet fully accepted the idea that "All in all a larger prop doesn't really do that much.", but I'm working on it. <g> Which is not to say you're wrong. It is merely how I learn.

The trouble I'm having relates to practical experience and other indicators.

I have some telemetry data taken back in 1999 which addresses the question of amplitude vs prop inertia. I did two runs with a mahogany prop and two more with maple prop of slightly higher inertia, all in the same day. I dug up an old raw data file for the runs and sure enough, the maple prop had generally higher first mode vibratory shaft torque values. I've been digging around for the measured MMI values for the two props; if I can find them I'll compare the run torque to the MMI's. I don't expect it to be conclusive, because the MMI's as I recall were not that different. I wish I had done a third telemetry run with a much heavier prop!

Which is not to say I didn't ever try a heavy prop. The very first time I fired up the JN-4C, I was using a 72" Sensenich classic brass-tipped birch prop borrowed from my Piper L-4. It was my first introduction to torsional resonance, and the start of all this craziness. That early version was a "hard" belt drive from a vendor (note: "Fully Tested!"); at about 1800 RPM I thought the airplane was going to be shaken apart. It wasn't until much later when I learned to call it a "resonant intersection of F1 and the 1-1/2 order" (3 cyl 4-stroke) <g> The perceived amplitude was lower when I later mounted a smaller flight propeller sized for the airplane.

Then we have the published Rotax prohibition against high MMI propellers, complete with SB describing how to measure MMI. And I think Ross mentioned trying a high MMI prop when he was doing development runs for the 912 EFI system.

Ross, can you report on your 912 prop swaps? And thank you for the data on the three running EJ22 systems. That kind of "vibration range" information has been hidden way too long. I have some comments about each, but it will wait.

Don,
<<One of the comments just jumps out at me all the time. "Clearly it could be seen that the resonance could be excited by the compression strokes alone.>>

Yes. Anything that serves to introduce a periodic variation in shaft angular velocity will excite the system if it matches a natural frequency.

<<The correlation is that when we put on one of these heavy props we will be moving the system towards the "soft system" that Don was describing in the paper.>>

When Don said "soft" he was referring to a connecting stiffness. A heavy prop is an inertia. The third player in the opera is damping. Damping is quite distinct from the first two players.

<<Without dampening the system can just "hang up" at one of the low frequency harmonics and just shake the plane apart!>>

Rotax had that problem with the first C-box 582's, if the user hung a high MMI prop on them (the usual culprit was a 3-blade Warp Drive). It was cured with the substitution of a slightly stiffer rubber donut, not a damping change.

There is a link to a white paper near the beginning of the Egg technical thread. It contained a nice note about resonance hang.

<<Best idea is to tune F1 completely below the operating range.>>

If you can do it, yeah buddy! However, it is going to be a very soft system. The powerful 2nd order firing frequency is only 33 hz for a 4-cyl 4-stroke (or a twin rotor Wankel if I remember right) at 1000 engine RPM. You would need an F1 of 25 hz or less to avoid a resonant period.

First runs on the 912 were with a very light GSC 2 blade wooden prop. This one cavitated at high rpm so were went with a much heavier but smaller diameter Hoffman 4 blade test club to get proper rpm data above 5500 rpm . My very rough guess would be that the MMI was about 50% higher on the club.

I was not paying too much attention to the exact TV range with each prop but the amplitude at low rpms was noticeably higher with the club. This was in the 600-1000 rpm range. We were diddling with the EFI to get the idle speed up. I was not intentionally holding it there because it was pretty severe and it was not my engine.

The test stand was made from 1 inch .065 square tubing and not well triangulated where the engine was mounted so there was quite a span in the middle. When the engine hit resonance, it would flex the upper tubes on the stand a good 3/8 to 1/2 and inch and the gearbox set up a fair racket as well. I got it up above 1200 rpm and it was as smooth as glass.

Seems that we just need a disposable/gearbox engine with bad TV on a test stand and switch prop MMIs while observing rpm where the highest amplitude occurs.

DanH said:

Rotax had that problem with the first C-box 582's, if the user hung a high MMI prop on them (the usual culprit was a 3-blade Warp Drive). It was cured with the substitution of a slightly stiffer rubber donut, not a damping change.

Click to expand...

Rubber is as a spring and a damper. The damping properties of rubber is used in the legendary Morris Mini (the old original one, not the "reborn" one made by BMW). Here the entire suspension is made of rubber. Changing the rubber will also change the damping properties.

<<Seems that we just need a disposable/gearbox engine with bad TV on a test stand and switch prop MMIs while observing rpm where the highest amplitude occurs.>>

Observing RPM tells you F1 frequency with some accuracy, but leaves you guessing about actual amplitude. We're all in agreement regarding frequency shift with a change in prop inertia.....it ain't much. For example, Alex posted frequency values for a two mass system:

W1 = 314 rad/s (.5, .05, 4500)
W2 = 307 rad/s (1.0, .05, 4500)
W3 = 304 rad/s (1.5, .05, 4500)

The familiar Hertz (cycles per second) is radians per second (rad/s) divided by 2pi (6.28, or to be precise, 6.2832). 314/6.28 = 50hz, 307/6.28 = 48.9hz and 304/6.28 = 48.4 hz. Three times the prop inertia lowered F1 by only 1.6 hz.

The spread gets a little larger with a more realistic multi-inertia model, but the frequency shift rule-of-thumb still holds....not much change in frequency when you change prop inertia.

Running the above live test with a strain gauge on the prop shaft (units of torque) or encoders at both ends of the system (units of angular deflection) would tell you amplitude. Amplitude is what we really want to know; it equates directly to shaft and gear strain.

<<Rubber is as a spring and a damper.>>

Technically correct of course. As I've written previously, the rubber-in-compression donut-style couplers do bring a small damping value to the application. The Centa catalog, for example, lists "Relative Damping Factor C" (0.6 for Shore 50 and 0.78 for Shore 78). Bj?rnar already knows the term, but for others, C is defined as the ratio of damping work to elastic deformation work of a period of vibration, Ad/Ae=C.

I usually ignore the damping value of rubber couplers when discussing torsional subjects because of common confusion regarding the meaning of stiffness, inertia, and damping. In a similar fashion, we all routinely ignore the inertia value of a small diameter shaft and treat it strictly as a connecting stiffness. Doing otherwise introduces complication and confusion.

In the context of Bill's comment and my response, consider the change from a Shore 50 coupler to a Shore 78 coupler. Damping factor increases by only 0.18, but in the case of a Centa appropriate for the 582 Rotax, dynamic torsional stiffness increases from 900 Nm/rad to 1500 Nm/rad.

BTW, Bj?rnar, I notice you are a fan of Einstein, and I'll bet you read the recent Isaacson biography. I'm happy to play Besso <g>

DanH said:

Don,
<<One of the comments just jumps out at me all the time. "Clearly it could be seen that the resonance could be excited by the compression strokes alone.>>

Yes. Anything that serves to introduce a periodic variation in shaft angular velocity will excite the system if it matches a natural frequency.

<<The correlation is that when we put on one of these heavy props we will be moving the system towards the "soft system" that Don was describing in the paper.>>

When Don said "soft" he was referring to a connecting stiffness. A heavy prop is an inertia. The third player in the opera is damping. Damping is quite distinct from the first two players.

Dan, So that you know, I do know the difference between inertia and stiffness. My point was that the RELATIVE stiffness of the system is less when the prop is considerably higher mass/inertia.

<<Without dampening the system can just "hang up" at one of the low frequency harmonics and just shake the plane apart!>>


<<Best idea is to tune F1 completely below the operating range.>>

If you can do it, yeah buddy! However, it is going to be a very soft system. The powerful 2nd order firing frequency is only 33 hz for a 4-cyl 4-stroke (or a twin rotor Wankel if I remember right) at 1000 engine RPM. You would need an F1 of 25 hz or less to avoid a resonant period.

Click to expand...

Agreed, many systems will become impractical. The thing that I note is that the stiffness of the rotary e-shaft is so high compared to a piston engine crankshaft PowerSport went the high-stiffness route

If we recognize the problem areas it makes it easier to chose the correct path. Dan your efforts to bring this to the attention of the alternate engine crowd is a great service. I think I'll invest in the balance and sensor equipment when I get my FWF running.
Bill Jepson

DanH said:

Technically correct of course. As I've written previously, the rubber-in-compression donut-style couplers do bring a small damping value to the application. The Centa catalog, for example, lists "Relative Damping Factor C" (0.6 for Shore 50 and 0.78 for Shore 78). Bjørnar already knows the term, but for others, C is defined as the ratio of damping work to elastic deformation work of a period of vibration, Ad/Ae=C.

....

In the context of Bill's comment and my response, consider the change from a Shore 50 coupler to a Shore 78 coupler. Damping factor increases by only 0.18, but in the case of a Centa appropriate for the 582 Rotax, dynamic torsional stiffness increases from 900 Nm/rad to 1500 Nm/rad.

Click to expand...

Considering that the C is what is also commonly named the "specific damping capacity", an increase from 0.6 to 0.78 is no small change. The change is almost 30%. Related to amplitude, C = 2*delta where delta = ln(x1/x2). x2 is the amplitude one period after x1 for a damped system. It gives a measure of how fast (in periods of oscillations) the amplitides in a system goes to zero after an exitation for an underdamped system (a system that oscillates toward zero and don't just go steadily back to zero).

So ln(x1/x2) = C/2 or x1/x2 = e^(C/2). This means that the amplitude x2 = x1*e^(-C/2). If the initial amplitude, x1, was 1.0 for both cases, then after one period the amplitudes would be 0.86 for C=0.6 and 0.82 for C=0.78. The third amplitude would be 0.74 vs 0.68 and so on. An important point here is that this damper (the rubber) will do this regardless of other stiffness'es and masses in the system. If you have to move past certain RPMs where ressonance occurs, then the value of C will be critical for how large the amplitudes builds up to be.

It seems to me (from these previous examples) that the inertia of the propeller is so much larger than the other masses, so I wonder if inertia of the engine itself is just as important, if not more?

I should build my airplane instead, but I had to dig up an old book For a system consisting mainly of descrete elements, the key to prevent too large amplitudes at ressonance is damping elements of some kind (rubber, clutch, shock absorbers - whatever fits). There really is no other way. The propeller is both an inertia and a damper, but a very complex damper that can vary between zero, practically speaking, to more than enough damping to stop any and all ressonances.

C = 2*delta, which is approximately equal to 4*pi*zeta. So that zeta = C/(4*pi). What is importent is the so called amplitude ratio: x/delta_st. This is the deflection the driving force causes (the force in one pulse from the engine for instance), so that in general delta_st = F0/k. The amplitude ratio is a function of frequency and zeta.

A zeta value of 0.3 causes an amplitude ratio of approx 1.8, which means that the pulses from the engine will only be amplifies 1.8 times in amplitude at ressonance. A zeta value of 0.5 leads to an amplitude ratio of 1.17 and so on (there are charts for this).

That rubber with C=0.6 have a zeta of 0.05, and this doesn't really do much in terms of damping at ressonance. It is only at start/stop of the engine that this rubber will have any function. However, if this C is the loss coefficient, that is the energy dissipated per radian over the total strain energy, then a C of 0.6 equals a zeta of 0.3 and a C of 0.78 equals a zeta of 0.4. zeta=0.3 gives an amplitude ratio of 1.8 while zeta=0.4 gives an amplitude ratio of only 1.3. (Or maybe the C given is a material property, where the actual C for the piece must be calculated?)

A clutch is preferable because it does not alter any frequency in the system and only work when needed (at overload) as well as being much more robust, othervise it is the exact same principle as with this zeta factor of viscous or internal/rubber damping.

I'll throw something else into the mix. From observed results on my 6A and another airplane when we ran with no prop, just the PSRU- no vibration periods- dead smooth from 500-5500 rpm. No with virtually zero inertial we have virtually zero TV- at least what we can feel. It seems to me from this elementary example and the Rotax experiment that prop MMI can make a significant impact on amplitude. With a very heavy prop, the prop becomes the tail that wags the dog so to speak.

Comments?

<<I should build my airplane instead, but I had to dig up an old book >>

We all should, but you have more than a few folks very interested in what you're writing.....don't quit now.

Ok, let me see if I can supply the definitions.

Regarding the meaning of "Relative damping factor - C"; Centa defines properties using the terms spelled out in the German flexible coupler standard, DIN 740. The Greek symbol for relative damping factor in my translation (obtained from Lovejoy, the US distributor) appears to be psi, the "trident" symbol.

Also note Vr, "Resonance Factor". The catalog values for Vr are:
Shore 50 = 10
Shore 60 = 8

Here's a scan from the translation:



And here is the "Note 6" referred to in the definition of Vr:

Bill,
Please excuse the stiffness/inertia reminder...lost track of who I was speaking with. Heck, I even called you "Don".

Appreciate your kind comments, but I think it is Bj?rnar with an important contribution today. Quantifying the damping power of a good off-the-shelf rubber coupler (is it a little or a lot?) has a huge practical benefit.

No offense taken!

DanH said:

Bill,
Please excuse the stiffness/inertia reminder...lost track of who I was speaking with. Heck, I even called you "Don".

Appreciate your kind comments, but I think it is Bj?rnar with an important contribution today. Quantifying the damping power of a good off-the-shelf rubber coupler (is it a little or a lot?) has a huge practical benefit.

Click to expand...

Dan absolutely no problem here! This is a very interesting discussion with very real numbers being provided, that is A GOOD THING. As we learn how these mass changes effect our systems I think it is very informative! This is the reason a lot of us got into engineering for. The ability to PREDICT the behaviour of the system before we put the thing together. Test will then show us if we properly predicted everything. I have always been facinated by the soft system examples. I always like hearing about specific examples to widen the knowledge base.
Bill Jepson

The Vr is also called the "quality factor, Q", and the relation to zeta is:
Vr = 1/(2*zeta). This also means that the rubber has a zeta value of 0.05 or thereabout. In fact the quality factor is normally only used when zeta < 0.05.

With a Vr of 10, the amplification is 10. So if you somehow can predict or measure the pulse from the engine at a certain RPM, then you can calculate delta_st, and with a Vr of 10, the amplitude at ressonance will be 10*delta_st. I may have been a bit too fast in saying that a zeta of 0.05 is too small, since the driving pulses may not be that large in comparison to the mean torque. A Vr of 10 may be more than adequate, but it certainly will need to be calculated and related to the strains.

<<So if you somehow can predict or measure the pulse from the engine at a certain RPM, then you can calculate delta_st, and with a Vr of 10, the amplitude at ressonance will be 10*delta_st. I may have been a bit too fast in saying that a zeta of 0.05 is too small, since the driving pulses may not be that large in comparison to the mean torque.>>

In rough terms I've used 1.5 or 2.0 x mean torque for the combustion order with gas engines. The example in DIN 740 lists 3.0 x mean for a 4-stroke diesel. A more precise set of values is referenced in "Mechanical Vibrations", a published paper with calculated torque for the first 18 or so orders across a variety of engine types. Den Hartog chose a 4-cyl 4-stroke diesel for his example (same one in the mode shapes plots). I recall the 2nd order as being 2.36 x mean. Left the book at the office; I'll post the reference tomorrow.

Great thread gentlemen.

Of course. It must be higher than the mean torque because the power stroke for each cylinder only works a small portion of each 720 degree rotation. This certainly doesn't make it any easier for you Dan Turbines are so much nicer in this respect.

The German DIN 740 standard offers an approach to determining an approximate resonant torque value for a simplified two-mass system, the goal being the selection of the correct rubber coupler. The listed formula for "drive through resonance" is:

TKmax = Ma * TAi * VR * Sz * St

Where:

TKmax = the maximum vibratory torque

Ma = Mass Factor (for drive side) = load side inertia / (engine side inertia + load side inertia)
Don't forget to multiply the engine and flywheel inertia by gear ratio^2 when establishing engine inertia

TAi = peak periodic torque of the driver for the order (i) of interest (for approximate purposes, this is mean torque x order multiplier (1.5 to 3) discussed in the previous post. I would use WOT mean torque at the intersection RPM to see the max TK value. In the example below I've used a part-throttle value. In the DIN 740 example, the TAi value was obtained from the engine supplier. Not much chance of that in our case.)

VR = from the catalog, or (6.28 / relative damping)

Sz = Start Up Factor, always 1 for our gas engine application with a low F1 frequency

St = Temperature Factor = For NBR coupler material, 1 if the coupler temperature is less than 60C, and 1.2 if over 60C. (Note; this is why the flywheel-coupler area of the installation should be vented)

Using inputs taken from a past project (I-3 Suzuki) for which I have measured vibratory torque values (units in slugs-ft^2 and ft-lbs):

Ma = .30656/[(.0529*2.12^2)+.30656] = .5632

and assuming 16 ft-lbs mean torque at 1500 RPM part throttle, x 2 for the harmonic multiplier...

and further assuming a VR of 10 (don't remember which coupler I used)...

Thus:

TKmax = .5632*32*10*1*1 = 180 ft-lbs

....which was the actual measured vibratory torque. Note the assumptions above before drawing any detailed conclusions. This is just an example.

Ross, my part-throttle mean torque data is questionable. Didn't you have an I-3 on the dyno some time back? Got an accurate mean torque @1500 RPM? Given the high (peak torque/mean torque) ratio of an engine with few cylinders, the multiplier may have been 3x, ie a mean part-throttle torque of 10.6 ft-lbs to arrive at 180 ft-lbs in the above equation.

We were only running the G10 3 cylinder on a test stand with no load unfortunately. These are nasty little things just above idle if I remember. The factory specs show about 43 lb. ft. at 1500 rpm.

<<The factory specs show about 43 lb. ft. at 1500 rpm.>>

Hmm. How about 1100 RPM?

The chart does not go that low but I'd extrapolate it to around 40 lb./ft. at 1100.

Ok, when I get home tonight I'll recheck at the TAi definition in DIN 740, check a telemetry plot for resonant RPM in the last runs, and take another look at my mean torque data. Then I'll return to the DIN method as a quick way to predict resonant amplitude.

Switching to a different observation, it is interesting to use the DIN formula for different prop inertias.

Using the original assumptions of 32 ft-lbs for TAi and 10 for VR, we have:

0.15 slugs ft^2 prop inertia = 123.8 ft-lbs vibratory torque
0.3 = 180
0.6 = 229.2
0.9 = 253.1
1.2 = 267.0

Doubling driven inertia does not double vibratory torque amplitude (my proposition at the beginning of this thread remains wrong), nor does it remain stable regardless of prop inertia, as indicated by Bjørnar's equal strain energy example. Hmmmmmm.

I went back and ran the inertia values for the original example given in the first thread post (in metric values); 0.5 prop, 0.05 flywheel, 0.05 crank, but reduced them to a 2-mass model by combining the flywheel and crank inertias, then correcting them for a gear ratio of 2.12 (original example was not geared). That makes total engine inertia 0.4491 kg m^2 for purposes of calculation. TAi remained at 32 and VR remained at 10, because they don't matter for this comparison.

0.25 Kg m^2 prop inertia = 114.4 Nm vibratory torque
0.5 = 158.5
1.0 = 220.0
1.5 = 246.2
2.0 = 261.3

If you plot the torque figures from either example set, they form a flattening curve. As the ratio of prop inertia to engine inertia becomes larger and larger, the curve gets more and more flat. "Flat" means additional prop inertia indeed makes little change. I suspect the curve is truly flat when prop inertia reaches infinity.

So, we have a clue as to the discrepancy. The above included a gear ratio correction, while the values used previously by Bjørnar did not. Gearing makes the engine inertia effectively larger. The gearing correction multiplies the fast side inertia (the engine) by ratio squared, in this case 2.12 squared, or 4.494. That makes the ratio of prop to engine inertia smaller:

was 0.5/.1 = 5
now 0.5/(0.1 x 4.494) = 0.5/0.4494 = ~1 (1.1126)

.......and moves the system down the curve.

(Later: Corrected an error in the above. Was .05 engine inertia, now 0.1; the original example had two engine inertias of 0.05 each, now combined to form one side of the two-mass model.)

To expand on the flattening curve observation, consider the original example without gearing. The three propeller inertias selected made the ratio of prop/engine inertia larger with each larger propeller, moving them further up the curve:

0.5/0.1 = 5
1.0/0.1 = 10
1.5/0.1 = 15

For the moment, pretend the above engine inertias were the result of a correction for 2.12 gearing, ie, the actual engine inertias were 4.494 times smaller. Per the DIN formula for run through of resonance, we have:

0.5 Kg m^2 prop inertia = 266 Nm vibratory torque
1.0 = 290
1.5 = 300

Starting to get flat, yes?

At the moment, I'm thinking I started the thread with an unrealistic example, one that neglected gearing.

I was just thinking if the torsional fireing amplitudes are 2-3 times the mean torque, the Vr is 10 and Ma is 0.5, this means that the torque amplitude at ressonance is 10-15 times the mean torque. This would need some heavy shafts and heavy wheels. Consider a Thielert with 300 Nm of engine torque, this means the gearbox has to be designed to withstand 4500 Nm of oscillating torque (3300 lbft). Add in some fattigue, and the shafts would have to be designed for at least 25000 Nm (18500 lbft). Now we are talking engine torques for large ships, not small aeroplanes

Looking at Thielert, Rotax and Verner, the three most selling engine/gearbox manufacturers, they all use a clutch. HKS is a much smaller engine, and use only a dog wheel spring. Somehow there must be a reason for the use of clutch and/or spring, and I think the the main reason is those 25 kNm.

Excellent details of the Verner enginge and gear can be found here.

Using a spring only, will cure all ressonance problems. It is just a matter of making it so soft that ressonance occurs below idle. One problem is that a spring will allways be working, and probably will not last that long.

A clutch only, will limit the torque to a preset value. This will totally break oscillations from building up, but without limiting throw it can probably weir out?

A clutch and a spring (like in the Verner) will be vastly superior. This system will only be in action when the torque is above a preset value. When the torque exceeds that value, for instance due to ressonance, the stiffness in the system will change because the springs start to act. The ressonance frequency has changed to a different value (much lower I presume), and is by itself enough to completely stop the amplitudes from building up further. The clutch will also work as an excellent damper (for instance at a prop strike), but I would think the main function it performs is to let the spring start acting only when needed.

<<A clutch and a spring (like in the Verner) will be vastly superior.>>

Here is the the appropriate image:



Conceptually, it is a torsional soft element in parallel with a friction damper. The dedicated damper offers a far higher damping rate than what you found in the rubber coupler.

The concept is not new, at least not in alternative engines. Jeron Smith's Raven belt drives have a dry friction damper (with a nylon face) in parallel with a soft element, located in the upper sprocket. He first showed them at Oshkosh about 10 years ago.

Back in 1999 I built an experimental viscous damper running in parallel with a Centaflex rubber soft element. Unlike the above examples, it had no "stick-slip" behavior; the rubber element could deflect under all conditions, while the combination had a far higher damping rate than the coupler alone. Remember our conversation about propshaft fatigue? The viscous damper addition is how vibratory torque went from 180 ft-lbs to 90 ft-lbs.....which is why I said there isn't much true damping in a rubber coupler, at least not in comparison to what is really useful.



<<When the torque exceeds that value, for instance due to ressonance, the stiffness in the system will change because the springs start to act. The ressonance frequency has changed to a different value (much lower I presume), and is by itself enough to completely stop the amplitudes from building up further.>>

The torque necessary to start slipping the clutch disks at the limit of each oscillation is the same as the slip torque when not in resonance. Same effective stiffness. I think the assembly is simply a damper.

Elegant design in many ways. Note that even if the damper clutch slips without restraint (worn out, damaged, whatever), torque is still transmitted by the springs. Compare that to the design of the Thielert drive system.

The Verner illustrates the problem of few cylinders. Opposed twin, so the combustion order is 1 and the recip inertia order is 2. The most powerful exciting frequency would only be 16.6 hz if you assume a 1000 RPM idle speed. Impossible to move the 1st natural frequency below idle, so they were forced to design a system that allowed passing through it at low vibratory torque.

Motorcycle Clutch

It's funny Dan sometimes you start heading down a road and then some one shows you it has been done before. The Clutch shown in your previous image is a standard multi-plate motorcycle clutch element. I was going to ask if a small multi-element clutch with controlled slip rates would work. As far back as 1975 we found that the old standard motorcycle wet clutches were starting to slip in high hp applications. Putting really stiff springs in there to control the slip didn't work unless you had the left forearm of a weight lifter to pull in the lever. The solution that appeared was a light spring with a bobweight in the clutch case. It was a simple solution and worked really well. The inner plates, (well the output shaft plates, but I digress), and the frictions alternate with the last outer plate being a inner output plate. There are posts that pass thru the friction plate with a weight and an 'L' shaped actuator attached. The pivot is in the 90? corner of the L the long arm carries the weight and the short leg pushes on the friction plate. The faster it turns the harder it pushes. Usually three legs were enough, but I've seen drag racers with 7. The point is the clutch can be almost loose and as the shaft spins up the system pushes harder and harder. I believe this is the system Bud Warren is using on his drive, but with a automotive clutch plate, instead of the motorcycle multi pack. Seems like a good solution if you have room for it. Simple in our aircraft arangement, just pick springs that will slip a bit until spinning fast enough for higher RPMs and low RPM reversals would just slip the clutch a bit, and the weights would ensure a zero-slip system at normal cruise RPMs. More parts than getting the stiffness right, but available and fairly cheap. FWIW
Bill Jepson

Bill,
<<As far back as 1975 we found that the old standard motorcycle wet clutches were starting to slip in high hp applications>>

Well, I can confirm that...it cost me the '86 WERA Clubman Expert title. Failed to install a new set of plates before the race, and slipped (pun alert!) from 1st to 4th in 30 miles around Road Atlanta. Can you say stoooooopid? Got the Formula II #2 later that day, with new plates. Ahhh, the good 'ole days. Young and dumb <g>

I too like Bud Warren's approach, although I know almost nothing about the mechanical details. If clutch engagement RPM is above the RPM where F1 and the combustion order intersect, it can't resonate. Which is not to say you can't have problem intersection with another order further up the RPM scale.

Slightly off topic.

DanH said:

Bill,
<<As far back as 1975 we found that the old standard motorcycle wet clutches were starting to slip in high hp applications>>

Well, I can confirm that...it cost me the '86 WERA Clubman Expert title. Failed to install a new set of plates before the race, and slipped (pun alert!) from 1st to 4th in 30 miles around Road Atlanta. Can you say stoooooopid? Got the Formula II #2 later that day, with new plates. Ahhh, the good 'ole days. Young and dumb <g>

I too like Bud Warren's approach, although I know almost nothing about the mechanical details. If clutch engagement RPM is above the RPM where F1 and the combustion order intersect, it can't resonate. Which is not to say you can't have problem intersection with another order further up the RPM scale.

Click to expand...

Completely agree about the high RPM resonance. I think most people notice the 1st order shakes though since it is usually in the idle range. It is one of the easily noticed peaks. That is not to say that tuning out the higher order peaks isn't just as important.

Off topic; I ran several amature RR classes on the west coast and one of the bikes was a Yamaha FZR 600 circa '89 it had a notoriously weak clutch. I got to the point where I replaced all the friction plates each race as a normal wear item. I am a big guy too so it just made it worse. (The joke among my friends was "A road racers brain in a linebackers body.") The fact is that we can use the same elements in a dry environment, so it should be easier to make a compact dampening element.
Bill Jepson

Bill,
<<I ran several amature RR classes on the west coast and one of the bikes was a Yamaha FZR 600 circa '89...>>

Ahh, memory lane. I had a few hot laps on one of those and endurance raced it's predecessor, the FJ600 (The Sled). Kept an FRZ1000 several years; best street bike ever made.

<<I am a big guy too so it just made it worse. (The joke among my friends was "A road racers brain in a linebackers body.")>>

Big isn't all bad. Nobody sneaks up the inside if you stick a lot of knees and elbows out there. And you generally win the bumping contests <g>

We better get back on topic or we'll both be checking rulebooks for "Seniors" classes.

<<The fact is that we can use the same elements in a dry environment, so it should be easier to make a compact dampening element.>>

Remember the basic rules of friction. Static friction is always higher than dynamic (sliding) friction, so you get stick-slip behavior; high torque to start it slipping, lower torque to keep it slipping. A dry clutch is probably worse in this regard. A wet clutch may close the gap; static near dynamic values. I say "probably" and "may" because I have no hard data.

The Verner and the Rotax 912 are both wet, but I think they have very different purposes. I suspect the Verner does a lot more slipping than you might guess at first glance; as noted before, a true damper in parallel with a spring. Seems unlikely that only two skinny friction plate sets would carry normal operating torque by themselves, and they're backed up by the springs in this regard. The Rotax 912 clutch does carry all the operating torque. I suspect the Rotax is intended to be a torque limiter, and doesn't slip much (if at all) in flight. I think it slips in passing through the first resonant period during start-up; the 912 system appears to idle above the F1 intersection.

The whole point of the viscous damper experiment was eliminating the stick-slip. Think of it this way. The suspension of your car has a spring and a damper, in parallel, at each corner. Automotive designers long ago stopped using friction dampers in that application.

Rotary10-RV said:

It's funny Dan sometimes you start heading down a road and then some one shows you it has been done before. The Clutch shown in your previous image is a standard multi-plate motorcycle clutch element. I was going to ask if a small multi-element clutch with controlled slip rates would work. As far back as 1975 we found that the old standard motorcycle wet clutches were starting to slip in high hp applications. Putting really stiff springs in there to control the slip didn't work unless you had the left forearm of a weight lifter to pull in the lever. The solution that appeared was a light spring with a bobweight in the clutch case. It was a simple solution and worked really well. The inner plates, (well the output shaft plates, but I digress), and the frictions alternate with the last outer plate being a inner output plate. There are posts that pass thru the friction plate with a weight and an 'L' shaped actuator attached. The pivot is in the 90° corner of the L the long arm carries the weight and the short leg pushes on the friction plate. The faster it turns the harder it pushes.

Click to expand...

To the best of my knowledge, this was first developed in the dragster world. Late 60s IIRC.

It was used to allow higher engine speeds for launch, but still allow some slipping---then lockup at full RPM. Gave the same effect as a transmission, lockup time/rpm adjustable by changing washers on the bob weights.

Shaffer clutch was big in this arena, as I recall. Also Crower http://www.crower.com/pdf/189-196.pdf

Centerforce http://www.centerforce.com/ uses the same concept in a diaphragm setup.

Interesting how the old becomes new again.

Now, I wonder if someone will point out that this technology was actually developed back in aught6

They were called "slipper clutches"

Bj?rnar,
<<I was just thinking if the torsional fireing amplitudes are 2-3 times the mean torque, the Vr is 10 and Ma is 0.5, this means that the torque amplitude at ressonance is 10-15 times the mean torque.>>

Could it 10-15 times peak torque per combustion cycle, rather than mean engine torque? I'm still rooting around in old data (had to recover some of it, which is why I'm taking so long), but what I have so far suggests peak.

In the run data sheet for the I-3 Suzuki I have in front of me right now, throttled mean torque was between 3.5 and 4 ft-lbs at 1500 RPM, steady state operation. 10-15 times 4 ft-lbs would be 40 to 60 ft-lbs resonant torque, way lower than reality. 3x 4 ft-lbs x 10 to 15 would be 120 to 180 ft-lbs resonant torque. Actual measurement was 180 ft-lbs (RMS x 1.41) for the system without a dedicated damper, just the rubber coupler.

Ferofluid?

DanH said:

Bill,
Remember the basic rules of friction. Static friction is always higher than dynamic (sliding) friction, so you get stick-slip behavior; high torque to start it slipping, lower torque to keep it slipping. A dry clutch is probably worse in this regard. A wet clutch may close the gap; static near dynamic values. I say "probably" and "may" because I have no hard data.

The dry clutches we tested at Kawasaki showed MORE LINEAR behavior than the wet clutches. Perhaps due to the lubrication of the engine oil? I do agree about stick-slip though.

The Verner and the Rotax 912 are both wet, but I think they have very different purposes. I suspect the Verner does a lot more slipping than you might guess at first glance; as noted before, a true damper in parallel with a spring. Seems unlikely that only two skinny friction plate sets would carry normal operating torque by themselves, and they're backed up by the springs in this regard. The Rotax 912 clutch does carry all the operating torque. I suspect the Rotax is intended to be a torque limiter, and doesn't slip much (if at all) in flight. I think it slips in passing through the first resonant period during start-up; the 912 system appears to idle above the F1 intersection.

The whole point of the viscous damper experiment was eliminating the stick-slip. Think of it this way. The suspension of your car has a spring and a damper, in parallel, at each corner. Automotive designers long ago stopped using friction dampers in that application.

Click to expand...

Actually friction dampers worked pretty well. I've a friend who does classic cars. (pre 1935) The problem was they did it in both directions unless you had some really odd ratcheting mechanism! My point about the slipper clutch idea is that we could start with a slipable clutch and the bobweights would in effect lock up the pack at higher rpms. Any reversal that was of a large enough magnitude to back the shaft up would slow the weights and should allow the clutch to slip again.

I work in the vacuum industry and one of the things I have always been facinated by is Ferrofluid. Magnetic particles suspended in a "carrier". Ferro fluids have the possibility of working as both a clutch and damper. With no electromagnetic current flowing the device would work like one of the Dodge couplings from the Molt Talor examples posted earlier in the thread. With the current on it acts like a solid shaft. Just some seals at the shaft and they are usually turning WITH the shaft, only moving when there is actually a differential. It is truly tough to find something that will act like BOTH a coupling and a damper.
Bill Jepson

DanH said:

The torque necessary to start slipping the clutch disks at the limit of each oscillation is the same as the slip torque when not in resonance. Same effective stiffness. I think the assembly is simply a damper.

Click to expand...

I disagree. The whole purpose of the system is to stop torsional vibrations. A clutch is a "dry" friction element, there is no "stiffness" in that element. But, this is not my field of expertice. I am simply trying to understand how these things work, and that is not easy because they all seem to be different, not only design differences, but different physical principles altogether . With the clutch-spring system (particularly from Verner) I see the same principles as can be found in typical large-displacement non-linear systems.

Consider this: Engine is halted, someone turns the propeller, and angular displacement is plotted as x-axis and torque as y. The k will be the tangent for that line or the slope, and if it is a straight line it will be constant (the basics as you know). Whith only a clutch installed, the line will break off at the preset torque and become horizontal, a torque larger than the preset torque will simply spin the propeller continuosly even though the engine has stopped. Physically the stiffness has become non-linear, and is dependant on amplitude. A driving frequency coinciding with the ressonance frequency for small oscillation, will not coincide with the ressonance frequency at larger amplitudes, because the ressonance frequency changes with amplitude. (with the clutch only, the system is no longer even an oscillating system when the amplitude becomes larger than the preset value, so there will be no phase shift vs the driving frequency, and the oscillations will continue at the amplitude where the clutch starts to slip).

With a spring in there in parallel to the clutch, the effective stiffness, the slope, will break off, but not to a horizontal line. I guess it would be possible to preload the springs with enough force and go without a clutch altogether, but in any case since the system has effectively changed stiffness, the driving frequency will be out of phase when the amplitude returns from the "dip" into the softer spring/clutch area and this will throw the system out of ressonance (untill it builds up again). I don't think the clutch really do much in terms of damping, it mostly enables you to design a light-weight system with small and light springs with low preload. I guess the system could be designed so that the clutch-spring system was operational most of the time, but I don't see any reason to do this (afterall, the propeller is still there with a tremendous amount of damping in most of the operational range).

Bjørnar,
<<Consider this: Engine is halted, someone turns the propeller, and angular displacement is plotted as x-axis and torque as y. The k will be the tangent for that line or the slope, and if it is a straight line it will be constant (the basics as you know). With only a clutch installed, the line will break off at the preset torque and become horizontal,>>

Good illustration! I accept the logic. Please disregard my "same effective stiffness comment".

<< (with the clutch only, the system is no longer even an oscillating system when the amplitude becomes larger than the preset value, so there will be no phase shift vs the driving frequency, and the oscillations will continue at the amplitude where the clutch starts to slip).>>

Agree, a torque limiter, like the late-model Rotax 912 w/clutch

<<(with a spring-clutch combination) ...since the system has effectively changed stiffness, the driving frequency will be out of phase when the amplitude returns from the "dip" into the softer spring/clutch area and this will throw the system out of ressonance (untill it builds up again).>>

Interesting thought. I don't understand phase shift well and had not considered it. Clever, thanks for pointing it out. This is the same principle behind dual-rate torsional spring applications, yes?

Our views on the Verner system only vary in one basic parameter. I believe the torque capacity of the clutch section is low, and you believe it is high. The difference results in two different operating theories, damper in parallel with springs, vs a phase shift device (or detuner, so to speak).

Unfortunately, we can't know for sure without a torque value for the clutch and stiffness value for the torsional springs. I'm thinking those two little clutch plates with small clamp pressure springs can't transmit 115 Nm (85 ft/lb) mean torque, and certainly not 2 or 3 times mean. The torsional springs look stiff too.

Either way it is a nice design; compact, light, mechanically redundant.

This is a great thread.

Bj?rnar,
Moving back closer to topic, would you have comments in reference to posts #33 and #41?

That must be seen in relation to the actual DIN standard. That calculation is only approximate, only valid for a 2 mass system, and is only valid when damping is very small. There could be large errors here.

If the mean torque is 100, the fireing amplitude is 2 times mean torque, Vr is 10 and Ma is 0.5, then the torque amplitudes will be (roughly) 100*2*10*0.5 = 1000, which is 10 times mean torque. For your suzuki it would be 40 times mean torque. Maybe the fireing amplitudes are much larger at lower RPMS?

Another thing is that amplitude is not always amplitude. Sometimes peak to peak is used instead of peak (which is the "real" amplitude).

<<That calculation is only approximate, only valid for a 2 mass system, and is only valid when damping is very small. There could be large errors here.>>

I agree. Even the standard calls it an approximation; useful only to determine a rough value for vibratory torque in resonance. It's underlying purpose is to assist in the selection of the correct rubber coupler.

I'm more interested in the big picture (our original topic), change in prop inertia vs change in shaft strain. To review, the DIN formula for "run through of resonance" is

Max torque = Ma*Ta*Vr*Sz*St

In our application, Ma = prop inertia / (prop inertia + engine inertia)

Ta is the exciting torque, something like 1.5 to 3 times mean (more later).

Vr is the "resonance factor", 2pi/c in the vicinity of resonance, c being 0.6 for Shore 50 and 0.78 for Shore 60 couplers.

Sz and St are factors for start-ups per hour and temperature. They can be ignored here.

So what we have is relative inertia x a torque x a factor which includes the coupler damping. The torque and the factor are both simple multipliers. Set them aside and we're left with the relative inertia calculation Ma=J1/(J1+J2)

I plotted Ma for a range of relative inertias selected to include realistic values found in our application as well as the dumb examples with which I began this thread. The realistic values were taken from my own Suzuki, and from a recent set of inertia figures for a 4-cyl Subaru crank and aluminum flywheel combined with the inertia of an MT-7 prop. In each case engine inertias were multiplied by ratio^2 to correct for gearing, those ratios being 2.12 and 2.0 respectively. The dumb examples were the 0.5-0.1 and 1.5-0.1 inertias from the first post (0.05+0.05 for the engine inertia). Here is the plot for the whole range:


I think I mislead you with the original poor examples, as they did not consider gearing. Your strain energy calculation was based upon them, and the plot closely mimics your conclusion; additional prop inertia makes little difference when prop inertia is already quite large compared to engine inertia.

The left side of the curve is where we find the actual examples. The indications of the curve (large change in amplitude with a change in prop inertia) match practical observation as well indicators like the Rotax restrictions on large-inertia propellers.

BTW, I realize a two mass model does not fully represent reality, but a system with a very soft torsional stiffness inserted in the middle (soft spring or rubber coupler) tends to act very much like a two mass model.

So, a layperson question; is J1/(J1+J2) an inappropriate equation for this general trend conclusion?

The exact solution

Considering two masses with a rubber coupling, the exact (analythical) solution for the displacement of the prop vs the engine will be (if my math is correct ):

theta_p = T_e * 1/((a*b/c)-c)

where
a = -J_e*om^2 + k + c*j*om
b = -J_p*om^2 + k + c*j*om
c = k + c*j*om

j is complex (as in the complex number z = a + j*b)

Then I calculate theta_p/theta_e = b/c to obtain the oscillating torque and displacement between these to masses.

I made a quick and dirty excel sheet with this, and it seems to produce reasonable results regarding frequencies and amplitudes for different k, c and Js. (The first time ever I have tried complex numbers in excel, and I don't think I ever will do it again )

Dan, I can send it to you in a mail if you want.

Bj?rnar,
<<I can send it to you in a mail if you want.>>

Yes please! And would you also define "om"?

Bj?rnar,
Got it. Nice tool, frequency and amplitude in a few clicks. I'll need some time to play with it.

Sure is nice to have a mathematician around here <g>