Propeller Inertia vs Torsional Amplitude

[DanH]

<<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?

[SvingenB]

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.

[rv6ejguy]

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.

[Rotary10-RV]

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

[DanH]

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.

[rv6ejguy]

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.

[SvingenB]

Originally Posted by DanH

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.

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.

[DanH]

<<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>

[Rotary10-RV]

Originally Posted by DanH

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.

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

[SvingenB]

Originally Posted by DanH

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.

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?