Propeller Inertia vs Torsional Amplitude

[DanH]

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.

[Rotary10-RV]

Originally Posted by DanH

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.

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

[SvingenB]

Originally Posted by DanH

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.

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).

[DanH]

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.

[DanH]

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

[SvingenB]

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).

[DanH]

<<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?

[SvingenB]

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.

[DanH]

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

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

[DanH]

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>