Propeller Inertia vs Torsional Amplitude

[SvingenB]

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.

[rv6ejguy]

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?

[DanH]

<<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:

[DanH]

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.

[Rotary10-RV]

Originally Posted by DanH

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.

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

[SvingenB]

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.

[DanH]

<<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.

[SvingenB]

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.

[DanH]

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.

[rv6ejguy]

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.