n+1 and n-1 excitation of crankshaft torsional vibrations 1

[GregLocock]

Please could someone (Tom?) point me in the direction of a good discussion of the source and the 'correct' way of thinking about this. I know that it is concerned with the difference between rotating and stationary frames of reference, and that it affects orders, but not frequencies.

I'd even hazard a guess that it has a great deal to do with intermodulation.

I'm pretty sure it is covered in Kerr-Wilson, but the only copy I've ever read of that is two decades and 10000 miles away.



Cheers

Greg Locock

 

[ivymike]

Greg, I've been waiting a couple of days to see what responses you get on this one, and so far none have materialized. I'm not entirely sure what you mean by n+1 and n-1, so there's a good chance that I won't be able to answer your question, but if you could clear that up for me I'd appreciate it.

 

[GregLocock]

OK, when you plot TVs on a Campbell's plot or waterfall you get 'phantom' excitations. For instance, on a 12 cylinder you'd expect a strong 6th order firing line, but you also (reputedly) get 7th and 5th appearing at the appropriate speeds, rather stronger than you'd expect.

I am less than 100% convinced by this, and it is several zillion years since I read about it, but it has just come up again.

I have strong suspicions from a physical point of view that it is an instrumentation issue rather than a real thing.





Cheers

Greg Locock

 

[ivymike]

First thing in the morning I'm going to go have a look at some campbells and see if they're there.

Besides instrumentation "smearing" the signal, how about the harmonic content of the firing pressure traces? Would you think that the irregular shape of the cyl pres trace might result in significant firing+1 and firing-1 excitations?

 

[GregLocock]

No, what /I/ think is happening is that the first order irregularities in the toothed wheel tend to modulate the other signals. Almost everybody used to use the same (A&E) demodulator, so our downstream instrumenation issues were all similar.

This is not what the official story is, that's just my guess, unless I see a convincing argument in favour of the rotating frames of reference explanation.

So on your plots at say 300 Hz, first crankshaft torsional, I'm talking about peaks at 3600 rpm 5th order and 2900 rpm 7th order, for the V12.


Cheers

Greg Locock

 

[ivymike]

I'm not familiar with the rotating frames of reference explanation - how does that one go?

 

[ivymike]

I've just taken a look at some V12 cranknose displacement predictions, based on a forced-damped lumped mass crankshaft representation with 24 half-orders of harmonic excitation due to cylinder pressure and inertia of the reciprocating assy, with the cranknose damper removed.

I note a crank resonance at about 52.5Hz in the results, which compares fairly well with a 1-node mode frequency of 54.7Hz calculated by the holzer table method.

There are five significant 1-node mode resonances within the running range studied:
rpm / order / amplitude
420 / 7.5 / 0.4deg <- n+1.5
530 / 6.0 / 1.17deg <-fundamental
570 / 5.5 / 0.3deg
700 / 4.5 / 1.08deg <- n-1.5
1050 / 3.0 / 0.43deg

Torsional excitation orders applied at each crankpin (due to cyl pres + inertia):
order / amplitude (N.m) / phase (deg) / big resonance?
3.0 / 2633.6 / -15.4 yes
3.5 / 2180.1 / -25.1
4.0 / 1681.6 / -31.4
4.5 / 1352.4 / -40.5 yes
5.0 / 1003.2 / -46.5
5.5 / 761.2 / -55.3 sorta
6.0 / 597.5 / -62.2 yes
6.5 / 487.4 / -71.3
7.0 / 381.4 / -78.7
7.5 / 284.0 / -87.7 yes

Off of the top of my head, I can't tell you why the crank favors the 3.0, 4.5, 6.0, and 7.5 orders (to a lesser extent 5.5). My guess is that the phasing adds favorably given the firing order of this engine (note consistent 1.5 order separation between the four "biggies").

Since these are simulation results, there isn't any instrumentation error introduced. Is this the sort of phenomenon you're discussing?

 

[ivymike]

sorry, the excitations shown above were cyl. pres. only. The crank responses given were due to cyl pres + inertia. It will take a little extra work to get out the combined excitation... in progress.

 

[ivymike]

at 500rpm, inertial excitations are as follows:
order / amplitude / phase
1.0 980.7 0.000
1.5 0.0 180.000
2.0 1865.8 180.000
2.5 0.0 180.000
3.0 738.9 180.000
3.5 0.0 0.000
4.0 61.8 180.000
4.5 0.0 180.000
5.0 9.6 0.000

(note that these components fall only on whole-number orders, and peak at 2.0, which makes sense for the recip assy. Also note that the forces will increase with increased rpm.)

 

[ivymike]

for the firing angles of this particular engine (somewhat unusual v angle that I probably shouldn't mention), the following orders seem to add constructively (based on a quick hand calc):
6.0
12.0
9.0
3.0

 

[GregLocock]

That's an interesting approach - if it doesn't show up in a "good" simulation then I'd guess the probability of it being a measurement artefact is much higher.

Dredging the rotating frames of refernece explanation up from memory it runs a bit like this:

The (say V12) crankshaft is rotating, and is excited by the combustion force six times per rev. However, it has rotated once in that rev, so per revolution it only sees five following or 7 leading impulses????????

No, that just confuses me. I have found a few mentions of n+1 excitation, but nothing resembling an explanation. We've reserved a copy of Kerr-Wilson, so a solution is a couple of weeks away.

Cheers

Greg Locock

 

[ivymike]

um, the frequency of the excitation is the same whether the crank sits or spins, right? The natural frequency of the crank is the same either way, right? Then whaaa?

 

[ivymike]

and if it makes any difference, the anonymize results above are for an actual engine, and the results agree with calculations performed by at least three separate companies, and they supposedly correlate well with measurements (I haven't seen the measurements).

 

[GregLocock]

I agree, I was naive when it was first explained, now I am much older, much more cynical, and frankly I don't believe it. None the less, I've been asked to check it out.

Cheers

Greg Locock

 

[ivymike]

well, if you'd like anyone to do a torsional vibration analysis (analytically) to help, your favorite consultancy would be happy to get the work (although I expect you could probably pull together something pretty fancy on your own)

 

[GregLocock]

Like I said, we get the book of all knowledge in two weeks, so I'll get back to you with story then.

Actually I've got a good mind to interrogate the guy who asked in the first place.



Cheers

Greg Locock

 

[ivymike]

I got a chance to look at some measured vibes from the nose of an I6, and it showed both 3-order and 4-order peaks, but no significant 2-order. After some discussion with another guy at work, we still strongly disbelieve the "it does the hokey pokey while turning itself around" explanation, and favor the idea that certain harmonic components of the firing pressure trace are combining favorably along the crankshaft to result in the observed nose displacements.

 

[ivymike]

got the book yet?

 

[GregLocock]

Yeah... sort of. It is in three volumes, I've only got vols 1 and 2 so far. I'm losing hope, vol 3 is the most likely to have it in, but neither of the others mention it that can find.

We've ordered vol 3.



Cheers

Greg Locock

 

[dangnm]

Dear GregLocock, I read something about "Vibration Order Shift" in the past and maybe you are looking for something like that...

The problem comes from the reference system you are considering.
Let's start with shaft bending vibration: if you are ON the rotating shaft, you can perceive its vibration (orders and resonances): x(t), y(t). The transducers are in the stationary frame.
The relation between rotating and stationary coordinates (of shaft center line in a plane normal to rotation axis) is:

X(t)=x(t)cosT-y(t)sinT
Y(t)=x(t)sinT+y(t)cosT

being:

X(t),Y(t): displacements of shaft axis in stationary reference, i.e. what accelerometers can measure!!
T: rotation angle between two reference frames.

Because of shaft rotation f: T= 2*pi*f*t

If you replace x(t) and y(t) with whichever harmonic vibration component (e.g: A*sin(2*pi*fi*t) and you
change domain (from time to frequency), you will have spectrum lines at (fi-f) and (fi+f) for X(t) and Y(t).
Consider that X(t) and Y(t) are exactly what your transducers are measuring!!!
That's why in Campbell diagrams of X(t), Y(t) you have rotor unbalancement at f (not fixed, if you are in run down), while, in x(t), y(t) Campbell diagram, unbalancement has to be seen like static inflection (f-f=0Hz, which ever the running speed), and physically it makes sense...
And probably that's why an integer shaft order nf (in rotating frame) is measured by transducers like (n-1)f AND (n+1)f...
The same for resonances excitated by shaft order...

I found an article in the net on this subject, with a detailed math discussion, but I didn't find it anymore, and I remember the author fitted and tested the previous considerations (made for bending vibrations) also on crankshaft torsional vibrations.

In my opinion it depends on which kind of vibration you are interested...probably, for torsional crankshaft vibrations (I'm not involved in such matter), the best reference to be used is the rotating ones, and, if your transducers are in the stationary frame, you'd need an "order shifting"...

Cheers