n+1 and n-1 excitation of crankshaft torsional vibrations
n+1 and n-1 excitation of crankshaft torsional vibrations
(OP)
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.
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





RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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?
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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?
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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.)
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
6.0
12.0
9.0
3.0
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
Cheers
Greg Locock
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
Actually I've got a good mind to interrogate the guy who asked in the first place.
Cheers
Greg Locock
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
We've ordered vol 3.
Cheers
Greg Locock
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
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
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
Cheers
Noisun
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
Without going into a lot of detail, a reciprocating engine can produce both integer and half-integer frequency components of running speed. The exact orders and strength of the components depends on the number of cylinders, cycle type (2 or 4), and firing order. These components are primarily torsional in nature but can couple to produce lateral vibrations. We have tested 12 cylinder diesels and those engines produce harmonics starting at 1/2 of running speed and go up to 10/rev, with predominate components at 2, 2 1/2, 3, 3 1/2, 4, 4 1/2, and 5 per rev. If you are interested, I can send you a sample spectrum.
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
Cheers
Greg Locock
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
We have copies of S&V going back to the mid-90's, if I can find the article I can scan it and send it to you.
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
S&V 2001 Volume 35 fascicolo 9
22 Computation of Vibration Order Shift M. Turgay Bengisu
Could you send it to the very spammed up address :
greglocock at yahoo dot com dot au
thanks
Cheers
Greg Locock
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
Here's the mickey mouse explanation, he goes into maths later:
The simplest form is an unbalanced shaft rotating at 600 rpm. In an idealised experiment a strain gauge on the shaft will measure a static bending only, ie f=0Hz. An accelerometer on the bearing will measure a vibration at 10 Hz. So in this case the true physical situation has been shifted by +1 order.
He also does a worked example with some real data, and shows where n-1 comes from as well. If I sound a bit unenthusiastic, well, there ya go.
Cheers
Greg Locock
RE: n+1 and n-1 excitation of crankshaft torsional vibrations
FWIW, I worked briefly on this. The order transformation can help explain how resonances in mount vibration can be related to crankshaft torsion & bending. It's extremely difficult to measure unless one "demodulates" the entire waterfall, as Turgay did in his paper. His references give good additional background, especially Ochiai