Negative Frequency? 1

[Tobevibrationexpert]

Hi,

Can anyone explain to me the significance of Negative Frequency? I have observed this in a vibration report (Spectrum Plot) from a 15 MW vertical hydro turbine-generator, operating at 250 RPM and under 32 m working head. The instrument used was ADRE 208 and 7200 & 3300 series non-contact eddy current probes from Bently Nevada.

 

[SomptingGuy]

Fourier transforms on time-domain data produce spectra that have redundant information in them. You get the useful positive frequencies (up to half the sample rate) and then a load of repeats (the complex conjugates of all the positive frequencies). Most people would just chop off the conjugates, but they have their uses and can be thought of as negative frequencies.

I could go further if this is the right direction.

- Steve

 

[electricpete]

Bently Nevada presentation uses a graphic presentation of x and y motion called full spectrum.

At a given frequency magnitude, we can have positive frequency to represent forward (in direction of rotation) orbitting and negative to represent reverse rotating.

If you have motion in a straight line, the positive and negative frequencies are equal.

You might find some info if you google on "full spectrum"

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[electricpete]

Here is a link that will explain it:

http://www.bently.com/articles/articlepdf/1293southwick.pdf

By the way, Steve comments above are absolutely right from a math perspective. But I think that in the context of vib reporting for large machinery, his comments do not apply. This useage of the term "negative frequency" is something different than what he described.

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[electricpete]

In the above article, focus on figure 7. The right hand side frequency is labeled as positive and "forward" while the left hand side is labeled as negative and "backward"

The discussion above that describes the math on how we can convert the two vectors x and y into two vectors + and - representing forward and reverse.

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[SomptingGuy]

Interesting. I'm glad I stopped when I did, given that I was going in the wrong direction.

This sounds a bit like decomposing sound fields into forward travelling and backward travelling waves.

- Steve

 

[Tobevibrationexpert]

I have a friend Tim who has to share this with me. I thought this might as well educate others. I would also like to thank everyone who shared their views on this subject, specially electricpete. That was a very educative article.

The spectral data you are looking at is separated into forward precession right side) and reverse precession (left side) components.

Bently developed this plot format after many years of working with Orbit plot analysis. When you filter the Orbit to a specific frequency, you can determine whether the vibration is actually moving with the shaft rotation or against it.

For discussion lets look at raw unbalance of a shaft. If a shaft is perfectly balanced and there is little or no radial loading on the bearing,then the orbit should be a perfect circle. Now what happens when you unbalance the shaft? The orbit gets bigger but the shape does not change.
The vibration from the unbalance condition is moving with the shaft.

Now lets make the unbalance load higher driving the Orbit amplitude higher until it causes a rub between the rotor and the casing. The Orbit shape will start to flatten. As the orbit becomes more flat and the rub becomes more severe many things can happen, but we will keep this simple for the moment.

As the rub initiates, now the '1X' vibration is caused by imbalance and the rub. The rub is actually 'dragging' the shaft and that is what is causing the 'additional amplitude'. The amplitude now has the rub and the imbalance
components in it. The 'drag' of the shaft causes a portion of the vibration amplitude to be in the opposite (or reverse) direction to the shaft rotation.

That 'reverse precession' information is available in the Orbit plot, so Bently developed the 'Full Spectrum' plot to review all the component frequencies and what portion of the frequency was in forward and reverse precession.

The most typical causes for reverse precession would be rubs or heavy bearing loading due to misalignment.

 

[TPL]

Another way to picture this is to make a circle between your thumb and forefinger - this represents the bearing.

Push a pencil (to represent the shaft) through the bearing clearance.

Turn the pencil to represent normal operation.

Now, keep turning the pencil and allow it to contact the bearing clearance - whilst maintaining the same direction of rotation, it runs against rotation around the bearing clearance - this is reverse precession as generated by a heavy rub, although the actual rub location is more likely to be a seal than a bearing

I cannot imagine how misalignment causes reverse precession unless the misalignment causes a rub.

BTW - you must be 100% sure of the actual direction of shaft rotation and the location of the 2 probes required to generate the orbit. Get any one of these wrong and you will 'see' reverse precession. In machinery diagnostics applications, the most common cause of reverse precession is 'crossed probes' where the labelling of the X and Y (or vertical and horizontal) probes is indavertently swapped.

As always, never rely on just one piece of evidence to make a diagnosis - whislt a heavy rub might generate reverse precession, the presence of reverse precession does not indicate a rub. Look for addtional supporting info such as abnormal shaft centreline plots and non-steadt and non-repeatable vibration.

 

[electricpete]

I cannot imagine how misalignment causes reverse precession unless the misalignment causes a rub.

It is not really physical reverse precession.

The math transform provided transforms two vectors (x and y magnitude/phase at a given frequency) into two other vectors (forward and reverse magnitude/phase at a given frequency).

If we have pure circular motion (x magnitude matches y magnitude) in the forward direction (x leading y if rotating CCW), that gives a pure positive frequency vector.

If we have pure circular motion (x magnitude matches y magnitude) in the reverse direction (y leading x if rotating CCW), that gives a pure negative frequency vector.

Any other combination of x and y vectors which is not purely circular (equal magnitude) can not transform into pure positive or pure negative and therefore must transform into a combination of positive and negative frequencies.

If we have pure linear motion (phase of x matches phase of y), then we get equal magnitude positive and negative frequency components. This particular case is well familiar to those dealing with electrical motors - the linearly oscillating field of a single phase motor can be analysed in terms of a sum of equal forward and reverse rotating fields. Also the simplest (textbook) 3-phase motor has three linearly oscillaing fields (one per winding). Each of these three fields has a forward and reverse component. The spatial and time arrangement of the three windings is such that the reverse components of the three phases cancel and the forward add giving pure rotating field.

Misalignment creates a preload which MIGHT create something resembling a linear orbit with equal positive and negative frequencies (also might create banana shaped with harmonics or other stuff). For that matter unequal H and V stiffness can cause non-circular orbit.

An interesting case where physical reverse precession does occur is when very unequal H and V stiffness give a "split critical" (different resonant frequency H and V direction). If we are far above the H critical but far below the V critical, then the 180 phase shift caused by increasing speed through the H critical causes reverse precession. The negative frequency will likely be higher than the positive frequency in this region.

Actually I don't think Don Bently was the very first person to conceive of this transformation applied to rotating equipment. I think W Foiles was the very first (sometimes posts here). There are a lot of others on this forum as well that work with this stuff a lot more than I do. Steve S, Steve C, Walt S. etc. Maybe some of those guys will chime in if I have said something wrong.

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[wolf39]

If a shaft/rotor is perfectly balanced: Why should an orbit develop with a perfect circle? Instead the shaft will wobble around in its bearing clearance in an unpredictable manner, limited only by the dynamic oil film thickness or seal and bearing clearances. Don't forget the stochastic forces acting on the turbine shaft portion having their origin in whirl/vortex conditions of the hydro turbine. These forces excite the shaft and prevent a perfect circle. Shaft and coupling misalignmement and out-of-plumb are also factors to be considered.

Regards

Wolf

http://www.hydropower-consult.com

 

[GregLocock]

Why should an orbit develop with a perfect circle?

Because there is a self excited perturbation.

As an example, if the flow of lubricant is dynamic, then if a small perturbation results in a reduction in lubricant film thickness it will cause an increase in velocity, and a decrease in pressure, so the perturbation can increase.
That sort of phenomenon is a very common form of non linear excitation.




Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[WCFoiles]

'If a shaft/rotor is perfectly balanced'

There's the rub, so to speak. This is impossible. Besides, there are other forces to consider.

A perfect circle is unlikely, also. Support asymmetry split the natural frequencies, so do gyroscopic effects. If the x and y dominating natural frequencies aren't equal with 'rotated' mode shapes, the rotor motion is elliptical, even reverse. Elliptical motion can be decomposed into forward and backward circles (circular orbits, when thought of as a parametrically generated ellipse, which vibration is).

One all too common problem found when doing full spectra is that the x and y probes are switched.


The 'Full Spectrum" performs this decomposition and has a nice visualization. I had no input to the visualization; the commercial development of this occurred after I left Bently Nevada.

When it was more popular to watch the orbits on oscilloscopes during startups, steady state, or coast downs, one naturally saw reverse precession occur between the split criticals. Typically, the orbit would expand in the x-direction, more or less, flip over as the phase change occurred that relates to the x-direction resonance. Then as the y-direction resonance was approached the x-direction reduces and the y-direction expands with another phase change, putting the orbit back into forward precession. Only trying to create a mental picture - If you have seen it, you know (or we could resort to math and superposition of modes, which would only be an approximation for a rotor system).







Regards,

Bill