Here are some excerpts from paper titled "Phase analysis, part 2" in March 2007, UPTIME issue.

On page 43, Fig. 9
"... For overhung machines ... because of the circular motion, there will be approximately 90* between the vertical and horizontal readings"

Further down on the same page in Misalignment section:
" When machine is misaligned there are characteristic forces at play in proportion to the degree of offset and angle between rotational centerlines of the shafts. ...if phase angle between vertical and horizontal is NOT between 110* and 70*, then there is a good chance that the machine is misaligned".

Further down the page:
" 2) If machine is misaligned we would not expect to see 90* difference between the vertical and horizontal readings taken at the same bearing. Instead they are likely to be closer to 0* or 180* ".

First of all, these smeared statements, like "there is a good chance", "are likely to be" do not specify as to when "there is a good chance".
Secondly, isn't this common knowledge that even a pure unbalance won't result in 90* phase difference between vertical and horizontal due to 2-3 times usual difference between vertical to horizontal stiffness (at least for horizontal machines).

Isn't that also true that in practicality phase readings ( at least on the same bearing) are such that by themself can not interpret machine condition ( misalignment vs. unbalance)?

What do you think?

IMO: Vert/hor readings way off 90 degrees are a strong indicator of resonance in the structure and you better first get rid of the this resonant condition before aligning or balancing.

This is part of the problem in our industry. People take good vibration analysis rules of thumb that were developed for shaft probes, and then try to apply them to casing readings (or vice versa). It just does not work they are two different measurements.

On shaft probes I would generally expect close to 90 degrees difference between horizonal and vertical. Not necessarily for casing readings because of stiffness issues you mentioned.

quote:

Originally posted by David_G:
Secondly, isn't this common knowledge that even a pure unbalance won't result in 90* phase difference between vertical and horizontal due to 2-3 times usual difference between vertical to horizontal stiffness (at least for horizontal machines).

Actually, the rule that unbalance causes 90 deegrees phase shift between H and V works with different stiffnesses as long as both directions are either far above or far below resonance. It can be an elliptical orbit and still have the 90 degree phase shift. Certainly as you point out does not hold for all machines, particularly if one or more directions is close to resonance.

I agree that simple application of the rules regarding phase can be misleading and need to be used with some caution.

FYI...An exact circular filtered orbit will yield a 90 degree phase lag difference between the horizontal and vertical signals. Once you depart from an exact circular orbit, the only time you will get an exact difference of 90 degrees is when the major axis of the filtered orbit is directly in line with a transducer.

John

quote:

Originally posted by electricpete:

Actually, the rule that unbalance causes 90 deegrees phase shift between H and V works with different stiffnesses as long as both directions are either far above or far below resonance.

For a single degree of freedom system:

tan & = cw / (k-mw^2)

( could be derived from a vector diagram)

& - phase angle between force and vibration
c – damping
m – mass
w - angular velocity
k – stiffness

For “w” far below then that at resonance,
mw^2 << k
and can be ignored. Therefore,

tan & = cw / k

or phase angle “&” is approximately inversely related to stiffness “k” at “w” far below the resonance. Closer to resonance this relationship becomes more complicated.

Therefore, in case of imbalance, when vertical stiffeness is, say, 3 times higher then that in horizontal, phase difference between V and H may significantly deviate from 90 deg.

If one plugs numbers into this equation he will get a feel as to how much it is different. Maybe those +/- 20 deg deviation from 90 deg mentioned in the paper account for stiffness difference.

John – I agree. The particular case under discussion is unbalance in presence of different stiffnesses H and V (for example V three times stiffer than H) and what happens to the H/V phase difference. The expected response is an ellipse with a major axis in the H directions and the minor axis along the V direction. Since we are talking about the phase shift H to V, it is clear these are also our monitoring directions. So in this case we expect the 90 degree phase shift in presence of unbalance (provided both far above or far below resonance per my comments), which I believe is consistent with your comments.

David – I agree with your math and I stand by my statements. Stiffness can vary over a wide range without affecting phase lag as long as we remain either far above or far below resonance. If we are far below resonance as you have shown, cw/k is a very small number close to 0 and the phase lag between force and displacement is very close to 0. We can change k over a wide range and we will still be very close to 0 as long as we remain far below resonance.

An example
cw/k = 0.001
alpha = arctan(0.001) * (180 degrees / pi radians) = 0.06 degrees.

decrease stiffness k by a factor of 10 while keeping damping cw constant:
cw/k = 0.01
alpha = arctan(0.01) * (180 degrees / pi radians) = 0.6 degrees.
(still pretty darned small)

So in this example, we could have a factor of 10 difference in stiffness between V and H and as long as both are far below resonance, we expect phase lag of both directions approximately the same (approx 0) and the 90 degree H / V still applies. Far below resonance certainly does not always apply and if the V is not tremendously far below it might have a phase lag of 30 while H has a phase lage of 0... then the rule no longer holds so well. If we had the luxury of having coastdown data in both H and V directions, we could adjust our expectation for the H/V phase difference expected for that machine in presence of unbalance away from 90 as appropriate.

This message has been edited. Last edited by: electricpete,

I posted the comment about there only being a 90 deg phase difference when the major axis is in line with a proximity probe because I am always amazed about the number of people who question data that doesn't have a 90 deg difference. Many people assume that since the transducers are at 90 deg physically, then the pahse lag angles should ALWAYS differ by 90 deg.

I first encountered this at Philadelphia Gear when I ran the test area and many QC people would ask for a calibration of the equipment since the angles rarely differed by 90 deg. Even now, in teaching seminars, I pose this issue and find many people that think that the difference should be 90 deg.

John from PA

If you look at what John said about the transducers being at a major axis, one has an interesting interpretation.

First the 1X vibraition is eliptical. Second, ellipses have major axis. Third, rotate the transducers and you have your 90 degree shift.

From this it follows that since all 1X vibration is elliptical then given the correct choice of transducer location all 1X vibration can have a 90 degree shift. It just depends upon the viewing directions. So, the theorem is:

All 1X vibration has a 90 degree seperation from a choosen set of orthogonal viewing positions.

Does that mean that all 1X vibration that results are balance problems?

Clearly not.

The discussion from my perspective was on a thumbrule involving cause/effect in one direction (left to right):

unbalance => 90 degree phase shift H and V under certain conditions.

1 - The arrow of causation points to the right. To my knowledge no-one in this thread has yet discussed turning the arrow around or discussing any other faults besides unbalance.
2 - The context is bearing housing vibration, there is only one standard set of radial orientations (H and V) in the world of housing vibration monitoring (on machines without prox probes), and these are also the planes in which we generally expect the maximum variation in stiffness. So the discussion about other monitoring planes doesn't seem to provide any relevance to discussion of the H/V rule to me. If we found ourselves in a situation where either H/V are not the monitoring planes or H/V are not the directions of min/max stiffness, then it would be relevant.

I have never been a big fan of putting too much emphasis on phase measurements, and we have not had tremendous luck using it.

I think from first principles in simple geometries, we can deduce expected phase relationships for unbalance fairly easily. For misalignment, it becomes more complex. For one thing there are a variety of types of misalignment, the mechanisms by which it translates to vibration are more complex etc. I can easily imagine that pure angle misalignment in presence of coupling with stiffness varying at 1x and uncoupled H / V stiffness (no rocking) can result in 0/180 phase between H and V housing vibration 1x component. At the same time, a coupling misaligned to the shaft can cause 1x with 90 degree phase difference. All of this under the assumption both directions far below resonance.

Neverthelesss, if I saw 0/180 phase difference between H and V on a machine operating far below resonances on a very solid base, that fact would point me more in the direction of misalignment than unbalance. If I saw 180 axial phase difference accross the coupling, that would also again push the decision towards misalignment. If also relatively high axial vibration, another nudge in that direction of misalignment. If a little bit of 2x had appeared in addition to the 1x (but TWF does not look like looseness), that would also nudge me in that direction. .

It seems many times, the indicators don’t line up pointing in one direction. The phase may not appear at either extreme +-90 or 0/180. We take our best guess. But the more tools we have (including the rule that we expect 90 degree H/V difference in presence of unbalance under conditions where both H and V are either far above or far below resonsnce), the better is our guess.

Just my opinion... always interested to learn more.

This message has been edited. Last edited by: electricpete,

Going back to the issue of difference in stiffness and its affect on phase difference between H and V ( measured on bearing housing)in a case of pure unbalance.

Pete, you were correct. I have plugged some practical numbers into the equation and even with values relatively close to resonance, such as, W/Wres = 0.25 and W/Wres = 0.5, damping ratio of 0.1, deviation from 90 deg turned out to be insignificant - just 7 deg.

But this very fact brings up the following important issue. Why so often then not we observe (in far from resonance region cases ) V/H phase difference such as 40 deg, 50 deg, or sometimes even close to 0 deg ?

What are the forces at play causing that? Dynamic forces due to Misalignment ?

David

This message has been edited. Last edited by: David_G,

The assumption appears to be normal modes and not complex modes. Rotor systems have complex modes.

Can you briefly explain what is meant by complex modes vs normal modes?
A difference in the damping?

Normal modes have either a 0 or 180 degree phase relationship amoung the physical points in the system. Complex modes may have other relationships; typically in rotor systems one talks about forward and backwards modes.

Most often these modes do not have a pure 90 degree difference between the H and V transducer locations.

Let’s try an example. This could represent a rigid symmetrical rotor in two fluid film bearings (Use a process fluid if you don’t like fluid film bearings.) with a force in the middle.

A simple model of a mass in a bearing can be used considering motion at the two bearings to be the same (not pivoting). Below is a scaled version of a bearing stiffness matrix, 2x2, similar in terms to a real bearing. The scaling is so that a unit mass matrix works – the displacement and forces will have to be re-scaled to look nice – after all it’s just units conversion.

k =

[ 40000. 10000.
- 100000. 200000.]

M = mass matrix, diagonal

1. 0.
0. 1.
(Consider small damping, so ignore if not at a resonance.)

The resonances are the eigenvalues (sqrt of), which are approximately

2059.5357 cpm and
4200.4391 cpm


Let the running speed be w=3600 rpm, well away from an Undamped resonance (Note: This has 180 degree phase change at the resonance, not just near it, because the system is Undamped.)

K – w^2 M =
[
- 102122.3 10000.
- 100000. 57877.697 ]


Give this an imbalance type force

F=
[cos(wt)
sin(wt) ]

In order to solve for response one needs A=(K-w^2M) =

Actually use a scaled version to get response(made up) units nice (maybe micrometres)

1000000*A=

[
- 11.786269 2.0364095
- 20.364095 20.796283 ]


Multiply by F on the right to get response of

x = - 11.786269 cos(wt) + 2.0364095 sin(wt)
y= - 20.364095 cos(wt) + 20.796283 sin(wt)

Use some standard trigonometry to get the following response

x = 11.96 sin(wt – 80.2 degrees)
y = 29.11 sin(wt – 44.4 degrees)

This does not have a 90 degree phase difference between x and y. Also, note the asymmetric response in amplitude difference.

If you like add a little damping and see if it changes much.

Interesting stuff. That assymetric K matrix leads to some very weird results. For simplified linear systems, we typically assume reciprocity (for example we get the same transfer function bumping at location and measuring at location B as we do bumping at location B and measuring at location A) which leads involves symmetric stiffnesses, right?. I guess when there is fluid involved, the rules change.

As a clarification, would it be reasonable to expect that we wouldn't see this type of behavior on a rolling element bearing machine with that has no possible fluid effects such as motor and possibly fan?

Gyroscopics gives a skew term in the velocity terms, also. This couples the x and y degrees of freedom. A small cooling fan in a small motor should have little effect.

Keep reciprocity (with a positive definite stiffness matrix and mass matrix) but add assymetry in the x and y directons.

If the x and y stiffnesses are diagonal then you still get the approximate 90 degree seperaton under the assumptions. This has a separate x resonance and a y resonance. Gyroscopics should couple these degrees of freedom to obtain forward and backward resonances with possible non-90 degree difference I would think (did not do this example) - damping differences (add damping too) between the forward and backwards modes could affect all this.

Couple the x and y directions in a stiffness matrix also changes the phase difference - not easy to think of a physical example off the cuff.