A question to all:

Assuming that machine is running well below the resonance, a 20-30deg lag is a common number.

What if a machine is running below resonance ( was verified by both bump and coastdown tests) but the lag angle is in the neighbourhood of 80-110deg? (The lag angle was established after a trial run as the angular difference between the vibration vector T caused by the trial weight (TW) and TW angular location.)

Could such a large lag angle be a result of misalignment rather then machine running close to resonance?

Thanks.

In velocity, 100+ degrees (even 90) would be believable, but not in displacement. Velocity leads displacement by 90 degrees. Velocity leads the force by 90 degrees at low speed, i.e. well below resonance.

One needs to align the force and measurement systems to get a physical lag from a balance weight addition. This would be the best method to determine physical lag. This is great for evaluating resonance location.

The trigger and the measurement point need to be aligned or adjusted for the difference. The balance plane phase reference needs to be adjusted to the trigger physical location; the balance plane is the force input. One needs to account for the balance weight location in this consistent coordinate system.

The lag angle is the angle of the influence coefficient, how much you moved the vibration with the balance weight corrected for balance weight position, etc.

Assume for simplicity that the reference point and vibration sensor are aligned and units of measurement are mils.

Phase lag can be determined during the trial run in a following manner.

If one placed a trial weight TW @ 130 deg, which in turn has produced vector T @ 150 deg( as vectorial difference between original and trial runs) , then the lag angle for this rotor is 150-130 = 20deg. In physical terms it means that TW passes the reference point first, and 20 deg later maximum vibration is sensed.

Is anything wrong in this approach?

For rotors runing above first critical the lag angle could be close to 180 deg.

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

quote:

Originally posted by Dave_man:
Assume for simplicity that the reference point and vibration sensor are aligned and units of measurement are mils.

Phase lag can be determined during the trial run in a following manner.

If one placed a trial weight TW @ 130 deg, which in turn has produced vector T @ 150 deg( as vectorial difference between original and trial runs) , then the lag angle for this rotor is 150-130 = 20deg. In physical terms it means that TW passes the reference point first, and 20 deg later maximum vibration is sensed.

Is anything wrong in this approach?

For rotors runing above first critical the lag angle could be close to 180 deg.

This looks like you are using consistent conventions (Ensure that weights are measured lag if the vibration is lag.). As such, you generate the influence coefficient angle, which is the true lag if the coordinate conventions line up.

This is the correct approach. You are using a perturbation method to generate a transfer function (frequency response function). Of course, one can compensate for the trigger not being aligned with the transducer by adding another lag angle.

The influence coefficient in consistent coordinates is the the synchronous vibration effect for a unit balance weight placed at 0 degrees. Hence, the angle is the rotor response lag to the input force.

Your method and assumptions are correct.

quote:

Originally posted by Rusty:
The problem with this approach, is the trial weight is not the actual "heavy spot" -- the actual heavy spot is the vector sum of the original imbalance (the imbalance that is there before you put your trial weight on) + the trial weight. If your rotor were perfectly balanced before you put the trial weight on, then your assumption would be correct. Otherwise, it's not.

Assuming you have an imbalance present, the lag is the difference between the "actual" heavy spot (imbalance + trial weight) and the resultant phase on the trial weight run.

I calculate lag after I'm done, because if I've balanced the rotor successfully, I know the initial heavy spot (imbalance) is 180 degrees from my balance weight (assuming I put it in the right place). And my original, reference phase is the response (high spot) caused by the initial imbalance. So the lag is the difference between the actual heavy spot, and the high spot.

First of all, by definition the lag angle is the angular difference between the "heavy spot" and the "high spot".

It could be calculated based on correction wight angular location + 180deg and the original vibration phase. But absolutely same result could be achieved during a trial run regardless of whether or not a rotor had original imbalance.

TW is a heavy spot introduced by the balancer. It produces a unique vector with an amplitude and a phase depending only on rotor parameters (at a given TW angular and radial position, and weight ). Assuming a linear system, any heavy spot in a rotor, including the original one, will produce the same lag.

Regards,
Dave

There are several thing that ca affect the response to imbalance and stability of a rotor, they are stiffness, damping and inertia.
A only ball or roller bearing has no damping but like you have a floating cilindrical roller bearing, may be you have a lot of dampin.
You need to move your critical speed in order to not to be excited for for speed. You could change your damping replacing floating cilindrical roller bearing for a roller bearing with elastomeric bearing dampers.
Please read :ASME Paper No. 68-LubS-9 and
ASME Paper No. 77-DET-27

quote:

TW is a heavy spot introduced by the balancer. It produces a unique vector with an amplitude and a phase depending only on rotor parameters (at a given TW angular and radial position, and weight ). Assuming a linear system, any heavy spot in a rotor, including the original one, will produce the same lag.

Dave,

Are you saying, that in reality the original imbalance produces a lag of "X" degrees and then if a trial weight, large enough to override and create a new imbalance (which is the purpose of the trial weight), is added at any position, the system will still have a phase lag of "X" degrees which is the same lag as the original "X" lag that is produced by the original imbalance?

Say for example:
the original amplitude was 10 mils at 10 degrees,
and the known phase lag was 30 degrees,
and a weight was added, at some position, and changes the amplitude to 12 mils at 75 degrees, then the phase lag would still be 30 degrees, since the transducer is responding to the trial weight imbalance now instead of the original imbalance.

Makes sense since the original lag was caused by the original imbalance and now the "balancer" has created a new imbalance on the same rotor by adding a weight, so the lag of the system should still, in theory, be the same.

We all know that the trial weight only creates a new imbalance so a vector calculation can be performed between the original imbalance and the induced imbalance, to determine where a correction weight can be added to offset the original imbalance. Therefore, the phase lag should always remain the same with or without a trial weight,,,,,,,, Unless the added weight causes a change in the mass of the rotor and then this mass changes the lag angle, but then that is another story .

Of course I could be totally wrong and will more than gladly delete this response if need be.

quote:

Originally posted by Ralph Stewart:

Are you saying, that in reality the original imbalance produces a lag of "X" degrees and then if a trial weight, large enough to override and create a new imbalance (which is the purpose of the trial weight), is added at any position, the system will still have a phase lag of "X" degrees which is the same lag as the original "X" lag that is produced by the original imbalance?

Ralph, Rusty,

Yes, that is exactly what I am saying. They do not teach this way in vbration schools and this is something I arrived on my own, but why not. Think about it. If a system is linear, it responds to an imbalance disturbance in a same way as far as SENSITIVITY (which we calculate during the TW stage) and PHASE LAG (which we also can calculate at this stage) are concerned regardless whether or not it is an original or additional imbalance.

In fact the phase lag calculated at the TW stage is going to be even MORE accurate then that calculated at the end of the balancing procedure since in the latter case the heavy spot location will not be accurate since we do not bring original vibration completely to zero at the end of a balancing procedure.

On another hand, accuracy of the phase lag calculated as angular difference between T vector and TW location is not influenced by anything except measurement accuracy.

You can calculate phase lag both ways and determined this for yourself.

David

The verbiage has gotten confusing as of late, at least for me.

One uses the principle of superposition for a linear system to get the lag angle and influence coefficient magnitude. One calculates the effect in vibration by vector subtraction, T as referenced, that the trial weight has, TW. T is not the actual vibration vector, unless one started with 0 vibration – then one wouldn’t be balancing.

The lag is the lag angle for T minus the lag angle for TW assuming consistent coordinate systems and measurement systems. If one had an instrument angle, then this could be factored in too.

Example.

O = original vibration 75 micro metres @45 degrees
TW = 100 g-cm @ 180 degrees
O+T = vibration with TW 50 micro metres @90 degrees

The T=(O+T)-O = 53.1 micro-metres @ 183 degrees

The lag angle would then be 183 – 180 = 3 degrees

ic = The influence coefficient would be in complex arithmetic (O+T)/TW
= 53.1@183/100@180 micro-metres/gm-cm
=0.531@ 3 micro-metres/gm-cm

The balance (can be used for 1-shot balancing) using the ic, CW=-O/ic as complex numbers.


CW=75@45/.53@3 g-cm=141 g-cm@ 222 degrees.

I probably am totally wrong, but.... the trial weight does in fact create a new heavy spot, but the new heavy spot is NOT at the trial weight position... the new heavy spot is the vector sum of the orgingal imbalance and the trial weight.... am I the only one who this seems obvious to?

Now as to how/when you calculate the lag angle, Dave may be correct in how he does it. (Bill says he is, so it must be so.) But until I verify this with a rotor kit, or some good balance data of my own, I'm holding to my right to (possibly) disagree.

Back when people were realizing the properties of linear response and balancing, Rathbone performed some famous experiments.

T. C. Rathbone~( author = {Thomas. C. Rathbone},
title = {Turbine Vibration and Balancing},
journal = {Transactions Amearican Society of Mechanical Engineers},
year = 1929,
volume = {51 - Part I},
pages = {267-284}), an experimental engineer in the Large
Turbine Division of Westinghouse at the South Philadelphia Works, used a strobo-vibroscopeto study the vibration of a large rotor (50 tons). The strobo-vibroscope used a microscope, reflective foil mounted to the bearing housing, and a strobe light. The strobe activated a neon flash which caused a pink spot to appear on the observed Lissajous figure indicating the angular orientation. A second strobe, synchronized to the first, illuminated an exposed portion of the shaft which had been painted to give an angular reference. In a series of experiments Rathbone applied various size balance weights that showed the amplitude responded linearly; he also placed a trial weight at different angular locations with the vibration amplitude remaining the same but the vibration phase shifting by the same amount as the changes in the trial weight angle. These experiments also found a difference between the housing and shaft vibration.

Rathbone in 1929 described a balancing method that used unit motions similar to influence coefficients for orbits, to reduce the vibration amplitudes at each end of a machine. The technique used linear superposition to simultaneously reduce the elliptical vibration pattern at both ends of the rotor. The unit motions were the elliptical motion that resulted from a known (unit) imbalance; the ellipses were referenced at a constant shaft rotation throughout the procedure. The author stated that J. P. Den Hartog, who worked for Westinghouse at this time, had an analytic solution to this problem.

Rathbone showed that the ellipse method produced two solutions, and he reasoned that data from only two vibration directions were needed, either the vertical or horizontal vibration would suffice. Using a shaft reference system, Rathbone expressed the vibration in one direction as an amplitude and phase, a vector.

He then used known calibration weights to derive the rotating ``vectors representing the influence of the unit motions alone,'' which we now know as the influence coefficients (vectors); these vectors could be denoted by an amplitude and phase. When using the vertical motion, phase would be computed by stroboscopic determination of the angular rotation of a mark on the shaft from the vertical plane at the moment the vibration (motion) reached its peak. This phase convention would correspond to a lag angle in today's terminology. The amplitude of the vector would be the magnitude of the vibration (presumed to be mostly at $1 \times$ rotation).

Rathbone then used an iterative graphical technique to reduce the vibration at both ends of the rotor. However, he knew that his solution involved the solution of linear equations, and although he did not present the results, he stated that the mathematical solution which was ``quite involved'' had been solved by an undergraduate at the University of Copenhagen named Nils O. Myklestad, whom we know along with Phrol from GE for the transfer matrix technique for calculating beam and rotor resonances.

quote:

the new heavy spot is the vector sum of the original imbalance and the trial weight....

One problem is that no person knows what or where (which planes) the original imbalance is nor the contribution of non-imbalance forces. Using superposition, one can in effect cancel out these effects to produce the influence coefficient.

Also, at the end of the balance the vibration at running speed is generally not zero unless the machine is not running. So as mentioned earlier, there is some residual error in this method due to the remaining vibration.

What is even better when you have more than one balance shot is to create a statistical model for the IC’s instead of the simplistic approach I showed in the example above.

This message has been edited. Last edited by: William_C._Foiles,

When I am balancing a machine that has 3 mils of vibration at 900 rpm, and I use a 500 gram trial weight and reduce the vibration to 1.5 mils, then my trial weight is not the new heavy spot, right?

It could be but probably isn't.

The concern should not be where the heavy spot is so much as it is what effect did and does a balance weight have. This gives the lag information.

[Rusty]The trial weight will be the heavy spot as such (still not the best notion for this)in your example only if you got a 180 degree phase shift in the vibration, i.e. The weight was placed exactly in the correct location, which we all do all the time , but too much weight was added.

Also, when considering lag angle one should consider various points, particularly if there is a resonance that has some effect. Mode shape affects the vibration lag due to a force at a discrete location, like a balance weight. If couple weights or modal weights are used, this has to be considered, too.

Given a rocking or pivotal mode shape, it is not unusual to see a lag of 270 degrees at a resonance for the opposite end to which the balance weight is added.

This message has been edited. Last edited by: William_C._Foiles,

David,
every body have spoken about balance. I continue thinking the problem is that your system over critical speed and very near. Too the system has very high stiffness.
When shaft speed pass over crit speed in high stiff system, amplitude is almost zero (your case) and phase angle change is 180º
When shaft speed pass over crit speed in more damping system, amplitude isnt almost zero and phase angle change is something less than 180º
OB floating cylindrical roller bearing has high rigidity (read in any google web pages)
I feel the problem isnt easy to solve because you will not solve balancing. I think :
or move crit speed or move shaft speed.
Move shaft speed isnt justified. Move crit speed induce to change bearing support design with more damping.
There are a lot of actions to solve this kind of problems in sleeve bearing but in rolling element bearing the support is purely elastic and the natural frecuency is sqr(k/m)