As I noted on the Vibration Institute board.

The 180 degree shift in forced response is a relative shift (for a relative or absolute transducer). By this I mean that you can see polar circles drawn in polar format. From a Bode format, you may not see a 180 degree shift. If you re-center the polar plot you should get (for a simple resonance) approximately a 180 degree phase shift. Re-center at the beginning of the resonance and see a possibly small circle for structural resonances (possibly large in some cases) drawn. If you can re-center (like run-out subtract) on a polar plot you should see a 180 degree shift, also. On the polar plots resonances appear as circles, even without re-centering.

Structural resonances typically have low damping compared to rotor dominated modes. Thus the circles are traversed more quickly with respect to speed change required to go through the modal circle.

Some resonances being viewed (forced response of the natural frequency) have rigid rotors. The natural frequencies of which are spoken here may be primarily structural or support resonances.

One may be looking at a relatively small modal circle masked by a larger primarily rigid (stiff) type response. The absolute phase may not change significantly; one must view the polar circles, i.e. the relative phase change at a resonance.

Multi-mode systems, split criticals, etc. with the supperposition of response can be more complicated on transient plots (Bode, polar, even waterfall).

J, perhaps this plot will help. This is not a polar plot, it's just a phase plot I do every time I balance a machine to see where the trial weight goes. On the machines I balance, I seldom see a 180 phase shift. As I said in my first post, at the 1st critical (resonance) the 'lag' between the heavy spot and the high spot (the high spot lags behind the heavy spot) is exactly 90 degrees. If on a coast down, the critical is well defined (160 deg. in my example), then at the critical speed, I know that the lag is 90 degrees. In this case that would put the heavy spot at 70 degrees (160-90), and my 'light' spot (where the trial weight goes) is 180 from the heavy spot... 70+180=250. Sometimes as the machine coasts to a low speed, the phase will stop changing (when the 1x vector becomes small) or just start bouncing around. I would expect the phase to be around 70 degrees in this example. You could just use this as the heavy spot. But having a well-defined critical makes the process of locating the heavy spot easier.

This works well on large, heavy machines that run below or a little above the 1st critical... not so well on smaller, faster, less well damped machines. On those, I just assume it is running at the 1st critical, that is there is a 90 degree lag (heavy to high spot). So in the example if my at-speed phase reading is 190 deg. (high spot), I'd assume the heavy spot was at 100 deg. and put the trial weight at 280. Normally this puts you in at least the right quadrant, so the vibration goes down, and you only have to move your trial weight 30 degs. or so.

This explanation is probably not technical enough for some folks, but it's based on Art Crawfords explanation of resonance in his handbook which I find to be a very practical reference. And it works most every time. Don't be fooled by the "180 phase shift at resonance" -- most of the time, that's not what happens. It's usually less than 180.

Bear in mind that large turbines with fluid-film bearings are a different beast entirely (as Bill explains so often). But for the other 99.9% of equipment out there, my approach works very well.

I like the way Update treats this matter in the first paper Arief references. I'm not sure I'm in 100% agreement, but it's explained in plain english and is easy to follow.

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

Rusty,

quote:

(160 deg. in my example),

Is this the actual phase shift you see during a coast down? And is the 90 degree phase lag a constant with or without a resonant influence? I have had a lot of success using a 30 degree phase lag and if it goes through a resonance I go 180 degrees to compensate for this. I have also had a lot of balance jobs where my actual correction falls somewhere in between my calculated spot. This would be great if I could use the actual coast down phase shift to pin point where to put my trial weight. Another question comes to mind, does the phase lag vary with different types of balance equipment? I use a CSI 2120 with an accelerometer and I balance using Mils. I know there is a 90 degree phase shift from Displacement to Velocity and another 90 degrees from Velocity to Acceleration but didn't think those came into play unless I was trying to convert from one to another during a balance job which I would never do.

Thanks,
Ronnie

Ronnie, I forgot to say so, but my discussion is valid when using 'mils' to balance. I like displacement when balancing because it's what the customer is used to (usually), the numbers are larger (fewer decimal places), and the phase is easier to understand (for me at least).

In this example, the 160 is the phase reading from the coastdown plot which corresponds to the amplitude peak at resonance. The idea is that if you know at what speed you hit a resonance, then you know at this speed the 'lag' (phase shift) is 90 degrees. This phase will be be lower than your at-speed reading (190 in this example) by the amount of the additional phase shift.

The easy way to think of this, is that at low speed, the heavy spot and the high spot are at the same place. As the machine speeds up (think of a variable speed machine) the high spot starts to lag behind the heavy spot. AT the 1st critical the high spot lags the heavy spot by exactly 90 degrees. Essentially, the response (high spot) lags the force (heavy spot).

I don't think of this 'lag' as a resonance issue (which it may be in fact) but rather as the inability for the rotor response to 'keep up' with the imbalance force due to inertia. That's not very technical, but it has greatly helped me understand rotor behavior in the field. Again, I don't work with large turbines or flexible rotor machines (well, not many). So I am always trying to simplify things to speed my work along.

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

Rusty,
Thanks, I think I understand now. The 160 is not the amount of phase shift but the actual phase reading at resonance. The rest is a matter of math to determine the actual phase lag at running speed. Then this would only work if you are running above resonance. I wonder how it would work if you were running just below resonance, say you had a 30 degree phase shift on coast down so you are not quite at resonance but close enough to have an amplification factor. Does anyone have any thoughts on what the phase lag would be under these conditions?

Thanks,
Ronnie

I see as many machines running below resonance (based on coastdown) as above. If you have a 30 deg. phase shift on coast down (from 'at speed' to 'slow speed'), then that is the actual lag. The high spot lags the heavy spot by 30 degrees. This is typical for large baghouse fans that I balance.

With a 30 degree lag, if your 'at speed' phase is 100 (for example), then the heavy spot is at 70, and your light spot at 250.

If you have a lag angle of only 30 degrees, you are not 'just below resonance' -- you are well below it (usually). Folks tend to think that machines run at one end or the other of the 180 degree phase shift, but I've not found that to be true. You can be anywhere in that range. For instance, I quite often see machines running with a 110-130 degree lag angle. If you watch a coastdown of a machine running well above resonance, as it goes through resonance, there is no radical phase shift at resonance. It just doesn't happen. If the machine has much mass at all, I don't think it's possible for it to physically have a large, instantaneous phase change (as seems to be thought).

This may be contrary to what others believe, but my opinion is that resonance does not "drive" phase behavior, but instead describes the difference between force and response which is what generates phase lag. I do not get hung up on where the resonance is when balancing. I only care about the lag angle. Generally, if I know that, the weight of the rotor and the trial weight radius, I can get very close on the first trial.

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

Thanks Rusty. I was thinking that a 30 degree phase shift would result in a 30 degree phase lag but wasn't sure. I do a good number of balance jobs myself and have always used a rule of thumb of 30 degrees if below resonance and 180 if above. I think I will start documenting my balance jobs with coast downs and put together some case histories on phase lag. Thanks a lot for all the information.

Thanks,
Ronnie

quote:

I don't think of this 'lag' as a resonance issue (which it may be in fact) but rather as the inability for the rotor response to 'keep up' with the imbalance force due to inertia.

What is a natural frequency? A natural frequency is the frequency where the inertia force and the stiffness cancel, because they are opposite and equal at this frequency (fairly precise definition). Resonance has a forcing function coinciding with this frequency under most people’s definition.

Due to the vector relationships among the forces due to the mass, the stiffness, and the damping, the response lags the input force (imbalance). This is the origin of the phase shift, and it is because of resonance.

If you learn to use polar plots, you will see and understand the phase shifts more clearly. Once you get comfortable with polar plots you can accurately draw the heavy spots on the paper. What appears to be a 110 degree shift in angles may be something very different when viewed on a polar plot and taking into consideration the origin and terminal points of the modal circle. Polar plots help decipher the superposition of forces and modes.

If all you balance is sub-critical machines (depending upon the type), use a rule of thumb of 20 to 40 degrees lag, and you have much success. If you balance a variety of machine types, learn about polar plots (modes and mode shapes), and you will become a much better balancer.

One reason to have concern about the location of resonances is that the (trial) balance weight size required for a given response depends greatly on this.

Even on ‘slow speed’ machines like fin fans, polar plots are useful. Polar plots can average out the response due to other fans with a similar but slightly different speed.

Bill,
What are some good sources for learning polar plots (modes and mode shapes)? I am always interested in something that will make me better at what I do. Most of the balance jobs I do are below resonance and that is why my rule of thumb of 30 degrees works but I also have balanced fans that run at and above resonance and obviously that rule does not apply. If you know of some good articles or books that aren't too technical, please let me know.

Thanks,
Ronnie

Books and articles about modal analysis may have good information; thumb through them (table of contensts) first. Classical control theory covers frequency response functions and polar plots -- not exactly the same thing as forced response but a good background.

There is an excellent paper by Kennedy and Pancu from the 40's (?), but I don't have my computer for a few days.

Bently Nevada's course on balancing and their advanced course used to cover this (I put it in.), but I am not so sure they do an adequate job in recent years. The Vibration Institute will probably do a better job (The balance course may cover this, but I don't have the notes. The instructor [who I think is the instructor] is very knowlegeable. I hope to cover this somewhat in the VI course on Rotor Dynamics and Balancing this summer; although the major emphasis is on rotordynamics.).

I am no longer with a gas turbine OEM, but all of their big industrial GT’s had velocity transducers. Most of the large new technology ones had proximity probes too. Many times all I would have was seismic. Aero-derivatives may only have an accelerometer or two. Gear boxes often have accelerometers. I’ve looked at all these.

Seismic transducers are an excellent idea for equipment mounted on spring isolators, even with rigid shafts such as fans should show a resonance if properly isolated. The basics are similar whether on the casing absolute or on the shaft relative. A precise examination theoretically of the polar plots will show that some forms should be ‘exact’ circles and some not, but to the eye they have a similar appearance. One must know that velocity leads displacement by 90 degrees, and acceleration leads velocity by 90 degrees.

Thus the plots for each will be rotated due to this phase relationship among displacement, velocity, and acceleration. When viewing a mix (For me this has been usually velocity and displacement.), one must keep these relationships in mind, or the plots can confuse. With both casing and shaft modes present, the primary modal circles may appear at different frequencies for each.

I’ve also looked at shaft riders in both displacement and velocity in polar plot format. I’ve used dual probes (seismic integrated to displacement and added to a shaft relative probe) as well as the individual signals from the probe elements. The principles are similar.

Polar plots are easier to read than Bode plots in most cases, especially with more than one mode. With seismic data there should be no slowroll; so this generally simplifies Bode plots of machines with one resonance. When you spin a shaft the rotor resonances are generally split due to asymmetric stiffness and gyroscopics. Theoretically, in the lack of presence of either asymmetry or gyroscopic effects rotors could have two modes at the same frequency (i.e. horizontal and vertical modes or backwards and forwards as the rotor types like to describe them), but this would imply perfect supports, which is not really possible.

I found the following with a google search.

http://turbolab.tamu.edu/pubs/Turbo31/t31pg091.pdf -even if it is from Texas A&M it’s ok



http://www.engr.colostate.edu/~dga/me324/Labs/Lab%2011/ME324%20-%20Lab%2011.htm shows a comparison between a Bode plot and a polar plot for balancing a tire. You may have to replace the % with spaces.

Bently pressurized bearings company shows a reference to Don Bently’s book which explains the polar plot method for locating the heavy spot, http://bpb-co.com/bpb/book/pdf/toc.pdf .

Regarding shaft relative and casing measurements again: The new Orbit article, http://www.bently.com/articles/articlepdf/1Q05_CH_One-ShotBalancing.pdf makes the following point.

quote:

It is noteworthy that the gas turbines in this case history had proximity probes and casing-mounted velocity transducers installed. The velocity transducers were mounted vertically on the #1 and #2 bearings of each gas turbine, while the proximity probes were arranged in an X-Y configuration as shown in Figure 1. It is customary for GE to install both types of transducers on many of their industrial gas turbines, and the authors strongly advocate this as a best practice for any gas turbine (such as the 6FA) that exhibits compliant casing and support structures [1,2].

Polar plots were reviewed extensively for this balance to ensure the physics looked right. As the article explains data from factory tests was used to generate an influence coefficient mode. However, the factory tests did not have a gear or generator attached; so the polar plots helped confirm that the dynamics of the field turbine was similar to the test units. I believe one reason for leaving out the polar plots was that the ’story’ could be told without them, and there were space considerations involved.

Polar plots were used to map the extent of the thermal transient. This can be essential for machines with a significant thermal transient, like this turbine.

Rotor Balancing Without Trial Weights
A. El-Shafei, A. S. El-Kabbany, and A. A. Younan
Faculty of Engineering, Department of Mechanical Design and Production, Cairo University, Giza 12316, Egypt
(Received Dec. 2001; revised Mar. 2002)
The traditional balancing methods using trial or calibration weights are quite effective, yet too many trials may result in a lengthy balancing process. It had been suggested in the literature that it is possible to balance flexible rotors without the use of trial weights, if a rotor model is available. A procedure is developed in this paper to balance flexible rotors using complex modes and complex vibration measurements. It is shown that a complex rotor model is essential for the success of the technique. Moreover, careful calibration of the rotor model is the major cornerstone of the procedure. Experimental results illustrate the success of the procedure
http://64.233.167.104/search?q=cache:eT1ws807iAgJ:www.dsto.defence.gov.au/corporate/conferences/hums/2001/pdf/5-16-2Duke.pdf+polar+plots+and+balancing&hl=en has some references to this but ?? for helicopters.
http://www.romadyn.com/publications/mech_behavior_casehist.pdf - Don Bently’s service company has a related article.

Here are some polar plots that came from a Vibration Institute presentation.

To Balance the above the thermal vector had to be considered as well as any startup or coastdown effects for this three bearing machine. The startup is in blue, the coastdown is in green, and the at speed with the thermal/load transient is in red. After balance

Note: This run was on gas - little combustion noise, easier conditions to balance.

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

In another format -- the issue was not entirely balance related. Combustion noise added to the overall vibration; so, the balance was optimized until the combustion issue could be improved.

Once you have a good influence coefficient model (experience), one can center the polar plots also. Notice the thermal/load vector is on the order of 80+ micrometres (3.2+ mils).

Note: 50 Hz machine -- at speed in red
Vibration after the thermal transient was very low, seen in center of plot.

Very interesting. What was the hardware setup on this? What software/system was used? (In other words, what does it take to generate this kind of data?)

This was generated by ADRE®
. Other software/hardware packages can generate this information.

I added comments with PowerPoint®.

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

Was this from a set of prox probes on a fluid film bearing?

David, i suggest you record a run down (at 2X filter) and check if run speed is up or down of rotor natural frequency (i think run speed is near resonance), so you can to know what do you can to change (stiffness or rotor mass), using next equation:
Natural frequency = stiffness / mass