Hi,
I am interested in the static-couple balancing method. I have read here a lot about it, but I need help with the mathematic background of this method. can anybody help me with this? Do you know any link or can attach any document?

I would like a general example, not only in the case that the rotor is simmetrycal.

Is this method suitable for overhung rotors?
please help.

Regards,

can I have your e amil address to send the information

Hi Rubipako.
At the beginning of my career as a machinery engineer, when I first learnt about balancing, the rule of thumb that was drummed into me was to get rid of the STATIC out-of-balance first, then worry about the couple. I have applied this rule throughout my career, with such companies as GE, balancing their gas turbine and compressor rotors, and it's never let me down!
So, to your request. I have scanned the theory pages of my old balancing bible by Schenck and if you post your e-mail I'll send it to you. You can also look at this link which also explains the basics.

http://www.mpta.org/Primer.htm

Finally yes, this method is very applicable to overhung rotors. Very often, with a thin pump impeller, for example, you don't need to worry about the couple imballance once you have cancelled out the static.

Ok, thank you very much. My e-mail is rmerino@ideko.es

All the information you can send me will be helpful. As cheddar-caveman says I am learner in balancing. I am specially interested in static-couple method because I have heard it is usually employed to balance overhung rotors which I often have to, such as grinding wheels.

Another problem I have is the following:

The grinding machine control balances dynamically the radial vibration level in the overhung wheel, so the level decreases. However, once balanced (single plane in the wheel) the axial level increases. If I give again out of balance the wheel, the axial decreases again.

the weight of the wheel is quite heavy so I have supposed that the bearings could not be stiff enough to support it.

Thanks

Dear Cheddar-Caveman,

Since you have gone into the trouble of scanning your balancing bible by Schenck, I certainly would appreciate receiving a copy of it myself, I you please.

My email: leobeaulieu@videotron.qc.ca

Thanks,

MarkoLeo

I can recommend an excellent book called "Machinery Vibrations: Balance" by Victor Wowk. It has the best and most easily understood explanations of balancing in general and specific methods of balancing I have seen. It is available on Amazon.com and other sources as well I am sure.

Hi Cheddar-Caveman

I'm also interested, my email is afmn55@streamyx.com

Thank you

Hi Cheddar Caveman,
I have two books from Schenck
1-Balancing Technology By Hatto Schineder published by Schenck Germany
2-Dynamic Balancing published by Schenck Trebel,USA.
The book you have scanned-is it No.1 mentioned above or different?

The manual I have here is "Fundamentals of Balancing" from Schenck, 1980. I got this free when I bought a Schenck Trebel balance machine.

It takes one through the basic theory/maths of balancing, introduces one to the balancing machine, how they work and how to calibrate them, Balance tolerance nomograms, field balancing etc etc.

A bit of sound advice for up and coming balancers.
1/. Always do a "known weight check" on your rotor AFTER completing the balance. This immediately confirms that the balance is good and takes into account any residual errors there may be in the balance machine.
2/. Always carry out an "index-balancing procedure" when using end-drive adaptors or arbours to balance your rotor/disc etc.

This message has been edited. Last edited by: cheddar-caveman,

dEar cheddar-caveman,

Can I also have a copy please? Thank you.

my email: gerjes@maltanet.net

Does anybody have anything specific about the static-couple method? I mean, the mathematics of this method to balance a rotor.

I'm beginning to get a bit confused as to exactly what YOU think "static-couple" balancing is. All out-of-balance problems comprise static and couple forces.

In my thirty+ years of balancing, particularly when using a balance machine, the procedure has been to do an initial run. Then either the operator (in the early days) or the machine splits out the two out-of-balance components using a simple vector calculations. Then you correct the STATIC component by adding/removing weight. Re-run the machine and you should be left with purely couple unbalance. This may or may not be a problem depending on the rotor configuration. Very thin rotors/discs can run perfectly smoothly with considerable couple unbalance present.

This site is very good for this subject.

http://www.update-intl.com/BalancingBook.htm

Regards

Here's my take.

What you described cheddar caveman is a static couple solution.

The math model for a static/couple solution is
VStatic = ICstatic * Ustatic
VCouple = ICstatic * Ucouple
Where
Vstatic = (V1+V2)/2
Vcouple = (V1-V2)/2
Ustatic = (U1+U2)/2
Ucouple = (U1-U2)/2
There is assumed to be no cross-coupling assumed between static and couple problems, so solve each one separately using the "single-plane" balance solution method. This is simple enough to do on graph paper.

Compare that to the math model for a general 2-plane balance:
V1= IC11 * U1 + IC12 * U2
V2= IC21 * U1 + IC22 * U2
Here due to the assumed coupling, we can't break the solution into two uncoupled parts (for example plane 1 and plane 2 are not uncoupled), so we solve the problem all at once rather than breaking it into two parts. This solution is much more complex and very difficult to implement graphically. It almost always requires a computer solution.

The math model for the general 2-plane balance has 4 independent influence coefficients where the math model for the static-couple solution has only 2 independent influence coefficients. It should be evident that the static couple model is a special case of the more general 2-plane model. In fact you can mathematically derive the static-couple model from the 2-plane model IF you assume the rotor is symmetric end for end (IC11=IC22 and IC12=IC21).

If since the 2-plane solution is the more general method, if all measurements were accurate and the system was linear, it should always work as good or better than the static couple method (it should work better when there is an assymetry). But in the real world, the static couple method also works welln on a lot of problems that are not symmetric, and often better than the general 2-plane method.

I'm not sure I understand exactly why that is. My rambling thoughts: Apparently there is a large cross coupling from static to couple for overhung rotors. So small measurement errors can cause small error in static which creates large errors in apparent couple. So removing that static imbalance first and then calculating the required couple correction makes the process more tolerant to errors in measurement and weight placement and deviations from linearity.

Just my thoughts. But then again I have never personally done a balance job, so take it with a grain of salt.

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

Hi Pete,

Gosh... if RubiPaco was somewhat puzzled about force and moment balancing, I suspect that you have just blinded him more with your last post...

I do not doubt the veracity of your explanations and resume, mind you ! But, I've been in this business of balancing for more years than I care to count and I am totally confused by your post.

You are pushing up the balancing theory a few notches more... perhaps to a higher level of science that the ordinary technician cannot digest.

In my books, balancing is 30% theoritical and 70% common sense.

Thanks for your post... my friend !
No pun intended !!!

MarKoLeo

Sorry, I got carried away on that response.

My main point was to respond to cheddar caveman to identify that there is a difference between static/couple method and full 2-plane balance method as programmed into analysers. These are two different methods. Would you agree?

Hi Pete,

Yep... you are quite right and I agree.

There definitely is a difference.

Regards,

MarkoLeo

I also fully agree with you guys that there is a difference between static/couple method and full 2-plane balance method as programmed into modern analysers and balance machines.

Ruipako appears to be somewhat new to the world of balancing and I was only trying to pass on a few tips gained over the years.

We all, except electricpete, seem to have lost the original question, what is the mathematic background to static-couple balancing?

I think he now has enough info to keep him going for weeks!

Static-Couple (as defined for multi-mode systems - also applicable to other types, but theory differs) developed as a simplifed modal technique. One attempts to balance one (perphaps even or odd modes) mode at a time.

If the static and couple weights have modal properties the balance shots decouple; this means that a static shot (1st or 3rd mode) does not couple to a couple (2nd mode) shot and vice versa. In an ideal case where there is no actual coupling between shots, then the balances would be equivalent. However, in practice a static shot produces some, hopefully negliable, effect on the 2nd mode response. Modal balancing was extensively studied starting in the 60's.

If one uses static and couple shots and includes the cross effects then it can be shown that equivalent balances can be computed. In the balance calculation one can use the actual responses at the bearing locations instead of the static and couple responses; after all the goal is based on transducer vibration levels and not static or couple vibration levels. If one uses the vibration response measurements in the balance calculation, then the mult-speed multi-probe balanc programs can be used.

Mathematically it is not difficult to show that any balance state (that is achievable with only the two balance planes)can be achieved either with conventional weights or static couple weights.

Hey Bill, since you are an ex GE hand, could you decribe for me the vector approach GE uses for static/couple resolution. I was pretty indoctrinated by the Bently approach and I never really understood all those triangles the GE guys would draw to figure out how much was static and how much was couple....Thanks

GE didn't teach me this. This information is simple vector calculations. Also, Jim Lindsey's paper is on record for those who want to find it (circa 69).

First one draws the two 1X vectors, one from each end. Vectors U1 and U2

Next, connect the vectors. Graphically, this is the difference between the two vectors - U1-U2 and U2-U1 depending upon the direction (Put arrows at each end and you have both.).

Bisect the U2-U1 (Classically, one would complete the parallelogram, as if to add the vectors - draw the diagonals and they bisect each other including the desired U1-U2, U2-U1). If you have completed the parallelogram, the other diagonal is U1+U2.

By drawing both diagonals with the natural bisections, one has (U1+U2)/2, the static component, and (U2-U1)/2 and/or (U1-U2)/2, the couple components.

This was covered at a UVA short course this August. Also, this material is covered at Vibration Institute courses/material, including one I gave in New Orleans this year.