What i am asking is totally different, if a rotor is having correction planes at left plane , middle plane and Right  plane.I.e we have to use all the three planes at a  time, when the phase angle of left and right plane should in static mode only.

If we add some trial mass in the Middle plane, left and right plane mass should be distributed with reference to middle plane mass in such a way that the unbalance at low speed should not change and vibration at rated speed will be  reduced.

for eg : If left and right plane mass is added in zero degree , middle plane will be added in 180 degree.

Sample rotor pic attached for reference.

Pl. suggest if any one knows these calculation.



Images (1)


In that case, what you need is a literature a balancing method that is already well developed and known as a static-couple balancing method. What it does in simple words is that it balances the static unbalance in a way that will generate a couple imbalance and it balances the couple unbalance in a way that will not generate a static imbalance. Many times this is only done on two planes.

Please search on the forum by these keywords and you'll receive several related hits for threads that discussed this topic and some even offered codes for it.

Do you have a real case or you ask just for learning purposes?

Regards- Ali M. Al-Shurafa

This sounds a little like the n+2 method of balancing.  Kellenberger had a paper in early 70's (My guess is aroung 1971 without looking it up.)discussing this.  I don't believe it is needed.  Some manufacturers would use this method, at least in the past.

The idea is to balance a mode and not upset the low speed balance (rigid rotor balance).  As I recall, Parkinson and Bishop had a good reply to Kellenberger in the journal paper (There was a conference paper, too - Detroit ASME perhaps).  
Charlie Jackson had a paper (forget the reference) with a title something like "What happened to n+2 planes - this would not be exactly related to the logic used for an n+2 plane balance approach.
This sounds like what you mean.  If not, post again.

What one does to create a n+2 balance shot for a static couple pair.  Take a static pair of equal weights (1 -- 0 -- 1) at the two ends and 0 in the middle. You can balance out the low speed components with a shot (1 -- -2 -- 1), where the -2 is 2 units out of phase with the two on the ends.  I don't feel this is needed, and it has some disadvantages.

Balancing a couple would take 4 planes.  First mode, the static, 1 plane plus 2.  Another way to balance a static is as follows.

A static could be ( 0 -- 1 -- 0) the n+2 method would be ( -1/2 -- 0 -- -1/2) .

Last edited by William_C._Foiles

I noticed that the two static shots above really are the same, but not how the static part originates.  A center plane can be a static shot, 
( 0 -- 1 -- 0) balance out the low speed static with two opposite at the ends 180 out from the middle shot gives this.

The starting point for the other static would be (1 -- 0 -- 1).

Note a static couple pair that can be very effective is:
(0 -- 1 -- 0) static, and
(1 -- 0 -- -1) couple


Please help the forum member so they help you. If you want a clear answer, provide enough and clear details. The general question marries a general answer. Don't you agree?

I suggest explaining the case on your hand (if it is an actual case). If it is a question for general knowledge based on a reference or an event you attended, explain that as perhaps someone here had a similar experience.

I'm not sure what you'll use the "mass distribution calculation" for. For the center of wight, maybe?

Regards- Ali M. Al-Shurafa

As shown above, a static shot that will not upset the low speed balance is
(1 -- -2 -- 1) - 1 at each end in phase and 2 out of phase in the middle.  This is for a symmetric rotor.  This will neither upset the rigid body balance.

If the rotor is symmetric and flexible, the 2 in the middle should do more to balance the first mode than the two components at the ends.  1/3 1/3 1/3 will upset the low speed balance, the static component as would 1/3 -1/3 1/3.

I assume that OP is asking about a Flexible Rotor that operates above one or two critical speeds (balance resonances) like a gas or steam turbine. I have worked on field balancing a gas turbine, and it was nasty. Balance weights (at planes 1 & 3) could reduce the Dynamic vibration at operating speed, but then vibrations were floor shaking high when going through the 1st resonance. The midspan balance plane would have the greatest effect for correction of Static unbalance, but the weight location was not accessible! A compromise balance was achieved by guess and calculations.

I have not seen a handy general calculation solution to the general question you posted. Bill Foiles posted general comments for a flexible rotor. Here is a reference that may be of use:



I  agree with Walt strong, When we do static correction at 1st and last plane, if corrected mass added high, we cannot cross the even the 1st critical, to minimize this effect, mid span weight is also added in such a way that low speed unbalance will not change and will give good results for reducing vibrations.

@  Al-Shurafa, this is not for learning purpose, i am adding by guess calculation for balancing in Vacuum tunnel.

But actual calculation i am not aware, I heard some OEM Turbine  manufactures will use this type calculations where it is necessary.



IBut actual calculation i am not aware, I heard some OEM Turbine  manufactures will use this type calculations where it is necessary.



Many years ago there was a MS-DOS based program called "Rotorbal" that used a least squares method of rotor balancing.  I believe it was an effort by Dr. Edgar J. Gunter.  William Foils can possibly confirm that information.  I do have to say, the old DOS program bailed me out on several occasions.  Anyway, these days it has been adapted to use with WIndows as an optional component to a software package for rotor studies called Dyrobes.  Unfortunately, it may be an expensive package!

See https://dyrobes.com/features/o...components/rotorbal/ or  https://dyrobes.com/help1800/RotorBal/html/

Last edited by John from PA

As shown above, a static shot that will not upset the low speed balance is
(1 -- -2 -- 1) - 1 at each end in phase and 2 out of phase in the middle.  This is for a symmetric rotor.  This will neither upset the rigid body balance.

If the rotor is symmetric and flexible, the 2 in the middle should do more to balance the first mode than the two components at the ends.  1/3 1/3 1/3 will upset the low speed balance, the static component as would 1/3 -1/3 1/3.

That makes perfectly good sense, thanks


How to do the mass calculation:  Take your modal weights and add two planes.  You have asked about the static component.
If your static component is in two planes (it may be in one plane as previous examples show).  In general you need to add two more planes.
The static (any mode) shot upsets (possibly) the moment and the mass center of the rigid rotor.  There is one solution for the two extra planes you add to correct both the imbalance moment (mass property) and the mass center offset of the rigid body.  This is an algebra problem.

First you determine the moment (about center of mass or other point  - let's keep it simple use the center of mass) created by your static balance shot and the mass offset from the static shot - this is two numbers, M and Mc (moment and mass center offset about the center of mass for the rotor as a rigid body).

The two extra planes have offsets, l1 and l2 from the center of mass. l1 and l2 may be positive or negative (same side or different side from center of mass - you will need a sign attached to these for the calculation).  Your static will be in phase, consider this angle as 0, and the weights as positive entrees  at this angle.

You get two equations to solve.

l1*U1 +l2*U2 = -M and
U1 +U2 = -Mc
The U1 and U2 are the correction weights to add to the two extra planes.  These will correct the moment and mass offset from your static weight.

This gives you a static weight with low speed balance correction.  You may have the two extra planes in the balance bunker - good look trying to find them in the field.

I have balanced over 100 gas turbines, some steam turbines, and some generators, I have never needed this.  I believe there is a better way for the bunker, too.

What is usually done in a high-speed balance unit on a symmetrical rotor (typically a generator rotor) is to address the 1st critical with a static weight in the middle of the rotor and the 2nd critical or full speed with a couple weight (again usually an 'out of phase' configuration and normally of similar mass) at each end.

In-situ balancing of the same rotor normally end up with static weights at each end following by a couple weight set also fitted at each end.  Some cases, one set of static and one of the couple weight set are located at the same phase angle on one end of the rotor.

The N+2 method has been applied (by some) in the balance bunker.  At one time there was a disagreement (nay argument) in Europe.  The Brits were for N planes (N - number of modes) - Others were swearing by N+2 planes.  
Other papers had other ideas.  H. Black (and perhaps Nutal [sp?]) thought it needed 2N planes - due to left and right eigenvectors.  In practice, I don't think people followed this. I believe that I can show that this is not the answer.

Den Hartog had a theorm. The theorem says n masses and b bearings can be balanced in n+b planes - The paper looks at forces and responses from - seems like a rigid body approach.  This too, is not likely to be the case.

Using the N+2 plane method produces balance weights that are less effective per weight (mass- l) than the N plane method.

The first examples that I gave were from a practical approach. Like said above use the center plane in a bunker if you have it for the static, this can be very effective.  As noted by vibramac, then the second mode can be balanced with a couple at or toward/near the ends.  The couple will (symmetric rotor) have little (no) effect on the static balance (once won a bet with a Bently rotor kit when I was in Philadelphia).  The couple will not upset the static balance (generally done first).


I see Walt gave a link to one of my papers above.  I wrote another related multi-plane balancing paper some years ago, and it gives the background and a step by step example.  The paper’s example is using 5 planes for a flexible generator rotor, but equally applies to 3-plane balancing on a turbine.  


Do you know the machine’s sensitivity via a trial shot?  Do you have the ability to generate polar plots through the speed range at the two journals?  

A simple approach to distribute the balance correction is to determine an initial β€œ100%” correction (in effective oz-in) for the rotor rigid mode(s) based on an initial run and trial shot, which should be determined using the response vectors measured at just before 90deg of phase lag. Next, split that calculated correction, assigning 50% (in oz-in) in the mid-plane, and 25% on each end-plane, all at the same angle.  Then to adjust further, bias the β€œother 50%” of the total for the two end-planes in proportion with the peak magnitude of the two end-plane response vectors. 

For example, if the measured vectors are 6 mils - - 2 mils, then bias the correction weights to 37% -- 50% -- 13%.  This is oversimplified, but when the weight angle and total amount is correct and the axial distribution is correct, it should eliminate the first critical response, and should at the same time ideally prevent responses at all higher speeds as well as at operating speed.  

With further acceleration above the first critical speed toward running speed, if there is still an out-of-phase β€œrocking/pivoting” response (rigid rocking mode), the correction should not be done with a β€œcouple” across the two end-planes.  A rocking response observed here is nothing but an indication that the residual unbalance/eccentricity is still axially biased on one end. The easy way to determine the side with the axial bias is the one on which the peak amplitudes of the 1st and 2nd β€œcritical speeds” are in phase. The goal is to equivalently axially bias your correction weights toward that same end, keeping them all still in the same phase, with the end result being that your three planes of correction weights create a β€œvirtual” dynamic mass axis from the correction forces (oz-in) that mirrors and compensates the inherent mass axis due to the rotor’s distributed unbalance/eccentricities, so that the resultant net mass axis is brought coincident with the rotor’s journal centerline axis.  

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